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1. Introduction
A man is rushed to a hospital in the throes of a heart attack.
The doctor needs to decide whether the victim should be
treated as a low risk or a high risk patient. He is at high risk
if his life is truly threatened, and should receive the most
expensive and detailed care. Although this decision can save
or cost a life, the doctor must decide using only the avail-
able cues, each of which is, at best, merely an uncertain pre-
dictor of the patient’s risk level. Common sense dictates
that the best way to make the decision is to look at the re-
sults of each of the many measurements that are taken
when a heart attack patient is admitted, rank them accord-
ing to their importance, and combine them somehow into
a final conclusion, preferably using some fancy statistical
software package.
Consider in contrast the simple decision tree in Figure 1,
which was designed by Breiman et al. (1993) to classify
heart attack patients according to risk using only a maxi-
mum of three variables. If a patient has had a systolic blood
pressure of less than 91, he is immediately classified as high
risk – no further information is needed. If not, then the de-
cision is left to the second cue, age. If the patient is under
62.5 years old, he is classified as low risk; if he is older, then
one more cue (sinus tachycardia) is needed to classify him
as high or low risk. Thus, the tree requires the doctor to an-
swer a maximum of three yes/no questions to reach a deci-
sion rather than to measure and consider all of the several
usual predictors, letting her proceed to life-saving treat-
ment all the sooner.
This decision strategy is simple in several respects. First,
it ignores the great majority of possible measured predic-
BEHAVIORAL AND BRAIN SCIENCES (2000) 23, 727–780
Printed in the United States of America
© 2000 Cambridge University Press 0140-525X/00 $12.50
727
Précis of Simple heuristics
that make us smart
Peter M.Todd
Center for Adaptive Behavior and Cognition, Max Planck Institute for Human
Development, 14195 Berlin, Germany
ptodd@mpib-berlin.mpg.de
www.mpib-berlin.mpg.de/abc
Gerd Gigerenzer
Center for Adaptive Behavior and Cognition, Max Planck Institute for Human
Development, 14195 Berlin, Germany
gigerenzer@mpib-berlin.mpg.de
www.mpib-berlin.mpg.de/abc
Abstract: How can anyone be rational in a world where knowledge is limited, time is pressing, and deep thought is often an unattain-
able luxury? Traditional models of unbounded rationality and optimization in cognitive science, economics, and animal behavior have
tended to view decision-makers as possessing supernatural powers of reason, limitless knowledge, and endless time. But understanding
decisions in the real world requires a more psychologically plausible notion of bounded rationality. In Simple heuristics that make us
smart (Gigerenzer et al. 1999), we explore fast and frugal heuristics – simple rules in the mind’s adaptive toolbox for making decisions
with realistic mental resources. These heuristics can enable both living organisms and artificial systems to make smart choices quickly
and with a minimum of information by exploiting the way that information is structured in particular environments. In this précis, we
show how simple building blocks that control information search, stop search, and make decisions can be put together to form classes of
heuristics, including: ignorance-based and one-reason decision making for choice, elimination models for categorization, and satisficing
heuristics for sequential search. These simple heuristics perform comparably to more complex algorithms, particularly when generaliz-
ing to new data – that is, simplicity leads to robustness. We present evidence regarding when people use simple heuristics and describe
the challenges to be addressed by this research program.
Keywords: adaptive toolbox; bounded rationality; decision making; elimination models; environment structure; heuristics; ignorance-
based reasoning; limited information search; robustness; satisficing, simplicity
Peter M. Todd is a senior research scientist at the Max
Planck Institute for Human Development in Berlin,
Germany, and co-founder of the Center for Adaptive
Behavior and Cognition (ABC). He has published nu-
merous papers and books on modeling behavior, music,
and evolution, and is associate editor of the journals
Adaptive Behavior and Animal Cognition.
Gerd Gigerenzer is Director of the Center for Adap-
tive Behavior and Cognition (ABC) at the Max Planck
Institute for Human Development in Berlin, Germany,
and a former Professor of Psychology at the University
of Chicago and other institutions. He has won numer-
ous prizes, including the AAAS Prize for Behavioral Sci-
ence Research in 1991; his latest book is Adaptive
Thinking: Rationality in the Real World (Oxford Uni-
versity Press, forthcoming).
high risk
high risk
low risk
low risk
Is the minimum systolic blood pressure
over the initial 24 hour period . 91?
Is sinus tachycardia present?
Is age . 62.5?
yes
yes
yes
no
no
no
Todd & Gigerenzer: Simple heuristics
728 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
Figure 1. A simple decision tree for classifying incoming heart
attack patients into high risk and low risk patients (adapted from
Breiman et al. 1993).
tors. Second, it ignores quantitative information by using
only yes/no answers to the three questions. For instance, it
does not care how much older or younger the patient is than
the 62.5 year cut-off. Third, the strategy is a step-by-step
process; it may end after the first question and does not
combine (e.g., weight and add) the values on the three pre-
dictors. Asking at most three yes/no questions is a fast and
frugal strategy for making a decision. It is fast because it
does not involve much computation, and it is frugal because
it only searches for some of the available information. Its
simplicity raises the suspicion that it might be highly inac-
curate, compared to standard statistical classification meth-
ods that process and combine all available predictors. Yet it
is actually more accurate in classifying heart attack patients
according to risk status than are some rather complex sta-
tistical classification methods (Breiman et al. 1993). The
more general form of this counterintuitive finding – that
fast and frugal decision making can be as accurate as strate-
gies that use all available information and expensive com-
putation – forms one of the bases of our research program.
Our book, Simple heuristics that make us smart (here-
after Simple heuristics), is about fast and frugal heuristics
for making decisions – how they work, and when and why
they succeed or fail. These heuristics can be seen as mod-
els of the behavior of both living organisms and artificial sys-
tems. From a descriptive standpoint, they are intended to
capture how real minds make decisions under constraints
of limited time and knowledge. From an engineering stand-
point, these heuristics suggest ways to build artificially in-
telligent systems – artificial decision-makers that are not
paralyzed by the need for vast amounts of knowledge or for
extensive computational power. These two applications of
fast and frugal heuristics do not exclude one another – in-
deed, the decision tree in Figure 1 could be used to de-
scribe the behavior of an unaided human mind or could be
built into an emergency-room machine. (Note that while
decision trees are generally easy to use, their construction
in the first place can be computationally expensive. The
simple heuristics presented in the book can also avoid this
costly construction phase.)
In this précis we describe the framework of our explo-
ration of fast and frugal heuristics and summarize some of
the results that have been obtained so far by the ABC Re-
search Group. We begin by placing the study of simple
heuristics within the context of bounded rationality, distinct
from traditional views of unbounded rationality or opti-
mization under constraints. We then describe the building
blocks that go together to make up simple heuristics, and in
section 4 we show how they can be combined into a variety
of decision mechanisms for choice, categorization, estima-
tion, and other tasks. Next we introduce the concept of eco-
logical rationality, and explain how fast and frugal heuristics
can achieve reasonable performance by fitting particular in-
formation structures in the environment and being robust
to environmental change. In section 6 we cover the ways
that the performance of these heuristics can be measured,
and some of the evidence to date that people use such sim-
ple reasoning in particular decision tasks. We next relate
our research to other recent notions of heuristics in section
7, and describe in section 8 the metaphor of the adaptive
toolbox which organizes the mind’s collection of simple
heuristics. We conclude with a set of questions remaining
to be explored, and a summary of the view of bounded ra-
tionality presented in the book.
2. Visions of rationality: From demons
to bounded rationality
Humans and animals make inferences about their world
with limited time, knowledge, and computational power. In
contrast, many models of rational inference view the mind
as if it were a supernatural being possessing demonic pow-
ers of reason, boundless knowledge, and all of eternity with
which to make decisions. Such visions of rationality often
conflict with reality. But we can use them as points of com-
parison to help clarify our own vision of ecological rational-
ity – adaptive behavior resulting from the fit between the
mind’s mechanisms and the structure of the environment in
which it operates.
We start by considering two conceptual revolutions. The
first is the demise of the dream of certainty and the rise of
a calculus of uncertainty – probability theory – during what
is known as the probabilistic revolution (Gigerenzer et al.
1989; Krüger et al. 1987). The probabilistic revolution has
shaped our picture of the mind in fields ranging from cog-
nitive science to economics to animal behavior. Mental func-
tions are assumed to be computations performed on prob-
abilities and utilities (Gigerenzer & Murray 1987). In this
view, the laws of probability describe or prescribe sound
reasoning, judgment, and decision making. Probabilistic
conceptions of the mind have led to many elegant theories,
but also to thorny problems. The moment one moves be-
yond simple constrained settings such as the ones that psy-
chologists and computer scientists typically study to real-
world situations that people actually live through, the time,
knowledge, and computation that probabilistic models de-
mand grow unfeasibly large.
In this book, we push for a second revolution, one which
provides a different vision of how minds deal with the un-
certain world. We propose replacing the image of an omni-
scient mind computing intricate probabilities and utilities
with that of a bounded mind reaching into an adaptive tool-
box filled with fast and frugal heuristics. Our premise is that
much of human reasoning and decision making can be
modeled by such heuristics making inferences with limited
time and knowledge. These heuristics do not involve much
computation, and do not compute quantitative probabili-
ties and utilities. They are models of bounded rationality.
This world view embraces the earlier probabilistic revolu-
tion’s emphasis on uncertainty without sharing its focus
on probability theory, either as a description or as an at-
tainable norm of human behavior. But this second revolu-
tion is only just beginning – four major visions of rational-
ity still continue to struggle with each other today, as shown
in Figure 2.
Rationality comes in many forms. The first split in Fig-
ure 2 separates models that assume the human mind has es-
sentially unlimited demonic or supernatural reasoning power
from those that assume we operate with only bounded ra-
tionality. There are two species of demons: those that ex-
hibit unbounded rationality, and those that optimize under
constraints. There are also two main forms of bounded ra-
tionality: satisfying heuristics for searching through a se-
quence of available alternatives, and fast and frugal heuris-
tics that use little information and computation to make a
variety of kinds of decisions. We now explore each vision of
rationality in turn.
2.1. Unbounded rationality
In 1814, the astronomer-philosopher Pierre Simon Laplace
contemplated the ultimate genius, an omniscient superin-
telligence he characterized as follows:
Given . . . an intelligence which could comprehend all the
forces of which nature is animated and the respective situation
of the beings who compose it – an intelligence sufficiently vast
to submit these data to analysis . . . nothing would be uncertain
and the future, the past, would be present to its eyes. (Laplace
1814/1951, p. 1325)
Earlier, John Locke (1690/1959) had contrasted the omni-
scient God with us humble humans living in the “twilight of
probability”; Laplace secularized this opposition with his
fictitious superintelligence. From the perspective of God
and Laplace’s superintelligence alike, Nature is determin-
istic and certain; but for humans, Nature is fickle and un-
certain. Mortals cannot precisely know the world, but must
rely on uncertain inferences, on bets rather than on demon-
strative proof. Although omniscience and certainty are not
attainable for any real system, the spirit of Laplace’s super-
intelligence has survived nevertheless in the vision of un-
bounded rationality exemplified in various modern-day in-
carnations built around probability theory, such as the max-
imization of expected utility and Bayesian models.
Proponents of this vision paint humans in a divine light.
God and Laplace’s superintelligence do not worry about
limited time, knowledge, or computational capacities. The
fictional, unboundedly rational human mind does not ei-
ther – its only challenge is the lack of heavenly certainty. In
Figure 2, unbounded rationality appears in the class of
models labeled “demons.” We use the term in its original
Greek sense of a divine (rather than evil) supernatural be-
ing, as embodied in Laplace’s superintelligence.
The greatest weakness of unbounded rationality is that it
does not describe the way real people think. Not even
philosophers, as the following story illustrates. One philoso-
pher was struggling to decide whether to stay at Columbia
University or to accept a job offer from a rival university.
The other advised him: “Just maximize your expected util-
ity – you always write about doing this.” Exasperated, the
first philosopher responded: “Come on, this is serious.”
Because of its unnaturalness, unbounded rationality has
come under attack in the second half of the twentieth cen-
tury. But when one (unboundedly rational) head has been
chopped off, another very similar one has usually sprouted
again in its place: its close demonic relative, optimization un-
der constraints.
2.2. Optimization under constraints
To think is to take a risk, a step into the unknown. Our in-
ferences, inevitably grounded in uncertainty, force us to “go
beyond the information given,” in Jerome Bruner’s famous
phrase. But the situation is usually even more challenging
than this, because rarely is information given. Instead we
must search for information – cues to classify heart attack
patients as high risk, reasons to marry, indicators of stock
market fluctuation, and so on. Information search is usually
thought of as being internal, performed on the contents of
one’s memory, and hence often in parallel via our biological
neural networks. But it is important to recognize that much
of information search is external and sequential (and thus
more time consuming), looking through the knowledge
embodied in the surrounding environment. This external
search includes seeking information in the socially distrib-
uted memory spanning friends and experts and in human
artifacts such as libraries and the internet.
The key difference between unbounded rationality and
the three other visions in Figure 2 is that the latter all in-
volve limited information search, whereas models of un-
bounded rationality assume that search can go on indefi-
nitely. In reasonable models, search must be limited because
real decision makers have only a finite amount of time,
knowledge, attention, or money to spend on a particular de-
cision. Limited search requires a way to decide when to
stop looking for information, that is, a stopping rule. The
models in the class we call “optimization under constraints”
assume that the stopping rule optimizes search with respect
to the time, computation, money, and other resources be-
ing spent. More specifically, this vision of rationality holds
that the mind should calculate the benefits and costs of
searching for each further piece of information and stop
search as soon as the costs outweigh the benefits (e.g., An-
derson & Milson 1989; Sargent 1993; Stigler 1961). The
rule “stop search when costs outweigh benefits” sounds
Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 729
visions of rationality
demons bounded rationality
unbounded optimization satisficing fast and frugal
rationality under constraints heuristics
Figure 2. Visions of rationality.
plausible at first glance. But a closer look reveals that opti-
mization under constraints can require even more knowl-
edge and computation than unbounded rationality (Vriend
1996; Winter 1975).
The motivation for replacing unbounded rationality with
optimization under constraints was originally to build em-
pirically more realistic models that respect the limitations
of human minds. The paradoxical approach is to model
“limited” search by assuming that the mind has essentially
unlimited time and knowledge with which to evaluate the
costs and benefits of further information search. The dream
of optimization, threatened in its instantiation in unbounded
rationality, is thus salvaged by being incorporated into an
apparent competitor – constrained optimization invites un-
bounded rationality to sneak in through the back door.
Of course, few would argue that real humans have the
time and knowledge necessary to perform the massive com-
putations required for constrained optimization. Instead,
this vision of rationality is usually presented as a lofty ideal
that human reasoning should aspire to. But such aspirations
make real human reasoning look flawed and irrational in
comparison. In our view, it is these aspirations that are
flawed – we will argue that reasoning can be powerful and
accurate without requiring unlimited time and knowledge.
What certain forms of optimization under constraints can
offer – in contrast to unbounded rationality – is an analysis of
the structure of environments. For instance, in Anderson’s
rational analysis framework (Anderson 1990; Oaksford &
Chater 1994) constraints from the environment, rather than
on the decision maker, are used to modify one’s understand-
ing of what is optimal behavior in a particular context. Such
an analysis does not directly address the question of what
mental mechanisms could possibly yield behavior approach-
ing the optimal norm, but at least it allows us to create a more
realistic standard for assessing proposed mechanisms.
Instead of these demonic visions of reason, we turn to the
idea of bounded rationality. But many, if not most, re-
searchers in cognitive science, economics, and animal be-
havior interpret the term “bounded rationality” as synony-
mous with optimization under constraints, a (mis)use we
strongly reject. This interpretation may be responsible for
the frequent dismissal of bounded rationality in favor of
good old-fashioned demonic visions. The economist Thomas
Sargent (1993), for instance, in interpreting bounded ratio-
nality as constrained optimization, argues that when one
models people as “bounded” in their rationality, one’s mod-
els use a greater number of parameters and become more
demanding mathematically. He believes that the reason
why researchers (particularly economists) stick with mod-
els incorporating unbounded rationality is that their desire
for models with fewer parameters is not met by the bounded
approach: “a reduction is not what bounded rationality
promises” (p. 4). But this is a misleading interpretation of
bounded rationality – rationality need not be optimization,
and bounds need not be constraints.
2.3. Bounded rationality: Satisficing
The “father” of bounded rationality, Herbert Simon, has ve-
hemently rejected its reduction to optimization under con-
straints: “bounded rationality is not the study of optimiza-
tion in relation to task environments” (Simon 1991). Instead,
Simon’s vision of bounded rationality has two interlocking
components: the limitations of the human mind, and the
structure of the environments in which the mind operates.
The first component of his vision means that models of
human judgment and decision making should be built on
what we actually know about the mind’s capacities rather
than on fictitious competencies. In many real-world situa-
tions, optimal strategies are unknown or unknowable (Simon
1987). Even in a game such as chess, where an optimal (best)
move does in fact exist at every point, no strategy can calcu-
late that move in a reasonable amount of time (either by hu-
man minds or computers), despite the well-defined nature of
the possibilities to be searched. In less well-defined natural
situations, our hope of identifying a useable optimal strat-
egy is even further diminished. Because of the mind’s lim-
itations, humans “must use approximate methods to handle
most tasks” (Simon 1990, p. 6). These methods include
recognition processes that largely obviate the need for fur-
ther information search, heuristics that guide search and
determine when it should end, and simple decision rules
that make use of the information found. We explore these
classes of methods at length in our book.
The second component of Simon’s view of bounded ratio-
nality, environmental structure, is of crucial importance be-
cause it can explain when and why simple heuristics perform
well: if the structure of the heuristic is adapted to that of the
environment. Simon’s (1956a) classic example of this com-
ponent concerns imaginary organisms foraging according to
simple heuristics whose behavior can only be understood by
looking at the structure of the information in the environ-
ment. Simon was not the only one to make this important
point; it was made both before his work (e.g., Brunswik 1943)
and at various times since (e.g., Anderson 1990; Shepard
1990), including more extreme emphasis on studying the en-
vironment rather than the mechanisms of the mind (e.g.,
Gibson 1979). But in general the second part of Simon’s
(1956a) paper title, “Rational choice and the structure of en-
vironments,” has been neglected in mainstream cognitive
sciences (even by Simon himself – see Simon 1987).
We use the term ecological rationality to bring environ-
mental structure back into bounded rationality. A heuristic
is ecologically rational to the degree that it is adapted to the
structure of an environment (see below). Thus, simple
heuristics and environmental structure can both work hand
in hand to provide a realistic alternative to the ideal of op-
timization, whether unbounded or constrained.
One form of bounded rationality is Simon’s concept of
satisficing – a method for making a choice from a set of al-
ternatives encountered sequentially when one does not
know much about the possibilities in advance. In such situ-
ations, there may be no optimal method for stopping
searching for further alternatives – for instance, there
would be no optimal way of deciding when to stop looking
for prospective marriage partners and settle down with a
particular one (see Ch. 13 for more on satisficing in mate
search). Satisficing takes the shortcut of setting an aspira-
tion level and ending the search for alternatives as soon as
one is found that exceeds the aspiration level (Simon 1956b;
1990), for instance leading an individual with Jack-Sprat-
like preferences to marry the first potential mate encoun-
tered who is over a desired width.
2.4. Bounded rationality: Fast and frugal heuristics
Satisficing is a way of making a decision about a set of al-
ternatives that respects the limitations of human time and
Todd & Gigerenzer: Simple heuristics
730 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
knowledge: it does not require finding out or guessing
about all the options and consequences the future may
hold, as constrained optimization does. However, some
forms of satisficing can still require a large amount of de-
liberation on the part of the decision maker, for instance to
set an appropriate aspiration level in the first place, or to
calculate how a current option compares to the aspiration
level (Simon 1956b). Rather than let overzealous mental
computation slip back into our picture of human rational-
ity, we narrow our focus still more to concentrate on fast and
frugal heuristics for decision making.
Fast and frugal heuristics employ a minimum of time,
knowledge, and computation to make adaptive choices in
real environments. They can be used to solve problems of
sequential search through objects or options, as in satisfic-
ing. They can also be used to make choices between simul-
taneously available objects, where the search for infor-
mation (in the form of cues, features, consequences, etc.)
about the possible options must be limited, rather than the
search for the options themselves. Fast and frugal heuris-
tics limit their search of objects or information using easily
computable stopping rules, and they make their choices
with easily computable decision rules. We thus see satisfic-
ing and fast and frugal heuristics as two overlapping but dif-
ferent categories of bounded rationality: there are some
forms of satisficing that are fast and frugal, and others that
are computationally unreasonable; and there are some fast
and frugal heuristics that make satisficing sequential option
decisions, and some that make simultaneous option choices
(see sect. 4). We consider fast and frugal heuristics to rep-
resent bounded rationality in its purest form.
A prime example of the classes of fast and frugal heuris-
tics that we explore in our book is one-reason decision mak-
ing, in which only a single piece of information is used to
make a choice (we describe particular instances of this
class in more detail below). There is a sound rationale for
basing a decision on only one reason rather than on a com-
bination of several: Combining information from different
cues requires converting them into a common currency, a
conversion that may be expensive if not actually impossible.
Standard models of optimization, whether constrained or
unbounded, assume that there is a common currency for all
beliefs and desires, namely, quantitative probabilities and
utilities. Although this is a mathematically convenient as-
sumption, the way humans look at the world does not al-
ways conform to it. Some things do not have a price tag, and
cannot be reduced to and exchanged for any common cur-
rency (Elster 1979). Love, true friendship, military honors,
and Ph.D.s, for example, are supposed to be priceless, and
therefore incommensurable with items for sale in a shop-
ping mall. When reasons cannot be converted to a single
currency, the mind may do best by employing a fast and fru-
gal strategy that bases its decision on just one good reason.
As we demonstrate (in Chs. 4–6), however, incommensura-
bility is not the only reason for one-reason decision making.
Before we take a closer look at fast and frugal heuristics,
let us sum up our discussion so far. Bounded rationality has
become a fashionable term in many quarters, and a plethora
of proposed examples have been thrown together under
this term, including optimization under constraints. Figure
2 helps to make clear the distinctions between bounded ra-
tionality and the demonic visions of rationality. Unbounded
rationality is not concerned with the costs of search, while
bounded rationality explicitly limits search through stop-
ping rules. Optimization under constraints also limits search,
but does so by computing the optimal stopping point, that
is, when the costs of further search exceed the benefits. In
contrast, bounded rationality “bets” on the effectiveness of
simple ways of guiding and stopping information search
(described in the next section) that do not attempt to opti-
mize. Finally, the purest form of bounded rationality is to
be found in fast and frugal heuristics, which employ limited
search through objects (in satisficing) or cues and exploit
environmental structure to yield adaptive decisions.
3. The ABCs of fast and frugal heuristics
In Simple heuristics we explore the view that people oper-
ate with bounded rationality to make the majority of their
inferences and decisions – a framework that is also useful
for studying other animals and for developing decision-
making heuristics for artificial agents. This exploration of
boundedly rational heuristics involves (1) designing com-
putational models of candidate simple heuristics, (2) ana-
lyzing the environmental structures in which they perform
well, (3) testing their performance in real-world environ-
ments, and (4) determining whether and when people (and
other animals) really use these heuristics. The results of the
investigatory stages (2), (3), and (4) can be used to revise
the next round of theorizing in stage (1). The different
stages of this research program rest on multiple methods,
including theoretical modeling of heuristics, computer sim-
ulation of their performance, mathematical analysis of the
fit between heuristics and specific environments, and labo-
ratory experimentation. Across the next four sections we
consider each of these stages in turn.
A computational model of a heuristic specifies the pre-
cise steps of information gathering and processing that are
involved in generating a decision, such that the heuristic
can be instantiated as a computer program. For a fast and
frugal heuristic, this means the computational model must
include principles for guiding search for alternatives or in-
formation (or both), stopping that search, and making a de-
cision, as we now describe.
3.1. Heuristic principles for guiding search
Decisions must be made between alternatives, and based
on information about those alternatives. In different situa-
tions, those alternatives and pieces of information may need
to be found through active search. The heuristic principles
for guiding search, whether across alternatives or informa-
tion, are what give search its direction (if it has one). For in-
stance, cues can be searched for in a random manner, or in
order of some pre-computed criterion related to their use-
fulness (Ch. 6), or based on a recollection about which cues
worked previously when making the same decision (Ch. 4).
Search for alternatives can similarly be random or ordered.
Fast and frugal search-guiding principles do not use ex-
tensive computations or knowledge to determine where to
look next. But such simplicity need not lead to a disadvan-
tage in decision accuracy, because simple search strategies
can help heuristics to be more robust than those that at-
tempt to optimize their information search. For instance,
the choice heuristics we focus on (Ch. 4) use cue orderings
that are easy to compute, ignoring dependencies between
cues just as people have been reported to do (e.g., Armelius
& Armelius 1974). If instead the heuristics computed con-
Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 731
ditional probabilities between cues to determine search or-
der, or tried all of the enormous number of cue orders to
find the optimal one for a given data set, they might be
slightly more accurate – but only when fitting the data set
they already know. When making predictions about new
data, simple information search methods that ignore de-
pendencies between cues can actually yield more accurate
choices (Ch. 6).
3.2. Heuristic principles for stopping search
In our conception of bounded rationality, the temporal lim-
itations of the human mind (or that of any realistic decision-
making agent) must be respected as much as any other con-
straint. This implies in particular that search for alternatives
or information must be terminated at some (preferably
early) point. Moreover, to fit the computational capacities
of the human mind, the method for determining when to
stop search should not be overly complicated. For example,
one simple stopping rule is to cease searching for informa-
tion and make a decision as soon as the first cue or reason
that favors one alternative is found (Ch. 4). This and other
cue-based stopping rules do not need to compute an opti-
mal cost-benefit trade-off as in optimization under con-
straints; in fact, they need not compute any utilities or costs
and benefits at all. For searching through alternatives
(rather than cues), simple aspiration-level stopping rules
can be used, as in Simon’s original satisficing notion (Simon
1956b; 1990; see also Ch. 13).
3.3. Heuristic principles for decision making
Once search has been guided to find the appropriate alter-
natives or information and then been stopped, a final set of
heuristic principles can be called upon to make the decision
or inference based on the results of the search. These prin-
ciples can also be very simple and computationally bounded.
For instance, a decision or inference can be based on only
one cue or reason, whatever the total number of cues found
during search (see Chs. 2–6). Such one-reason decision
making does not need to weight or combine cues, and so
no common currency between cues need be determined.
Decisions can also be made through a simple elimination
process, in which alternatives are thrown out by successive
cues until only one final choice remains (see Chs. 10–12).
3.4. Putting heuristic building blocks together
These heuristic principles are the building blocks, or the
ABCs, of fast and frugal heuristics. Given that the mind is
a biological rather than a logical entity, formed through a
process of successive accrual, borrowing, and refinement
of components, it seems reasonable to assume that new
heuristics are built from the parts of the old ones, rather
than from scratch (Pinker 1998; Wimsatt 2000a). In this
light, we have used two main methods to construct compu-
tational models of fast and frugal heuristics: combining
building blocks and nesting existing heuristics. Heuristic
principles can be combined in multiple ways, such as the
several guises in which we find one-reason decision making
throughout our book, though of course not arbitrarily: For
instance, a fast and frugal heuristic for two-alternative
choice that stops information search at the first cue on
which the alternatives differ must also use a decision prin-
ciple based on one-reason decision making. Additionally,
entire fast and frugal heuristics can themselves be com-
bined by nesting one inside another. As an example, the
recognition heuristic (Chs. 2 and 3) works on the basis of an
elementary cognitive capacity, recognition memory, but it
can also serve as the first step of heuristics that draw on
other capacities, such as recall memory (Chs. 4 and 5; see
also sect. 8 below on combining tools in the adaptive tool-
box). Recognition memory develops earlier than recall
memory both ontogenetically and evolutionarily, and the
nesting of heuristics can similarly be seen as analogous to
the addition of a new adaptation on top of an existing one.
4. Classes of heuristics
All of the heuristics that the ABC Research Group has been
exploring can be thought of as enabling a choice of one or
more objects or options from a (larger) set of possibilities.
How many options there are in a particular decision situa-
tion, and how many are to be chosen, will partly determine
the heuristics that can be employed. The amount and kind
of cues available to make this choice can further constrain
the set of appropriate mental tools. Together, these features
divide the heuristics we have developed into the four main
classes presented in this section.
4.1. Ignorance-based decision making
The simplest kind of choice – numerically, at least – is to se-
lect one option from two possibilities, according to some
criterion on which the two can be compared. Many of the
heuristics described in our book fall into this category, and
they can be further arranged in terms of the kinds and
amount of information they use to make a choice. In the
most limited case, if the only information available is whether
or not each possibility has ever been encountered before,
then the decision maker can do little better than rely on his
or her own partial ignorance, choosing recognized options
over unrecognized ones. This kind of “ignorance-based rea-
soning” is embodied in the recognition heuristic (Ch. 2):
When choosing between two objects (according to some
criterion), if one is recognized and the other is not, then se-
lect the former. For instance, if deciding at mealtime be-
tween Dr. Seuss’s famous menu choices of green eggs and
ham (using the criterion of being good to eat), this heuris-
tic would lead one to choose the recognized ham over the
unrecognized odd-colored eggs.
Following the recognition heuristic will be adaptive,
yielding good choices more often than would random
choice, in those decision environments in which exposure
to different possibilities is positively correlated with their
ranking along the decision criterion being used. To con-
tinue with our breakfast example, those things that we do
not recognize in our environment are more often than not
inedible, because humans have done a reasonable job of
discovering and incorporating edible substances into our
diet. Norway rats follow a similar rule, preferring to eat
things they recognize through past experience with other
rats (e.g., items they have smelled on the breath of others)
over novel items (Galef 1987). We have used a different
kind of example to amass experimental evidence that peo-
ple also use the recognition heuristic: Because we hear
about large cities more often than small cities, using recog-
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732 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
nition to decide which of two cities is larger will often yield
the correct answer (in those cases where one city is recog-
nized and the other is not). In our experiments, over 90%
of the participants act in accordance with the recognition
heuristic, even after they have been taught further infor-
mation about the recognized cities that should lead them to
stop following this decision rule. Employing the recogni-
tion heuristic can lead to the surprising less-is-more effect,
in which an intermediate amount of (recognition) knowl-
edge about a set of objects can yield the highest proportion
of correct answers – knowing (i.e., recognizing) more than
this will actually decrease performance (Ch. 2).
The recognition heuristic can be generalized to cases in
which several options are to be chosen from a larger set of
possibilities, for instance when several social partners are to
be chosen for some collaborative activity such as resource
exchange or hunting. We have investigated a modern-day
equivalent of this type of choice: selecting companies for
investment. When deciding which companies to invest in
from among those trading in a particular stock market, the
recognition heuristic would lead investors to choose just
those that they have heard of before. Such a choice can be
profitable assuming that more-often-recognized companies
will typically have some of the better-performing stocks on
the market – a testable, but not obvious, assumption.
We tested precisely this assumption, and this approach to
fast and frugal investing, by asking several sets of people
what companies they recognized and forming investment
portfolios based on the most familiar firms (Ch. 3). In this
(admittedly short-term) trial of a simple heuristic in an un-
forgiving and often chaotic real social environment, we
found that ignorance-driven recognition alone could match
and often beat the highly trained wisdom of professional
stock pickers. This does not, of course, prove that people
use the recognition heuristic when making such choices
(though common investment advice suggests this is so) – at
this point we only have evidence that using this heuristic
can be a surprisingly adaptive strategy in complex environ-
ments. Experimental examination of whether or not people
employ the recognition heuristic (and others) in these types
of social domains remains an important upcoming chal-
lenge.
4.2. One-reason decision making
Returning to choices of one of two options, most of the time
we have more information than just a vague memory of
recognition to go on, so that other heuristics can be em-
ployed. When multiple cues are available for guiding deci-
sions, how can a fast and frugal reasoner proceed? The most
frugal approach is to use a stopping rule that terminates the
search for information as soon as enough has been gathered
to make a decision. In particular, as mentioned earlier, one
can rely on one-reason decision making (Ch. 4): Stop look-
ing for cues as soon as one is found that differentiates be-
tween the two options being considered. This allows the de-
cision maker to follow a simple loop, as shown in Figure 3:
(1) select a cue dimension and look for the corresponding
cue values of each option; (2) compare the two options on
their values for that cue dimension; (3) if they differ (e.g.,
if one value is larger or if there is positive information for
one option but not for the other), then stop and choose the
option with the cue value indicating the greater value on
the choice criterion; (4) if they do not differ, then return to
the beginning of this loop (step 1) to look for another cue
dimension.
This little four-step loop incorporates two of the impor-
tant building blocks of simple heuristics: a stopping rule
(here, stopping after a single cue is found that enables a
choice between the two options) and a decision rule (here,
deciding on the option to which the one cue points). One
other building block remains to be specified, however, be-
fore we can build a particular heuristic. We must determine
just how cue dimensions are “looked for” in step 1 – that is,
we must pick a specific information search rule. We have de-
veloped three fast and frugal one-reason decision heuristics
that differ only in their search rule (Ch. 4; see also Gigeren-
zer & Goldstein 1996a). Take the Best searches for cues in
the order of their validity – that is, how often the cue has in-
dicated the correct versus incorrect options. Take the Last
looks for cues in the order determined by their past success
in stopping search, so that the cue that was used for the most
recent previous decision (whether or not it was correct) is
Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 733
Select a cue and check cue values
of available alternatives
Decide on alternative indicated
by current cue
Does cue discriminate
between alternatives?
No
Yes
Figure 3. A flowchart of one-reason decision making. First,
search for a cue and the corresponding cue values of each alter-
native; next, check whether the values for that cue discriminate
between the alternatives; if so, then choose the indicated alterna-
tive; if not, select another cue and repeat this process. (Random
choice can be used if no more cues are available.)
checked first when making the next decision. Finally, the
Minimalist heuristic selects cues in a random order.
What we found when we tested the performance of these
one-reason decision-making heuristics was again surpris-
ing: Despite (or often, as we found later, because of) their
simplicity and disregard for most of the available informa-
tion, they still made very accurate choices. We compared
these heuristics against a set of more traditional informa-
tion-combining methods such as multiple regression, which
weights and sums all cues in an optimal linear fashion, and
a simple linear strategy (dubbed Dawes’s Rule) that counts
up all of the cues for and against a choice and looks at the
difference. We found that the simple heuristics always came
close to, and often exceeded, the proportion of correct in-
ferences achieved by multiple regression and Dawes’s Rule.
This unexpected performance was found first with the data
set that we have used as our simple “drosophila” example
in both human and simulation experiments: choosing the
larger of two German cities (Ch. 4). We then confirmed the
inference accuracy of these simple heuristics in a further 19
data sets selected for their variety in both number of objects
and number of cues available (Ch. 5).
The overall average performance across all 20 data sets
for two simple heuristics and two traditional decision meth-
ods is shown in Table 1 (under “Fitting”). The high accu-
racy of Take the Best and Minimalist was achieved even
though they looked through only a third of the cues on av-
erage (and decided to use only one of them), while multi-
ple regression and Dawes’s Rule used them all (see Table 1,
“Frugality”). The advantages of simplicity grew in the more
important test of generalization performance, where the
decision mechanisms were applied to a portion of each data
set that they had not seen during training. Here, Take the
Best outperformed all three other algorithms by at least
two percentage points (see Table 1, “Generalization”). The
finding that a simple heuristic can outstrip its less frugal
brethren particularly when generalizing to new decisions
demonstrates the potential robustness of fast and frugal
reasoning. These heuristics even performed nearly as well
as much more sophisticated Bayesian methods that employ
complex calculations to approach optimal behavior (Ch. 8).
(These results also show the well-known “flat maximum”
result that a linear model with equal-sized weights, e.g.,
Dawes’s Rule, can predict about as well as multiple regres-
sion; see Dawes 1979.) Thus, making good decisions need
not rely on the standard rational approach of collecting all
available information and combining it according to the rel-
ative importance of each cue – simply betting on one good
reason, even a reason selected at random, can do the trick.
But how? We turned to mathematical analysis (Ch. 6) to
uncover the secrets of success of one-reason decision mak-
ing. These simple heuristics are noncompensatory, mean-
ing that once they have used a single cue to make a decision,
no further cues in any combination can undo or compen-
sate for that one cue’s effect. When the information in the
decision environment is structured in a matching noncom-
pensatory fashion (i.e., the importance or validity of cues
falls off rapidly in a particular pattern), the Take the Best
heuristic can exploit that structure to make correct deci-
sions as often as compensatory rules. Take the Best also per-
forms comparatively well when information is scarce, that
is, when there are many more objects than cues to distin-
guish them. Finally, the particular ordering of cues used by
Take the Best, based on their ecological validity rather than
other possible measures of validity, seems to give this heuris-
tic great robustness when generalizing to new choices. We
discuss this issue of exploiting environment structure fur-
ther in section 5.1.
One-reason decision making may be at work in more
than just consciously deliberated choices. We hypothesize
that simple heuristics such as Take the Best can also play a
role in memory reconstruction, updating and amending our
recollection of the past in a rapid manner when further in-
formation is encountered (Ch. 9). But this adaptive updat-
ing in memory can cause as a side effect the curious phe-
nomenon of hindsight bias – the erroneous belief that one’s
past judgments were closer to one’s present state of knowl-
edge than they actually were (“I knew it all along”). A mem-
ory model incorporating Take the Best can make precise
predictions about when individuals will show hindsight
bias, something that previous models have not allowed.
Single reasons can also suffice in situations where there
are more than two options – particularly, when individual
cues are fine-grained enough (or at least have enough pos-
sible values) to differentiate all the options. We have looked
at the implications of this sort of single-cue decision mak-
ing in the domain of parental investment (Ch. 14), specifi-
cally asking: How can a parent decide which of several off-
spring it should give resources to first?
Parent birds, for instance, returning to their nest with a
juicy bug, typically face a number of gaping mouths that
they must decide between. The parent can use the weight,
hunger, age, or fixed position of each chick in the nest when
picking which one to feed. As in other tasks described ear-
lier, decision-making approaches based on traditional no-
tions of rationality (e.g., in Gary Becker’s economic analysis
of the family; see Becker 1991) would dictate that the par-
ent should assess and combine all of these cues to come up
with the best choice (where “best” in this case means the
choice that will lead to the greatest growth of the nestlings).
But because each of these cues provides a full ordering of
all the chicks (e.g., one is heaviest, one is next heaviest, and
so on), only one cue is necessary for an unambiguous deci-
sion. We found that one-cue feeding rules are not only pos-
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734 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
Table 1. Performance of different decision strategies
across 20 data sets
Accuracy (% correct)
Strategy Frugality Fitting Generalization
Minimalist 2.2 69 65
Take the Best 2.4 75 71
Dawes’s Rule 7.7 73 69
Multiple regression 7.7 77 68
Performance of two fast and frugal heuristics (Minimalist, Take
the Best) and two linear strategies (Dawes’s rule, multiple regres-
sion) across 20 data sets. The mean number of predictors available
in the 20 data sets was 7.7. “Frugality” indicates the mean number
of cues actually used by each strategy. “Fitting accuracy” indicates
the percentage of correct answers achieved by the strategy when
fitting data (test set 5 training set). “Generalization accuracy” in-
dicates the percentage of correct answers achieved by the strategy
when generalizing to new data (cross validation, i.e., test set ±
training set). (Data from Simple heuristics, Ch. 5.)
sible, but can also be advantageous – they perform signifi-
cantly better (again in terms of total chick growth) than
rules that combine all the available information in an at-
tempt to look forward in time and predict the optimal
course of action (Ch. 14). This is another way that the sim-
plicity of fast and frugal rules can become an advantage: In
situations in which repeated decisions must be made (as in
feeding and raising offspring), a simple cue-based heuristic
that sticks to present knowledge can outperform rules that
attempt to predict an uncertain future, because it avoids the
compounded noise that accumulates the further forward
one strains to look.
4.3. Elimination heuristics for multiple-option choices
As the bird-feeding example just given shows, not all
choices in life are presented to us as convenient pairs of op-
tions – often we must choose between several alternatives.
In situations where each available cue dimension has fewer
values than the number of available alternatives, one-reason
decision making will usually not suffice, because a single
cue will be unable to distinguish between all of the alterna-
tives. For instance, knowing whether or not each of 15 cities
has a river is not enough information to decide which city
is most habitable. But this does not doom the fast and fru-
gal reasoner to a long process of cue search and combina-
tion in these situations. Again, a simple stopping rule can
work to limit information search: Only seek cues (in an or-
der specified by the search rule) until enough is known to
make a decision. But now a different type of decision rule
is needed instead of relying on one reason. One way to se-
lect a single option from among multiple alternatives is to
follow the simple principle of elimination: Successive cues
are used to eliminate more and more alternatives and thereby
reduce the set of remaining options, until a single option
can be decided upon.
The QuickEst heuristic (Ch. 10) is designed to estimate
the values of objects along some criterion while using as lit-
tle information as possible. The estimates are constrained
to map onto certain round numbers (for instance, when es-
timating city population sizes, QuickEst can return values
of 100,000, 150,000, 200,000, 300,000, and other “sponta-
neous” numbers, following Albers 1997), so this heuristic
can be seen as choosing one value from several possibilities.
QuickEst is designed to work well in environments charac-
terized by a J-distribution, where there are many more ob-
jects at one end of a criterion range than at the other. To ex-
ploit this environmental structure, QuickEst first looks at a
cue that separates the most common objects from all of the
others (e.g., because most small cities in Germany do not
have a professional soccer team, this cue should be one of
the first checked when estimating a German city’s popula-
tion). QuickEst then looks at the next cue that separates the
remaining most common objects from the rest, and so on
until an estimate can be made. To estimate the criterion
value of a particular object, the heuristic looks through the
cues or features in this order until it comes to the first one
that the object does not possess, at which point it stops
searching for any further information (e.g., if a city pos-
sesses the first several features in order but lacks an expo-
sition site, search will stop on that cue). QuickEst then gives
the “rounded” mean criterion value associated with the ab-
sence of that cue as its final estimate (e.g., the mean size of
all cities without an exposition site). Thus in effect Quick-
Est uses features that are present to eliminate all common
criterion categories, and absent features to eliminate all less
common criterion categories, so that only one criterion es-
timate remains. No cue combination is necessary, and no
adjustment from further cues is possible.
QuickEst proves to be fast and frugal, as well as accurate,
in environments in which small values are frequent and
large values are rare, a distribution that characterizes a va-
riety of naturally occurring phenomena including many
formed by accretionary growth. This growth pattern applies
to cities (Makse et al. 1995), and indeed big cities are much
less common than small ones. As a consequence, when ap-
plied to the data set of German cities, QuickEst is able to
estimate rapidly the small sizes that most of them have.
We have also used the principle of elimination to build a
categorization heuristic called Categorization by Elimina-
tion (Ch. 11; see also Berretty et al. 1997). In this case, the
task is to choose the one category, from several possible,
that a given object falls into. The simple Categorization by
Elimination heuristic makes accurate category judgments
by using each successive cue to whittle away the set of
possible categories to which the object in question could
belong, until only a single possible category remains. Its
performance comes within a few percentage points of the
accuracy of traditional categorization algorithms including
exemplar and neural network models, and yet in our tests it
uses only about a quarter of the information that these other
models employ. In situations in which categorization must
be performed quickly and cues take time to search for, this
fast and frugal approach has clear advantages.
Such advantages are obvious in the case of trying to as-
certain and categorize the intentions of other animals (in-
cluding humans) we happen to encounter. If we can decide
quickly and with few cues whether an approaching person
or bear is interested in fighting, playing, or courting, we will
have more time to prepare and react accordingly (though in
the case of the bear all three intentions may be equally un-
appealing). Some of the most obvious cues of intention that
can be assessed at a distance (as opposed to facial expres-
sion, for instance, which requires closer scrutiny) are con-
tained in an organism’s motion: Is it coming at me or head-
ing away, slowly or quickly, directly or indirectly? We have
investigated just what motion cues (including velocity,
heading, and curvature of path) people can use along with
the Categorization by Elimination heuristic to judge the in-
tention of another organism in a fast and frugal manner
(Ch. 12; see also Blythe et al. 1996). We determined a set
of simple motion cues that can be combined (e.g., by a
neural network) to indicate intention correctly in over 80%
of our laboratory trials; Categorization by Elimination uses
only half of these cues and still correctly predicts two-thirds
of the intentions, similar to the performance of trained hu-
man observers.
4.4. Satisficing heuristics
All the heuristics that we have discussed so far for choosing
one option from more than one operate with the assump-
tion that all the possible options are presently available to
the decision maker: For instance, all the possible categories
of motion are known, and all the chicks are sitting patiently
in the nest. But a different strategy is called for when alter-
natives themselves (as opposed to cue values) take time to
find, appearing sequentially over an extended period or
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BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 735
spatial region. In this type of choice task, a fast and frugal
reasoner need not (only) limit information search, but (also)
must have a stopping rule for ending the search for alter-
natives themselves. One instance of this type of problem is
the challenge that faces individuals searching for a mate
from a stream of potential candidates met at different
points in time. Here, Simon’s (1956b, 1990) notion of a sat-
isficing heuristic can be adaptive: An aspiration level is set
for the selection criterion being used, and the search for al-
ternatives is stopped as soon as the aspiration is met.
We have begun our study of satisficing heuristics for se-
quential search, including mate search, by simulating their
performance in different mating environments (Ch. 13), fo-
cusing on simple methods for setting the aspiration level.
The goal was to find satisficing heuristics that would limit
both the time needed to determine a good aspiration level
and the average number of potential mates that had to be
considered before one was found exceeding the aspiration
level. We have identified a class of simple learning heuris-
tics that do indeed determine such adaptive aspiration lev-
els, while still coming close to the criterion-selection per-
formance of more optimal (and much slower) search rules.
The next step, of course, is to test these theoretically plau-
sible heuristics against data gleaned from observations of
real people engaged in the mating game.
5. Why and when do simple heuristics work?
The basics of ecological rationality
Traditional definitions of rationality are concerned with
maintaining internal order of beliefs and inferences (sect.
6.1). But real organisms spend most of their time dealing
with the external disorder of their environment, trying to
make the decisions that will allow them to survive and re-
produce (Tooby & Cosmides 1998). To behave adaptively
in the face of environmental challenges, organisms must be
able to make inferences that are fast, frugal, and accurate.
These real-world requirements lead to a new conception of
what proper reasoning is: ecological rationality. Fast and
frugal heuristics that are matched to particular environ-
mental structures allow organisms to be ecologically ratio-
nal. The study of ecological rationality thus involves analyz-
ing the structure of environments, the structure of heuristics,
and the match between them, as we demonstrate through-
out our book.
How is ecological rationality possible? That is, how can
fast and frugal heuristics work as well as they do, and escape
the tradeoffs between different real-world criteria including
speed and accuracy? The main reason for their success is that
they make a tradeoff on another dimension: that of general-
ity versus specificity. What works to make quick and accu-
rate inferences in one domain may well not work in another.
Thus, different environments can have different specific fast
and frugal heuristics that exploit their particular information
structure to make adaptive decisions. But specificity can also
be a danger: if a different heuristic were required for every
slightly different decision-making environment, we would
need an unworkable multitude of heuristics to reason with,
and we would not be able to generalize to previously unen-
countered environments. Fast and frugal heuristics avoid
this trap by their very simplicity, which allows them to be ro-
bust when confronted by environmental change and enables
them to generalize well to new situations.
5.1. Exploiting environment structure
Fast and frugal heuristics can benefit from the way infor-
mation is structured in environments. The QuickEst heuris-
tic described earlier, for instance (Ch. 10), relies on the
skewed distributions of many real-world variables such as
city population size – an aspect of environment structure
that traditional statistical estimation techniques would ei-
ther ignore or even try to erase by normalizing the data.
Standard statistical models, and standard theories of ratio-
nality, aim to be as general as possible, so they make as
broad and as few assumptions as possible about the data to
which they will be applied. But the way information is struc-
tured in real-world environments often does not follow
convenient simplifying assumptions. For instance, whereas
most statistical models are designed to operate on datasets
where means and variances are independent, Karl Pearson
(1897) noted that in natural situations these two measures
tend to be correlated, and thus each can be used as a cue to
infer the other (Einhorn & Hogarth 1981, p. 66). While
general statistical methods strive to ignore such factors that
could limit their applicability, evolution would seize upon
informative environmental dependencies like this one and
exploit them with specific heuristics if they would give a
decision-making organism an adaptive edge.
Because ecological rationality is a consequence of the
match between heuristic and environment, we have inves-
tigated several instances where structures of environments
can make heuristics ecologically rational:
Noncompensatory information. The Take the Best heuris-
tic equals or outperforms any linear decision strategy when
information is noncompensatory, that is, when the potential
contribution of each new cue falls off rapidly (Ch. 6).
Scarce information. Take The Best outperforms a class of
linear models on average when few cues are known relative
to the number of objects (Ch. 6).
J-shaped distributions. The QuickEst heuristic estimates
quantities about as accurately as more complex informa-
tion-demanding strategies when the criterion to be esti-
mated follows a J-shaped distribution, that is, one with
many small values and few high values (Ch. 10).
Decreasing populations. In situations where the set of al-
ternatives to choose from is constantly shrinking, such as in
a seasonal mating pool, a satisficing heuristic that commits
to an aspiration level quickly will outperform rules that sam-
ple many alternatives before setting an aspiration (Ch. 13).
By matching these structures of information in the envi-
ronment with the structure implicit in their building blocks,
heuristics can be accurate without being too complex. In
addition, by being simple, these heuristics can avoid being
too closely matched to any particular environment – that is,
they can escape the curse of overfitting, which often strikes
more complex, parameter-laden models, as described next.
This marriage of structure with simplicity produces the
counterintuitive situations in which there is little trade-off
between being fast and frugal and being accurate.
5.2. Robustness
How can simple domain-specific heuristics ever be about as
accurate as complex general strategies that work with many
free parameters? One answer lies in not being too specific.
Simple heuristics are meant to apply to specific environ-
ments, but they do not contain enough detail to match any
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736 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
one environment precisely. General strategies that can be
made to conform to a broad range of environments, on the
other hand, can end up being too highly focused to be of
much real use – having a large number of free parameters
to fiddle with can be a hindrance. This failure of general-
ization, a phenomenon known as overfitting (e.g., Geman
et al. 1992; Massaro 1988), stems from assuming that every
detail is of utmost relevance. As we show in various chap-
ters, models with many free parameters, from multiple lin-
ear regression to neural networks, can suffer from trying to
make sense of every piece of information they encounter.
Thus, there is an important difference between the two
typical applications of a strategy, fitting (modeling deci-
sions for a given set of data) and generalization (predicting
or inferring based on new data). In fitting, it is usually true
that the more parameters a model has, and the more infor-
mation (cues) it uses, the better it will fit given data. In gen-
eralization, in contrast, more is not necessarily better. A
computationally simple strategy that uses only some of the
available information can be more robust, making more ac-
curate predictions for new data, than a computationally
complex, information-guzzling strategy that overfits.
Robustness goes hand in hand with speed, accuracy, and
especially information frugality (Table 1). Fast and frugal
heuristics can reduce overfitting by ignoring the noise in-
herent in many cues and looking instead for the “swamping
forces” reflected in the most important cues. Thus, simply
using only one or a few of the most useful cues can auto-
matically yield robustness. Furthermore, important cues
are likely to remain important. The informative relation-
ships in the environment are likely to hold true even when
the environment changes to some degree – for instance,
April is likely to be associated with showers in northern lo-
cations year after year. In contrast, the random fluctuations
of noise and the effects of smaller systematic factors may
frequently change – for instance, May flowers may depend
on many variable factors like temperature, rainfall, seed dis-
persal, and insect pests that collectively vary more from one
year to the next. Because of this pattern, fast and frugal
heuristics that pay attention to systematic informative cues
while overlooking more variable uninformative cues can
ride out a degree of environmental change without suffer-
ing much decrement in performance. Laplace’s superintel-
ligence would never overfit because it does not have to
make uncertain predictions. But models of inference that
try to be like a Laplacean superintelligence are doomed to
overfitting, when they swallow more data than they can
digest.
Studying ecological rationality enables us to go beyond
the widespread fiction that basing decision making on more
information and computation will always lead to more ac-
curate inferences. There is a point where too much infor-
mation and too much information processing can hurt.
Cognition is the art of focusing on the relevant and delib-
erately ignoring the rest. We take the same approach to
modeling cognition.
6. How can simple heuristics be evaluated?
6.1. Performance in real-world environments
As mentioned earlier, bounded rationality is often charac-
terized as a view that takes into account the cognitive limi-
tations of thinking humans – an incomplete and potentially
misleading characterization. If we want to understand how
real human minds work, we must look not only at how our
reasoning is “limited” compared to that of supernatural be-
ings, but also at how our minds are adapted to real-world
environments. This two-sided conception of bounded ra-
tionality should inform our choice of criteria with which to
evaluate the performance of heuristics.
It is not enough merely to strive to compare human be-
havior to some optimal standard. As mentioned in section
2.3, many real-world situations do not have implementable
optimizing strategies. Many other situations have too many
possible optimizing strategies, because different definitions
of optimality follow from different assumptions about the
situation or the decision-maker’s goals. Where the assump-
tions must be uncertain, an optimizing approach becomes
uncertain as well, potentially leading to suboptimal out-
comes if the wrong guesses are made. Alternatively, a non-
optimizing fast and frugal strategy can nonetheless get
lucky and yield optimal outcomes. Hence, whether or not a
decision strategy attempts to optimize its performance is
not a sufficient evaluation criterion.
One set of criteria that is often used to assess judgments
and decisions is the laws of logic and probability theory.
These are often called coherence criteria because they are
primarily concerned with the internal logical coherence of
judgments rather than with how well they help us to make
useful decisions in the real world. Most experimental re-
search programs aimed at demonstrating the rationality or
(usually) irrationality of humans and animals have used ab-
stract coherence criteria. For instance, many claims that
there are systematic irrational fallacies in human reasoning
are based entirely on a violation of some rule or other of
logic or probability (e.g., Tversky & Kahneman 1983; Wa-
son 1983; see sect. 7).
In Simple heuristics we adopt a different, adaptive view
of rational behavior. We do not compare human judgment
with the laws of logic or probability, but rather examine how
it fares in real-world environments. The function of heuris-
tics is not to be coherent. Rather, their function is to make
reasonable, adaptive inferences about the real social and
physical world given limited time and knowledge. Hence,
we should evaluate the performance of heuristics by crite-
ria that reflect this function. Measures that relate decision-
making strategies to the external world rather than to in-
ternal consistency – measures such as accuracy, frugality,
and speed – are called correspondence criteria (Hammond
1996). As Egon Brunswik (1957) observed, the mind and
the environment are like a husband and wife couple who
must come to terms with one another by mutual adaptation.
However, owing to the focus on coherence in much re-
search on reasoning and decision making, the couple has
become estranged. Our aim is to get this couple corre-
sponding again, even if they cannot be coherent.
Indeed, the two kinds of criteria, coherence and corre-
spondence, can sometimes be at odds with each other. For
instance, in social situations, including some competitive
games and predator-prey interactions, it can be advanta-
geous to exhibit inconsistent behavior in order to maximize
adaptive unpredictability and avoid capture or loss (Driver
& Humphries 1988). In Chapters 4 and 5, we introduce
a similarly illogical heuristic – the Minimalist heuristic –
that violates transitivity but nevertheless makes fairly ro-
bust and accurate inferences in particular environments.
Thus, logic and adaptive behavior can be logically distinct.
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BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 737
To conclude: Heuristics are not simply hobbled versions
of optimal strategies. There are no optimal strategies in
many real-world environments in the first place. This does
not mean, though, that there are no performance criteria in
the real world. As a measure of the success of a heuristic,
we compare its performance with the actual requirements
of its environment, which can include making accurate de-
cisions, in a minimal amount of time, and using a minimal
amount of information. We have thus replaced the multiple
coherence criteria stemming from the laws of logic and
probability with multiple correspondence criteria relating
to real-world decision performance. But there is a further
difference between these two sets of multiple criteria:
While all coherence criteria must be met for a decision
method to be deemed rational, correspondence criteria can
be considered in relation to each other. In some environ-
ments, for instance, it may be more important to make a de-
cision quickly than completely accurately. However, one of
the surprising empirical results reported in our book is that
simple heuristics need not always make such tradeoffs. We
show that, when compared to some standard benchmark
strategies on a range of decision tasks, fast and frugal
heuristics can be faster, more frugal, and more accurate at
the same time. No tradeoff need be considered.
6.2. Do people use fast and frugal heuristics?
The research program described so far encompasses three
big questions: (1) What are reasonable heuristic principles
for guiding information or alternative search, stopping
search, and making a decision using the results of that
search? (2) When and why do these heuristics perform well,
that is, how can they be ecologically rational? (3) How well
do fast and frugal heuristics actually perform in real-world
environments? Exploring these three questions is sufficient
if we are interested in investigating new heuristics for vari-
ous applied settings – the realms of artificial intelligence
and decision-support systems, for instance. But if we are
also concerned with the principles that guide natural hu-
man and animal behavior, we must add a fourth question to
our research program: What is the evidence that humans or
animals use specific fast and frugal heuristics?
We know rather little about the heuristic principles of
limited search and stopping that people and animals use.
One major reason for this is that the typical experimental
task eliminates search in the first place (but see, e.g., Con-
nolly & Gilani 1982; Payne et al. 1993; Saad & Russo 1996).
Researchers usually sidestep questions of search by using
tasks in which all pieces of information – usually only two
or three – are already conveniently laid out in front of the
participant. Theories of cognition and the experimental
tasks used to test those theories often conspire hand in hand
to overlook limited search and stopping rules. More is thus
known about the heuristic decision principles that people
employ (e.g., Payne et al. 1993), and we have begun to in-
vestigate this with some of the fast and frugal heuristics de-
scribed in the book as well. Additionally, we have started to
make some inroads into the questions surrounding infor-
mation search by using an experimental setting in which
cues must be actively sought. We now give two brief exam-
ples of the kinds of empirical evidence we are gathering.
How can we distinguish whether people are using a sim-
ple versus a more complex decision strategy? One way is to
compare the decision performance of humans and algo-
rithms, using outcome measures that focus on the final de-
cision behavior. Experiments designed to test whether or
not people use the recognition heuristic, for instance (Ch.
2), showed that in 90% of the cases where individuals could
use the recognition heuristic when comparing the sizes of
two cities (i.e., when they recognized one city but not the
other), their choices matched those made by the recogni-
tion heuristic. This does not prove that participants were ac-
tually using the recognition heuristic to make their deci-
sions, however – they could have been doing something
more complex, such as using the information about the rec-
ognized city to estimate its size and compare it to the aver-
age size of unrecognized cities (though this seems unlikely).
Additional evidence that the recognition heuristic was be-
ing followed, though, was obtained by giving participants
extra information about recognized cities that contradicted
the choices that the recognition heuristic would make – that
is, participants were taught that some recognized cities had
cues indicating small size. Despite this conflicting informa-
tion (which could have been used in the more complex es-
timation-based strategy described above to yield different
choices), participants still made 92% of their inferences in
agreement with the recognition heuristic. Furthermore,
participants typically showed the less-is-more effect pre-
dicted by the earlier theoretical analysis of the recognition
heuristic, strengthening suspicions of this heuristic’s pres-
ence.
But often outcome measures are insufficient to distin-
guish between simple and complex heuristics, because they
all lead to roughly the same level of performance (the “flat
maximum” problem). Furthermore, comparisons made only
on selected item sets chosen to accentuate the differences
between algorithms can still lead to ambiguities or un-
generalizable findings (Ch. 7). Instead, process measures
can reveal differences between algorithms that are reflect-
ed in human behavior. For instance, noncompensatory al-
gorithms, particularly those that make decisions on the ba-
sis of a single cue, would direct the decision maker to search
for information about one cue at a time across all of the
available alternatives. In contrast, compensatory algorithms
that combine all information about a particular choice
would direct search for all of the cues of one alternative at
a time. We have found such evidence for fast and frugal
heuristics in laboratory settings where participants must ac-
tively search for cues (Ch. 7), especially in situations where
time-pressure forces rapid decisions. However, there is
considerable variability in the data of these studies, with
many participants appearing to use more complex strate-
gies or behaving in ways that cannot be easily categorized.
Thus much work remains to be done to provide evidence
for when humans and other animals use simple heuristics
in their daily decisions.
7. How our research program relates
to earlier notions of heuristics
The term “heuristic” is of Greek origin, meaning “serving
to find out or discover.” From its introduction into English
in the early 1800s up until about 1970, “heuristics” referred
to useful, even indispensable cognitive processes for solv-
ing problems that cannot be handled by logic and proba-
bility theory alone (e.g., Groner et al. 1983; Polya 1954). Af-
ter 1970, a second meaning of “heuristics” emerged in the
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738 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
fields of psychology and decision-making research: limited
decision-making methods that people often misapply to sit-
uations where logic and probability theory should be ap-
plied instead (e.g., Tversky & Kahneman 1974). We use the
term in the same positive sense as the earlier theorists, em-
phasizing their beneficial role in guiding search, and fol-
lowing Simon and Newell’s emphasis on creating precise
computational models. However, we break with the past
tradition of using well-defined artificial settings for the
study of heuristics, such as mathematical problems (Polya
1954) or the games of chess and cryptarithmetic that
Newell and Simon (1972) investigated. Instead, our re-
search addresses how fast and frugal heuristics can make in-
ferences about unknown aspects of real-world environ-
ments.
The research most closely related to the ABC program
on fast and frugal heuristics is that on adaptive decision
making and on simple classification rules in machine learn-
ing. In their study of the “adaptive decision maker,” Payne
et al. (1993) studied the trade-off between accuracy and ef-
fort for various choice strategies, including lexicographic
rules and Elimination by Aspects (Tversky 1972). Payne et
al. emphasized that a decision maker has a multitude of
strategies available and chooses between them depending
on their costs and accuracy given constraints such as time
pressure. One important distinction from the ABC pro-
gram is that Payne et al. focused on preferences, such as
between hypothetical job candidates or randomly selected
gambles, rather than on inferences whose correct answer
can be assessed, such as which soccer team will win or
which of two cities is larger. As a consequence, they mea-
sured a strategy’s accuracy by how closely it matched the
predictions of a weighted additive rule, the traditional gold
standard for rational preferences. Thus, in Payne et al.’s re-
search a heuristic can never be better than a weighted ad-
ditive rule in accuracy (though it may require less compu-
tational effort). In contrast, by measuring the performance
of all competing strategies against external real-world cri-
teria, we find that fast and frugal heuristics can be more ac-
curate than a weighted additive rule both in theory (Ch. 4)
and in practice (Ch. 5). Research in machine learning does
typically focus on inferences about real-world environ-
ments, allowing accuracy to be measured objectively. Work
on simple classification rules that use only one or a few cues
(e.g., Holte 1993; Rivest 1987) has demonstrated that fast
and frugal methods can be accurate, as well as being robust
generalizers owing to their limited parameter use.
A very different notion emerged in psychology in the
early 1970s, emphasizing how the use of heuristics can lead
to systematic errors and lapses of reasoning that indicate
human irrationality. This “heuristics-and-biases” program
launched by Tversky and Kahneman (1974) tainted the idea
of simple mental mechanisms by attaching them to the
value-laden “bias” term in a single inseparable phrase.
Within this program, heuristics were often invoked as the
explanation when errors – mainly deviations from the laws
of probability – were found in human reasoning. Although
Tversky and Kahneman (1974) repeatedly asserted that
heuristics sometimes succeed and sometimes fail, their ex-
perimental results were typically interpreted as indicating
some kind of fallacy, which was usually attributed to one of
three main heuristics: representativeness (judgments influ-
enced by what is typical), availability (judgments based on
what come easily to mind), or anchoring and adjustment
(judgments relying on what comes first). The reasoning fal-
lacies described by the heuristics-and-biases program have
not only been deemed irrational, but they have also been
interpreted as signs of the bounded rationality of humans
(e.g., Thaler 1991, p. 4). Equating bounded rationality with
irrationality in this way is as serious a confusion as equating
it with constrained optimization. Bounded rationality is nei-
ther limited optimality nor irrationality.
Our research program of studying fast and frugal heuris-
tics shares some basic features with the heuristics-and-
biases program. Both emphasize the important role that
simple psychological heuristics play in human thought, and
both are concerned with finding the situations in which
these heuristics are employed. But these similarities mask
a profound basic difference of opinion on the underlying
nature of rationality, leading to very divergent research
agendas: In our program, we see heuristics as the way the
human mind can take advantage of the structure of infor-
mation in the environment to arrive at reasonable decisions,
and so we focus on the ways and settings in which simple
heuristics lead to accurate and useful inferences. Further-
more, we emphasize the need for specific computational
models of heuristics rather than vague one-word labels
like “availability.” In contrast, the heuristics-and-biases ap-
proach does not analyze the fit between cognitive mecha-
nisms and their environments, in part owing to the absence
of precise definitions of heuristics in this program. Because
these loosely defined heuristics are viewed as only partly re-
liable devices commonly called on, despite their inferior
decision-making performance, by the limited human mind,
researchers in this tradition often seek out cases where
heuristics can be blamed for poor reasoning. For arguments
in favor of each of these views of heuristics, see the debate
between Kahneman and Tversky (1996) and Gigerenzer
(1996).
To summarize the place of our research in its historical
context, the ABC program takes up the traditional notion of
heuristics as an essential cognitive tool for making reason-
able decisions. We specify the function and role of fast and
frugal heuristics more precisely than has been done in the
past, by building computational models with specific prin-
ciples of information search, stopping, and decision mak-
ing. We replace the narrow, content-blind norms of coher-
ence criteria with the analysis of heuristic accuracy, speed,
and frugality in real-world environments as part of our study
of ecological rationality. Finally, whereas the heuristics-
and-biases program portrays heuristics as a possible hin-
drance to sound reasoning, we see fast and frugal heuristics
as enabling us to make reasonable decisions and behave
adaptively in our environment.
8. The adaptive toolbox
Gottfried Wilhelm Leibniz (1677/1951) dreamed of a uni-
versal logical language, the Universal Characteristic, that
would replace all reasoning. The multitude of simple con-
cepts constituting Leibniz’s alphabet of human thought
were all to be operated on by a single general-purpose tool
such as probability theory. But no such universal tool of
inference can be found. Just as a mechanic will pull out
specific wrenches, pliers, and spark-plug gap gauges for
each task in maintaining a car’s engine rather than merely
hitting everything with a large hammer, different domains
Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 739
of thought require different specialized tools. This is the ba-
sic idea of the adaptive toolbox: the collection of specialized
cognitive mechanisms that evolution has built into the hu-
man mind for specific domains of inference and reasoning,
including fast and frugal heuristics (see also Bettman 1979;
Cosmides & Tooby 1992; Payne et al. 1993). The notion of
a toolbox jumbled full of unique one-function devices lacks
the beauty of Leibniz’s dream of a single all-purpose infer-
ential power tool. Instead, it invokes the more modest but
surprising abilities of a “backwoods mechanic and used
parts dealer” (as Wimsatt 2000a describes Nature) who can
provide serviceable solutions to most any problem with just
the things at hand.
The adaptive toolbox contains psychological (as opposed
to morphological or physiological) adaptations (Tooby &
Cosmides 1992). These include so-called “lower-order”
perceptual and memory processes which can be fairly au-
tomatic, such as depth perception, auditory scene analysis,
and face recognition, as well as “higher-order” processes
that are based on the “lower” processes and can be at least
partly accessible to consciousness. Higher-order mental
processes include the examples we have discussed earlier of
inferring whether a heart attack victim should be treated as
a high- or low-risk patient and deciding whom to marry. The
focus of Simple heuristics is on fast and frugal heuristics for
higher-order cognitive processes that call upon lower-order
processes of cue perception and memory. We also apply this
constructive view to the mental tools themselves, creating
heuristics from combinations of building blocks and other
heuristics, as described in section 3. This feature distinguishes
the adaptive toolbox image from the similar metaphor of the
mind as a Swiss Army knife (Cosmides & Tooby 1992). Both
analogies emphasize that the mind uses a collection of many
specifically designed adaptive strategies rather than a few
general-purpose power tools, but the toolbox metaphor
puts more emphasis on the possibility of recombining tools
and building blocks and the nesting of heuristics.
Lower-order perceptual and memory processes such as
face and voice recognition are complex and difficult to un-
ravel, in part because they make use of massively parallel
computations. No one has yet managed to build a machine
that recognizes faces as well as a two-year-old child. Now
consider a higher-order decision mechanism that makes in-
ferences based on these processes, the recognition heuris-
tic introduced in Chapter 2. This fast and frugal heuristic
uses recognition to make rapid inferences about unknown
aspects of the world. Although the mechanisms of recogni-
tion memory may be intricate and complex, the recognition
heuristic can be described as an algorithm just a few steps
long. There is thus no opposition between simple and com-
plex processes operating in the mind – both have their
place, and can be studied somewhat independently. We do
not need to know precisely how recognition memory works
to describe a heuristic that relies on recognition. This ex-
ample illustrates an apparently paradoxical thesis: Higher-
order cognitive mechanisms can often be modeled by sim-
pler algorithms than can lower-order mechanisms.
This thesis is not new. It has been proposed in various
forms over the past century, as for example by proponents
of the Würzburg school of psychology in the early twenti-
eth century (Kusch 1999) and more recently by Shepard
(1967). The thesis has limits as well, of course: Some higher-
order processes, such as the creative processes involved in
the development of scientific theories or the design of so-
phisticated artifacts, are most likely beyond the purview of
fast and frugal heuristics. But we believe that simple heuris-
tics can be used singly and in combination to account for a
great variety of higher-order mental processes that may at
first glance seem to require more complex explanation, as
we demonstrate throughout our book.
9. Remaining challenges
Simple heuristics presents our efforts to date at advancing
a vision of ecological rationality arising from fast and frugal
decision mechanisms matched to their task environments.
Our successes have been modest in the face of the chal-
lenges that remain. Here we indicate the directions that this
research program must explore for us to gain a fuller un-
derstanding of how minds can make use of simple heuris-
tics.
Cognitive tasks. The first challenge is to explore fast and
frugal heuristics for solving tasks beyond those we consid-
ered so far. What other classes of decisions can be made by
simple mechanisms? How can fast and frugal cognition
help in tasks that extend over time such as planning or prob-
lem solving? Can simple heuristics be applied to perceptual
mechanisms as well? We expect so – a few researchers have
called perception a “bag of tricks” (e.g., Ramachandran
1990), full of quick and sometimes dirty mechanisms that
evolved not because of their consistency but because they
worked.
Adaptive problems. The next challenge is to study how
fast and frugal heuristics are applied to important adaptive
problems – how domain-specific should we expect simple
heuristics to be? The discovery of domain-specific heuris-
tics for important adaptive problems may help clarify how
the mind is organized – for instance, if heuristics used for
sequential mate search differ from heuristics for sequential
habitat search, this may indicate that mate choice and habi-
tat choice are distinct domains with specialized mecha-
nisms. What heuristics apply to adaptive problems such as
food choice (including modern forms of dieting), health
preservation (including visiting doctors and taking drugs),
and navigation (including getting from one end of a city to
another)?
Social norms and emotions. Simple heuristics can also be
advantageous for navigating the complexities of social do-
mains, and can be learned in a social manner, through imi-
tation, word of mouth, or cultural heritage. We suspect that
social norms, cultural strictures, historical proverbs, and the
like can enable fast and frugal social reasoning by obviating
cost-benefit calculations and extensive information search.
We also speculate that emotions may facilitate rapid deci-
sion making by putting strong limits on the search for in-
formation or alternatives, as when falling in love stops part-
ner search and facilitates commitment. Where can we find
further evidence for the decision-making functions of these
cultural and emotional processes, and how can they serve
as building blocks in precise models of fast and frugal
heuristics?
Ecological rationality. We do not yet have a well-developed
language for describing those aspects of environment struc-
ture, whether physical or social, that shape the design and
performance of decision heuristics. Here one can turn for
inspiration to other fields, including ecology and statistics,
that have analyzed environment structure from different
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740 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
perspectives. For instance, the statistical measures of two-
dimensional patterns developed in spatial data analysis
(e.g., Upton & Fingleton 1985) can be used when assessing
heuristics for spatial search in foraging or habitat selection.
Performance criteria. How should the performance and
usefulness of heuristics be measured? Ultimately, ecologi-
cal rationality depends on decision making that furthers an
organism’s adaptive goals in the physical or social environ-
ment. How can measures of decision speed, frugality, and
accuracy be augmented by and combined with measures of
adaptive utility? We have tested the generalization ability of
heuristics so far only in cross-validation tests. How can we
measure predictive accuracy and robustness in environ-
ments that are in a state of continual flux, with new objects
and cues appearing over time? Finally, we have focused on
adaptive goals in terms of correspondence criteria (e.g., ac-
curacy, speed, and frugality) as opposed to the coherence
criteria (e.g., consistency, transitivity, and additivity of prob-
abilities) traditionally used to define rationality. Is there any
role for coherence criteria left? Should one follow Sen
(1993) in arguing that consistency is an ill-defined concept
unless the social objectives and goals of people are speci-
fied?
Selecting heuristics. How does the mind know which
heuristic to use? Following our bounded rationality per-
spective, a fast and frugal mind need not employ a meta-
level demon who makes optimal cost-benefit computations
when selecting a heuristic. The fact that heuristics are de-
signed for particular tasks rather than being general-purpose
strategies solves part of the selection problem by reducing
the choice set (Ch. 1). But we have not yet addressed how
individual heuristics are selected from the adaptive toolbox
for application to specific problems.
Multiple methodologies. The combination of conceptual
analysis, simulation, and experimentation has deepened
our understanding of fast and frugal heuristics. However,
more evidence must be amassed for the prevalence of sim-
ple heuristics in human and animal reasoning. This need
not be done solely through laboratory experiments, where
we often find that alternative mechanisms can equally ac-
count for the observed behavior (as discussed in Ch. 7).
Collecting data from the field – whether that field is a jun-
gle habitat or an airplane cockpit – is also vital for discover-
ing new heuristics and teasing competing mechanisms
apart.
10. Summary of the ABC view of rationality
The research program described in Simple heuristics is de-
signed to elucidate three distinct but interconnected as-
pects of rationality (see also Chase et al. 1998):
1. Bounded rationality. Decision-making agents in the
real world must arrive at their inferences using realistic
amounts of time, information, and computational re-
sources. We look for inference mechanisms exhibiting
bounded rationality by designing and testing computational
models of fast and frugal heuristics and their psychological
building blocks. The building blocks include heuristic prin-
ciples for guiding search for information or alternatives,
stopping the search, and making decisions.
2. Ecological rationality. Decision-making mechanisms
can exploit the structure of information in the environment
to arrive at more adaptively useful outcomes. To under-
stand how different heuristics can be ecologically rational,
we characterize the ways that information can be structured
in different decision environments and how heuristics can
tap that structure to be fast, frugal, accurate, and adaptive
at the same time.
3. Social rationality. The most important aspects of an
agent’s environment are often created by the other agents
it interacts with. Thus, predators must make crucial infer-
ences about the behavior of their prey (Ch. 12), males and
females must make decisions about others they are inter-
ested in mating with (Ch. 13), and parents must figure out
how to help their children (Ch. 14). Social rationality is a
special form of ecological rationality, and to study it we
design and test computational models of fast and frugal
heuristics that exploit the information structure of the so-
cial environment to enable adaptive interactions with other
agents. These heuristics can include socially adaptive build-
ing blocks, such as social norms and emotions of anger and
parental love, which can act as further heuristic principles
for search, stopping, and decision.
These three aspects of rationality look toward the same
central goal: to understand human (and animal) behavior
and cognition as it is adapted to specific environments, both
ecological and social, and to discover the heuristics that
guide adaptive behavior. In some ways, this view leaves be-
hind a certain sense of beauty and morality associated with
the dream of optimal thought. Leibniz’s universal calculus
exhibits the aesthetics and the moral virtue of this lofty ideal,
as does Laplace’s omniscient superintelligence. Cognitive
scientists, economists, and biologists have often chased af-
ter the same beautiful dreams by building elaborate mod-
els endowing organisms with unlimited abilities to know,
memorize, and compute. These heavenly dreams, however,
tend to evaporate when they encounter the physical and
psychological realities of the waking world: Mere mortal
humans cannot hope to live up to these standards, and in-
stead appear nightmarishly irrational and dysfunctional in
comparison.
In the face of this dilemma, many researchers have still
preferred to keep dreaming that humans can approximate
the exacting standards of optimality, rather than surrender-
ing to an ungodly picture of human irrationality and stu-
pidity. The choice, however, is not between an unrealistic
dreaming rationality and a realistic nightmare irrationality.
There is a third vision that dispenses with this opposition:
rationality through simplicity, and accuracy through frugal-
ity. In Simple heuristics, we strive to paint in a few more of
the details of this hopeful vision.
NOTE
1. Gerd Gigerenzer, Peter M. Todd, and the ABC Research
Group are the authors of Simple heuristics that make us smart
(1999) Oxford University Press.
Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 741
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pecially encouraged.
The evolution of rational demons
Colin Allen
Department of Philosophy, Texas A&M University, College Station, TX 77843-
4237.
colin-allen@tamu.edu www-phil.tamu.edu/~colin/
Abstract: If fast and frugal heuristics are as good as they seem to be, who
needs logic and probability theory? Fast and frugal heuristics depend for
their success on reliable structure in the environment. In passive environ-
ments, there is relatively little change in structure as a consequence of in-
dividual choices. But in social interactions with competing agents, the en-
vironment may be structured by agents capable of exploiting logical and
probabilistic weaknesses in competitors’ heuristics. Aspirations toward the
ideal of a demon reasoner may consequently be adaptive for direct com-
petition with such agents.
Gigerenzer, Todd, and the ABC Research Group (Gigerenzer et
al. 1999) provide a compelling account of real-world decision mak-
ing. I very much like what they have accomplished and I do not
expect to say anything here that they would strongly disagree with.
But as someone whose livelihood depends to a considerable ex-
tent on attempting to inculcate “the baggage of the laws of logic”
(p. 365) into minds of varying impressionability, I wonder how
much to fear that my attempts to present first-order logic as a stan-
dard of good reasoning will be consigned to lectures to the Flat
Earth Society.
I take it that people (and not just philosophers) are sometimes
concerned that their reasoning satisfies what the authors call “co-
herence criteria” – criteria encoded in classical logics and proba-
bility theory. I take it also that dreams of “demon” rationality were
not implanted in us by a Cartesian deity. Humans, under their own
impetus, aspire to consistency in their beliefs and likelihood as-
sessments, and they reason accordingly. From whence comes this
aspiration? And is it an adaptation?
One of Gigerenzer et al.’s important principles is that fast and
frugal heuristics are successful because environments are struc-
tured in specific ways (Gigerenzer et al. 1999). The recognition
heuristic works because of a usually dependable relationship be-
tween the saliency of names in the environment and target prop-
erties such as population size or market performance. Other fast
and frugal heuristics take into account additional cues that are cor-
related with target properties. Simple heuristics that use only a
subset of the available cues to discriminate options can lead to re-
markably accurate assessments of the target properties. But fast
and frugal heuristics can also deliver inconsistent judgments. As
the authors point out, some heuristics can, in principle, return
judgments such as that city A is larger in population than city B, B
is larger than C, and C is larger than A.
Gigerenzer et al. (1999) provide no empirical evidence that
people actually make such inconsistent judgments. But if they do,
I would also like to know whether, in a given session, subjects hes-
itate or show other signs of uncertainty when they produce a judg-
ment that is inconsistent with others just produced. Except under
the most severe time pressures, I would be astounded if people
blithely produced the inconsistent series of judgments shown
above without revealing some sign of discomfort. By assigning a
penalty for wrong answers – a trick sometimes employed by my
colleagues who use multiple-choice examinations – one might
perhaps expect to induce consistency checking. So, in considering
when people might not use simple heuristics, I would like to sug-
gest investigating those situations where the cost of being wrong
exceeds the benefit of being right. Perhaps it is no accident that
Darwin attempted to consider all his reasons in deciding whether
to marry!
Where else might attempting to live up to the ideal of a demon
rationalizer be an adaptive thing to do? Here I think it may be in-
teresting to distinguish between the “passive” environment and
the “agentive” environment. According to this distinction the
structure of the passive environment is relatively independent of
an individual’s behavior or dispositions. The passive environment
contains what would be thought of as the nonsocial environment
as well as large-scale aspects of the social environment (such as the
stock market) which are not responsive to the isolated acts of in-
dividuals. For example, the environmentally-provided relation-
ships between fruit color and nutritional value or between com-
pany name recognition and company stock performance are not
going to change (in the short run) if an individual tends to rely
heavily on that cue to make feeding or investing decisions. (In the
long run, of course, there may be coevolution between plants and
feeders, and there will be an effect on the market if many indi-
viduals pick stocks on name recognition alone.) In contrast, in
dealing directly with other agents, an individual’s selection ten-
dencies can be exploited by a savvy opponent. Thus, for example,
if you know that I rely on presence of a university as the best cue
for estimating city size, you could lower my overall success rate by
presenting me with disproportionately many pairs of cities that vi-
olate the norm. Here, the structure of the encountered environ-
ment is not independent of the subject’s dispositions. Failures of
logical or probabilistic consistency provide additional vulnerabili-
ties that a logically or statistically proficient opponent might ex-
ploit.
We might see our imperfect implementation of demon ratio-
nality as an evolutionary artifact, the byproduct of other adapted
systems, or as itself a cognitive adaptation. I have never really liked
the often-produced hypothesis that intelligence is a social adapta-
tion but here, perhaps, is a place where it finds a home. Individu-
als who are smart because of fast and frugal heuristics alone can
be exploited in social interactions by those who are more profi-
cient in logic and probability. There may therefore be selection
pressure to develop more demon-like forms of rationality. Fast
and frugal heuristics certainly are part of what makes us smart. But
the “baggage” of logic and probability theory could be well worth
carrying when journeying among competing agents. I shall con-
tinue to load up my students with as much as they can bear.
Where does fast and frugal cognition stop?
The boundary between complex cognition
and simple heuristics
Thom Baguley,
1
and S.Ian Robertson
2
1
Department of Human Sciences, Loughborough University, Loughborough,
LE11 3TU, England;
2
Department of Psychology, University of Luton, Luton,
LU1 3JU, England.
t.s.baguley@lboro.ac.uk
ian.robertson@luton.ac.uk
Abstract: Simple heuristics that make us smart presents a valuable and
valid interpretation of how we make fast decisions particularly in situations
of ignorance and uncertainty. What is missing is how this intersects with
thinking under even greater uncertainty or ignorance, such as novice prob-
lem solving, and with the development of expert cognition.
Reading Simple heuristics led to a curious feeling of familiarity.
Many of the ideas were familiar, yet at the same time there was
a sense of discovery. The notion that evolution and ecological
constraints influence cognition is topical in recent research (Lans-
dale 1998), student texts (Robertson 1999), and popular science
(Pinker 1997). The idea that decisions draw on evidence provided
by our memories is also well established. Although several impor-
Commentary/Todd & Gigerenzer: Simple heuristics
742 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
tant contributions are made by the book we focus on what we con-
sider the most exciting one: the proposal of a flexible, modular,
ecologically rational toolbox of fast and frugal heuristics.
First, the toolbox approach offers the potential to balance the
costs of domain-general and domain-specific solutions to prob-
lems. Second, it attempts detailed process models of cognition.
Third, it may offer a way of integrating a range of work within and
without cognitive science. None of these potential benefits has
been fully realized, yet Simple heuristics is a promising sketch of
how such a toolbox might work (e.g., of how skewed environmen-
tal distributions can constrain our selection of search or decision
rules). The close relationship between environmental structure
and heuristics suggests that a drawing together of research on per-
ception, memory, and cognition is required. An earlier response
to such a proposal led to the development of large, far-from-
frugal, unified theories of cognition (Newell 1990). Unified theo-
ries such as SOAR or ACT-R try to model everything at once,
whereas the adaptive toolbox approach tries to find niches where
simple strategies can be applied in a modular way.
ACT-R and SOAR emerged from a tradition of research on
high-level cognition such as problem solving (Newell & Simon
1972). Where does fast and frugal cognition stop and where does
slow and lavish cognition such as reasoning or problem solving be-
gin? One extreme view is that all cognition is fast and frugal: think-
ing always involves some computational shortcut to solve a syllo-
gism, prove a theorem, or discover a solution. For example, skill
and expertise are often readily modeled by recognition of familiar
problems and application and modification of routine methods
(see Payne 1988). This position does not seem that far from the
sympathy expressed with Brooks’s program of research which es-
chews “building elaborate mental models” of the world (Ch. 15,
Goodie, Ortmann, Davis, Bullock & Werner, p. 334). At the other
extreme, it may be argued that because fast and frugal heuristics
require a certain “beneficial” level of ignorance this limits them to
a few narrow niches. There is no reason to take on either extreme
(at least where human cognition is concerned). However, it is nec-
essary to explicate the relationship between fast and frugal heuris-
tics and the existing body of research on complex cognition such
as problem solving.
When fast and frugal approaches fail are we then unable to
achieve our desired goal directly and therefore resort to problem
solving? We think that the fast and frugal approach can be more
intimately linked to traditional problem solving approaches than
this. Take one of several issues left open in Simple heuristics: that
of selecting heuristics (Ch. 16, Gigerenzer et al. 1999, p. 364). This
occurs in two guises: how heuristics become available for selec-
tion, and, once available, how one is selected. Humans may learn
new heuristics, new principles for selecting heuristics, or develop
expertise with their application through problem solving. Select-
ing and applying a heuristic seems to require a more-or-less elab-
orate representation of a domain. Adults are able to use heuristics
in a sophisticated way because they have a relatively rich concep-
tual representation of the world compared to infants. Many tasks
that appear simple for adults are predicated on rich expertise
(Wood 1988). Problem solving and reasoning are important for ex-
ploring unfamiliar situations and building up representations of
them (Baguley & Payne 2000). This takes time and effort (even if
relatively slow and frugal weak methods such as imitative problem
solving are used; Robertson, in press), but the dividends may be
very large. Once those representations are established, experts are
able to apply domain-specific solutions to problems just as mature
humans can apply heuristics such as “Take the Best” in familiar
environments with the appropriate structure. Reading Simple
heuristics sometimes gave us the impression that evolution is the
only candidate for the origins of the toolbox components. This
needs qualifying. Humans are innately equipped to develop and
learn certain classes of heuristics.
We suggest, therefore, that fast and frugal heuristics supple-
ment traditional problem solving research. They may be brought
to bear on selecting and applying operators under means-ends
analysis (e.g., where a recognition heuristic is used to avoid re-
turning to previous states). In conclusion, the adaptive toolbox has
much to offer. Important aspects remain to be fleshed out, and we
have reservations about some elements of the approach. The way
the toolbox draws on supposed end-products of memory (given that
the “binary quality of recognition” is itself the output of an incom-
pletely understood decision process) may be an over-simplification.
It may also be unwise to reject normative approaches out of hand,
although we agree that norms should not be applied unquestion-
ingly.
Keeping it simple, socially
Louise Barrett
1,2
and Peter Henzi
2
1
Evolutionary Psychology and Behavioural Ecology Research Group, School
of Biological Sciences, University of Liverpool, L69 3BX, United Kingdom;
2
Behavioural Ecology Research Group, School of Social Anthropology and
Psychology, University of Natal, Durban 4041, South Africa.
louiseb@liv.ac.uk henzi@mtb.und.ac.za
Abstract: Fast and frugal heuristics function accurately and swiftly over a
wide range of decision making processes. The performance of these algo-
rithms in the social domain would be an object for research. The use of
simple algorithms to investigate social decision-making could prove fruit-
ful in studies of nonhuman primates as well as humans.
Three and a half years ago, when we began a study of baboons
in the Western Cape, South Africa, we used a very simple one-
reason decision rule to pick our study troops: we selected the ones
who slept on the cliffs directly opposite our research house. We
have never regretted this decision, although a more thorough in-
vestigation of the baboon population might have yielded troops
with a more intriguing demographic composition or more unusual
ranging patterns. Our relatively uninformed search and decision-
making process yielded baboons that were good enough. As ad-
vocates of one-reason decision-making, we were therefore de-
lighted to discover that Gerd Gigerenzer, Peter Todd, and the
ABC Research Group had conducted a much more systematic in-
vestigation of simple heuristics, and were very impressed with the
results (Gigerenzer et al. 1999). One of the most satisfying ele-
ments of their analyses was the way in which the various algo-
rithms were tested in real-world situations, rather than against a
perfectly rational or optimal ideal. In the field of animal behav-
iour, we are all too often confronted with optimality models that
make unrealistic assumptions (“imagine your baboon is a sphere
moving in a vacuum”) and treat animals as perfect rational agents
with complete knowledge. If something as simple as the recogni-
tion heuristic can beat the stock market, that most fiendishly com-
plicated of human inventions, then, as Gigerenzer et al. (1999)
themselves suggest, it seems likely that this simplicity may also pay
dividends within the animal kingdom.
The “fast and frugal” approach is particularly interesting to us as
primatologists because of the essentially anthropocentric approach
taken with studies of primate cognition. If humans, with their rela-
tively enormous brains, can achieve more with less knowledge as
Gigerenzer et al. (1999) have demonstrated, then it seems reason-
able to suppose that the same might be true for our less well-en-
dowed cousins. This may seem obvious, but primates are often im-
puted to have extremely advanced cognitive skills and reasoning
abilities largely on the basis of their close relationship with humans,
rather than any firm demonstration that this is the case. Monkeys
and apes are often assumed to use complex mentalist analyses of
their social situation and be able to adopt manipulative courses of
action, as befits their increased neocortex size relative to other ani-
mals (see, e.g., Byrne & Whiten 1988). Perhaps, however, this in-
creased cortex is actually needed to help animals think more sim-
ply, rather than in more complicated ways. [See also Whiten &
Byrne: “Tactical Deception in Primates” BBS 11(2) 1988.]
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 743
Blurton-Jones et al. (1999) recently suggested that the need to
learn increasing amounts of information over the course of human
evolution would have selected for new ways of learning and pro-
cessing information. Fast and frugal heuristics could have been one
such mechanism to help speed decision-making in an ever more
complicated social world. The same argument could, of course, be
applied to the increase in social complexity over the course of pri-
mate evolution as a whole, and could explain the increase in primate
brain size over that of the other mammals. It is therefore an inter-
esting empirical issue as to whether fast and frugal heuristics are the
result of our primate heritage, or whether they truly do represent a
new way of using information that is not available to other primate
species. Is a large neocortex needed to make the initial inferences
about ecological (social) validities, correlations between cues and the
structure of the social environment that allow fast and frugal algo-
rithms to work so speedily and accurately? Rather ironically, is it the
case that large brains are needed in order to reason in the simplest
way possible? The success of the fast and frugal algorithm of parental
investment suggests that this need not be the case, but the social
world does present animals with an inherently more complex envi-
ronment consisting as it does of other individuals with their own
goals and interests at heart. Decisions made in the social domain may
therefore require more complex assessments, but once the initial
correlations and cue values are learned, the generalisation to a fast
and frugal heuristic would seem likely to pay dividends. Testing the
performance of fast and frugal heuristics in the social arena would
seem to be the logical next step for Gigerenzer, Todd, and their col-
leagues to take. It would be interesting to know the limits of these
algorithms under these more dynamic and interactive conditions.
Would a point be reached where simple heuristics failed to make us
smart, and more complex abilities such as “mind-reading” and the
attribution of mental states were needed to perform well? Or do
these abilities constitute fast and frugal heuristics in themselves?
The use of fast and frugal heuristics as an explanation of the so-
cial decision-making of other primate species also warrants fur-
ther attention. Our own data on baboons show that females make
short-term tactical decisions with regard to grooming partners and
social interactions and, therefore do not support the idea that
long-term strategic alliance formation is the key to primate so-
ciality (Barrett et al. 1999). It would be interesting to investigate
whether these short-term decisions can be modelled by a fast and
frugal algorithm such as Take the Best and whether females ex-
ploit their ignorance to good advantage. The fact that other social
decisions requiring mutual choice, such as finding a mate, can be
modelled using fast and frugal algorithms suggests to us that so-
cial decision-making of the kind we observe would be an excellent
candidate for investigating the power of simple heuristics from a
comparative perspective.
Rationality, logic, and fast
and frugal heuristics
José Luis Bermúdez
Department of Philosophy, University of Stirling, Stirling FK9 4LA, Scotland
jb10@stir.ac.uk www.stir.ac.uk/philosophy/cnw/webpage1.htm
Abstract: Gigerenzer and his co-workers make some bold and striking
claims about the relation between the fast and frugal heuristics discussed
in their book and the traditional norms of rationality provided by deduc-
tive logic and probability theory. We are told, for example, that fast and
frugal heuristics such as “Take the Best” replace “the multiple coherence
criteria stemming from the laws of logic and probability with multiple cor-
respondence criteria relating to real-world decision performance.” This
commentary explores just how we should interpret this proposed replace-
ment of logic and probability theory by fast and frugal heuristics.
The concept of rationality is Janus-faced. It is customary to dis-
tinguish the psychological laws governing the actual processes of
reasoning from the normative theories according to which such
reasoning is to be evaluated (Nozick 1993).
1
Authors who make
this distinction often enjoin us to ignore one of the faces to con-
centrate on the other – either instructing us, as Frege (1918–
1919) famously did, to ignore the messy details of psychology to
focus on the objective relations between thoughts that are the do-
main of logic, or, like Willhelm Wundt (1973, cited on p. 357), im-
ploring us to ignore the subtleties of the logician in order to ex-
plain the psychology of reasoning. It is clear that Gigerenzer et al.
(1999) favour the second of these positions. In fact, they seem to
be making an even stronger claim. They seem to be suggesting
that, where the dictates of the logician and the heuristics of the
quick and dirty reasoner come into conflict, it is logic and proba-
bility theory that must be sacrificed. But what exactly does this
mean in detail? Why should the prevalence of fast and frugal
heuristics have any implications at all for the normative theories
of logic and probability theory?
The notion of a fast and frugal heuristic has been around for a
long time, although not perhaps under that name (Kahneman &
Tversky 1973; Simon 1982). There is a standard way of interpret-
ing such heuristics so that they are not really in conflict at all with
the normative theories of logic and probability theory. One might
say, for example, that, although the normative theories provide the
standards by which practical reasoning ought to be judged (that is
to say, they tell us what ought to be done, or what it is rational to
do, in a particular situation when one possesses such-and-such in-
formation), there are nonetheless computational reasons why it is
often not actually possible to use such theories in the actual
process of decision-making. Because it is not always possible in
practice to assign numerical probabilities to possible outcomes, or
to give them numerical desirability ratings (let alone to use these
figures to work out the course of action that best maximises ex-
pected utility), we are impelled to use shortcuts. But what justi-
fies these shortcuts (what makes it rational to adopt them) is that
they lead us to do more or less what we would have done had we
actually put the normative theories into practice by working out
the figures and crunching the numbers. Proponents of optimal
foraging theory think that something like this holds of the “rules
of thumb” converging on optimality that natural selection has
thrown up (Dawkins 1995, Ch. 2). And, as the authors point out
(Gigerenzer & Todd, p. 26), the accuracy of fast and frugal heuris-
tics is often assessed in the literature by measuring how closely
they match the predictions of a weighted additive rule, like the
rule of maximising expected utility.
But this is emphatically not how Gigerenzer et al. view the op-
eration of heuristics like “Take the Best.” It can, by their lights, be
rational to use such heuristics even when they result in courses of
action that contravene the dictates of the normative theories. The
heuristics can trump the normative theories. Again, there is a rel-
atively innocuous way of understanding such a claim. One might
think, for example, that it might be rational to use a heuristic even
in a situation where it does not match the predictions of the nor-
mative rule simply because, when one takes a sufficiently long-
term view, the overall benefits of using the heuristic outweigh the
occasional benefits to be had by crunching the numbers each time.
But all this really amounts to is the claim that we should evaluate
a strategy rather than a particular application of that strategy. The
normative standards according to which we do the judging are not
themselves changed. Gigerenzer et al. certainly want to say some-
thing more controversial than this. But what?
Gigerenzer et al. say that they want to impose a new set of crite-
ria for judging the rationality of decision-rules – what they term
“multiple correspondence criteria relating to real-world decision
performance” (Gigerenzer et al. 1999, p. 22). For example, it be-
comes rational to select the companies in one’s investment portfo-
lio by a simple version of the recognition heuristic (viz. only put com-
panies with a high recognition factor into one’s portfolio) because,
as it happens, such portfolios seem to outperform both the relevant
indices and random portfolios of stocks (see Ch. 3). That is, success
becomes the sole determinant of rational decision-making.
Commentary/Todd & Gigerenzer: Simple heuristics
744 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
There are several problems with this; they point to a difficulty
with the research programme as a whole. First, there is a very im-
portant equivocation in how the stockmarket experiment is being
described. The authors write as if their strategy was a pure appli-
cation of the recognition heuristic. But this seems wrong. They did
not invest in companies that they recognised. Rather, they in-
vested in companies that had a high national and/or international
recognition factor, where this is calculated statistically by compar-
ing the recognition judgments of several different populations.
These are two very different things. The first would have been a
pure fast and frugal heuristic. The second, in contrast, seems
much closer to a calculated investment strategy. What makes this
equivocation important is that the notion of rationality applies very
differently in the two cases. It is hard to see how anything other
than a pure success-based criterion of rationality could be applied
to the fast and frugal version of the recognition heuristic. Or, to
put this another way, it is hard to see what reasons there might be
for holding that it is rational to make one’s investment decisions
solely according to whether one has heard of the companies in
question other than that the strategy more or less works over
time – and it is equally hard to see how, if the strategy doesn’t work,
it could then possibly be described as rational. But the same does
not hold of the sophisticated investment strategy of investing only
in companies with a statistically attested high recognition. There
are all sorts of reasons why this is a rational strategy to
adopt – quite apart from the well-documented “big company ef-
fect” in bull markets (to which the authors themselves draw at-
tention) and the simple thought that a company with a high recog-
nition factor will correspondingly have a high market share. That
is to say, even if it did turn out (as it probably would in a bear mar-
ket) that the strategy did not beat the index it might well still count
as a rational strategy to have adopted.
What this points us to is an important discussion in the concept
of rationality. A workable concept of rationality must allow us to
evaluate the rationality of an action without knowing its outcome.
Without this the concept of rationality cannot be a useful tool in
the control, regulation and evaluation of decision-making as and
when it happens. And it is precisely such a way of evaluating the
rationality of an action that we are offered by the orthodox nor-
mative theories of expected utility maximisation and so forth. But
is far from clear that Gigerenzer and his co-workers have offered
a genuine alternative to this. They claim to have replaced criteria
of rationality based upon logic and probability theory with a
heuristic-based criteria of real-world performance. but it doesn’t
look as if they’ve offered us criteria of rationality.
NOTE
1. For discussion of ways to strike the balance between these two facets
of rationality see Bermúdez 1998; 1999a; 1999b; 1999c; 2000 and the es-
says in Bermúdez and Millar (in preparation).
How smart can simple heuristics be?
Nick Chater
Department of Psychology, University of Warwick, Coventry, CV4 7AL, United
Kingdom
nick.chater@warwick.ac.uk
Abstract: This commentary focuses on three issues raised by Gigerenzer,
Todd, and the ABC Research Group (1999). First, I stress the need for fur-
ther experimental evidence to determine which heuristics people use in
cognitive judgment tasks. Second, I question the scope of cognitive mod-
els based on simple heuristics, arguing that many aspects of cognition are
too sophisticated to be modeled in this way. Third, I note the comple-
mentary role that rational explanation can play to Gigenerenzer et al.’s
“ecological” analysis of why heuristics succeed.
Gigerenzer, Todd, and the ABC Research Group have provided a
series of impressive demonstrations of how simple “fast and fru-
gal” cognitive heuristics can attain surprisingly impressive levels
of performance, comparable to human performance in a range of
tasks. They show, for example, that decision making based on a sin-
gle piece of evidence, rather than integrating across all available
evidence, can lead to close optimal performance in a wide range
of estimation tasks (Gigerenzer et al. 1999, Ch. 4, p. 75, Gigeren-
zer & Goldstein). Gigerenzer et al. interpret these results as hav-
ing radical implications for cognition in general – in particular, as
undercutting the view that cognition must involve well-optimized
cognitive machinery which behaves in accordance with classical
rational norms of probability theory, logic, and decision theory.
This line of thought raises the attractive possibility that the com-
plexity of the mind may have been dramatically overestimated.
Perhaps the mind is really just a collection of smart heuristics,
rather than a fantastically powerful computing machine. This is an
exciting and important thesis. This commentary focuses on three
challenges to this approach, which may open up avenues for fu-
ture research.
1. Empirical evidence.
Gigerenzer et al. focus on providing a
feasibility proof for the viability of a particular kind of simple rea-
soning heuristic. This task primarily involves providing computer
simulations showing that simple heuristics give good results on
specific decision problems, in comparison to conventional meth-
ods such as linear regression, and to other heuristic approaches,
such as unit-weighted regression. But there is little by way of ex-
perimental evidence that people actually do reason in this way,
aside from important but preliminary evidence reported in Chap-
ter 7. This is particularly important precisely because the simula-
tions in this book show that a wide range of algorithms give very
similar levels of performance. Hence, prima facie, all these algo-
rithms are equally plausible candidates as models of how people
might perform on these problems.
In the absence of a broader set of experimental tests there is
some reason to doubt that people make decisions by relying on
one cue only. As Gigerenzer et al. note, in perception and lan-
guage processing there is ample evidence that multiple cues are
integrated in recognition and classification, in extremely complex
ways (e.g., Massaro 1987). Gigerenzer et al. propose that these
cases are in sharp contrast to the operation of conscious decision-
making processes – determining whether this divide is a real one
is an important area for empirical research.
2. Scope.
One of the most startling findings in psychology is
that, across a very wide range of judgment tasks, including med-
ical diagnosis, expert performance does not exceed, and is fre-
quently poorer than, results obtained by linear regression over sets
of features of the cases under consideration (Meehl 1954; Sawyer
1966).
An equally startling finding, this time from artificial intelligence
and cognitive science, has been that in everyday reasoning, peo-
ple vastly outperform any existing computational model (Oaksford
& Chater 1998a). Even the inferences involved in understanding
a simple story draw on arbitrarily large amounts of world knowl-
edge, and people must integrate and apply that knowledge highly
effectively and rapidly. Attempts to model such processes compu-
tationally have become mired in the nest of difficulties known as
the “frame problem” (Pylyshyn 1987).
So cognition is, in some regards, remarkably weak; and in other
regards it is remarkably powerful. In the present context, the cru-
cial point is that the simple heuristics discussed in this book are
aimed at modeling areas where cognition is weak – indeed, where
cognitive performance is already known to be frequently outper-
formed by linear regression. But it is by no means clear that the
picture of the mind as a set of simple heuristics will generalize to
everyday reasoning, where cognitive performance appears to be
remarkably strong. Indeed, it may be that it is not that simple
heuristics make us smart (as Gigerenzer et al.’s title suggests);
rather it may be that we resort to simple heuristics to do the very
thing we are not smart at.
3.
Why
do heuristics work?
Gigerenzer et al. downplay the im-
portance of traditional conceptions of rationality in their discus-
sion of reasoning methods. Indeed, they note that a heuristic such
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 745
as Take the Best has not been derived from “rational” principles
of probability or statistics. Instead, they focus on an ecological no-
tion of rationality – does the heuristic work in practice on real
world data?
The viewpoint may appear to be an alternative to more tradi-
tional notions of rationality as used in psychology (Anderson 1990;
Chater et al. 1999; Oaksford & Chater 1998b), economics (Kreps
1990) and behavioral ecology (McFarland & Houston 1981), in
which behavior is assumed to approximate, to some degree, the
dictates of rational theories, such as probability and decision the-
ory. But it may be more appropriate to see the two viewpoints as
complementary. Gigerenzer et al. (1999) are concerned to demon-
strate rigorously which particular heuristics are successful, by
computer simulation on realistic data sets. Traditional rational the-
ories aim to explain why heuristics work. They characterize the
optimization problem that the cognitive process, economic actor
or animal faces; using rational theories (probability, decision the-
ory, operations research) to determine the “rational” course of ac-
tion; and conjecture that the heuristics used in actual performance
approximate this rational standard to some degree. From this
point of view, rational methods can be viewed as compatible with
the “ecological” view of rationality outlined in Gigerenzer et al.
(1999). Focusing on simple cognitive heuristics does not make the
application of rational standards derived from formal calculi un-
necessary. Instead, it gives a defined role for rational explanation
– to explain why and under what conditions those heuristics suc-
ceed in the environment. This perspective is, indeed, exemplified
in Gigerenzer et al.’s formal analysis of the conditions under which
the Take the Best heuristic is effective (Ch. 6) and consistent with
Gigerenzer et al.’s valuable comparisons between Take the Best
and Bayesian algorithms (Ch. 8).
This book shows an important direction for research on human
reasoning. It should act as a stimulus for empirical, computational,
and theoretical developments in this area.
Simple heuristics could make us smart;
but which heuristics do we apply when?
Richard Cooper
School of Psychology, Birkbeck College, University of London, London,
WC1E 7HX United Kingdom
r.cooper@psychology.bbk.ac.uk
www.psyc.bbk.ac.uk/staff/rc.html
Abstract: Simple heuristics are clearly powerful tools for making near op-
timal decisions, but evidence for their use in specific situations is weak.
Gigerenzer et al. (1999) suggest a range of heuristics, but fail to address
the question of which environmental or task cues might prompt the use of
any specific heuristic. This failure compromises the falsifiability of the fast
and frugal approach.
Gigerenzer, Todd, and the ABC Research Group (1999) are right
to criticise much contemporary psychological decision-making re-
search for its focus on mathematically optimal approaches whose
application requires unbounded time and knowledge. They have
clearly demonstrated that an agent can make effective decisions
in a range of ecologically valid decision-making situations without
recourse to omniscient or omnipotent demons. They have also co-
gently argued that biological decision-making agents cannot have
recourse to such demons. The question is therefore not “Do such
agents use heuristics?”, but “Which heuristics do such agents use
(and when do they use them)?” Gigerenzer et al. acknowledge that
this question is important, but address it only in passing.
Gigerenzer et al.’s failure to specify conditions that might lead
to the use of specific fast and frugal heuristics compromises the
falsifiability of the fast and frugal approach. Difficult empirical re-
sults may be dismissed as resulting from the application of an as-
yet-unidentified fast and frugal heuristic or the combination of
items from the “adaptive toolbox” in a previously unidentified way.
Gigerenzer et al. criticise the heuristics-and-biases approach of
Tversky and Kahneman (1974) on much the same grounds. They
note, for example, that both base-rate neglect and conservatism
(two apparently opposing phenomena) can be “explained” by ap-
pealing to the appropriate heuristic or bias (because Tversky &
Kahneman provide insufficient detail on the conditions that are
held to evoke particular heuristics or biases). Gigerenzer et al.
contend, quite reasonably, that such a post-hoc appeal does not
amount to an adequate explanation of the behaviour. It is sug-
gested that the use by the ABC Research Group of precise com-
putational simulation techniques avoids this criticism. The com-
putational simulations are very welcome and add a dimension
often lacking in decision making research, but they do not, in their
disembodied form, address the question of which heuristic might
be applied when.
The issue of heuristic selection is not entirely ignored by
Gigerenzer et al. The suggestion is that heuristics are either se-
lected (or built from components within the adaptive toolbox) on
a task-by-task basis. The challenge therefore lies in specifying: (1)
the conditions under which different established heuristics are
employed; (2) the conditions that provoke the construction of
novel, task-specific heuristics; (3) the basic components available
in the adaptive toolbox; and (4) the mechanisms by which appro-
priate heuristics may be constructed from these components. Of
these, only the third is discussed at any length – the building
blocks are held to involve elements that direct search, stop search,
and decide based on the results of search – but that discussion of
these elements is insufficient to allow the fourth concern to be ad-
dressed.
At several points in the book heuristic selection is conceived of
as a meta-level decision-making task, suggesting that one might
use a (presumably fast and frugal) heuristic to decide which fast
and frugal heuristic to apply in a given situation. Two issues of mi-
nor concern are the possibility of an infinite regress (How do we
select the fast and frugal heuristic to decide which fast and frugal
heuristic to apply in the first place?) and the possibility that (as-
suming the infinite regress is avoided) the fast and frugal heuris-
tic doing the selection might not yield the optimal fast and frugal
heuristic for the original decision-making task.
Speculation as to the environmental and task cues that might
lead to selection of the fast and frugal heuristics discussed in the
book does not yield an obvious solution. For example, it is implied
that one-reason decision making is appropriate (and presumably
employed) for binary choice and that Categorisation By Elimina-
tion (CBE) is appropriate (and presumably employed) for multi-
ple choice. However, both heuristics might be applied in both sit-
uations. The question of which heuristic to apply when remains.
The importance of heuristic selection is compounded by the lack
of evidence presented in favour of the use by human decision mak-
ers of many of the heuristics discussed. For example, both Quick-
Est and CBE are presented solely as heuristics that can be shown
to be fast and frugal. No comment is made on the psychological re-
ality of either of these heuristics. This seems particularly odd when
robust psychological findings that would appear to be of relevance
(such as those addressed by Tversky and Kahneman’s [1974]
heuristics-and-biases approach) are ignored. How, for example,
might the fast and frugal approach address the phenomena that
Gigerenzer et al. use to demonstrate the difficulties present in the
heuristics-and-biases approach (base-rate neglect and conser-
vatism), or the confirmation bias often seen in diagnosis versions of
categorisation? The latter, in particular, appears to be in direct con-
flict with the only categorisation heuristic proposed (CBE).
Fast and frugal heuristics have great promise. Human decision
making cannot result from the application of algorithms with un-
bounded costs. Gigerenzer et al. have shown that fast and frugal
heuristics can yield good decisions. They have not shown that hu-
mans use such heuristics, and by not addressing the question of
which heuristics might be applied when, they have, like Tversky
and Kahneman, given us a theory of human decision making that
is unfalsifiable.
Commentary/Todd & Gigerenzer: Simple heuristics
746 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
Psychological research on heuristics
meets the law
Christoph Engel
Max-Planck-Projektgruppe, Recht der Gemeinschaftsguter, Poppelsdorfer
Allee 45, D 53115 Bonn, Germany.
engel@mpp-rdg.mpg.de
www.mpp-rdg.mpg.de
Abstract: Heuristics make decisions not only fast and frugally, but often
nearly as well as “full” rationality or even better. Using such heuristics
should therefore meet health care standards under liability law. But an in-
dependent court often has little chance to verify the necessary informa-
tion. And judgments based on heuristics might appear to have little legit-
imacy, given the widespread belief in formal rationality.
The mind is one of the last unknown territories of this world.
Gigerenzer, Todd, and the ABC Research Group (1999) make an
expedition into this territory and find it inhabited by strange and
unexpected beings. They have baptized them fast and frugal
heuristics, with given names like Take the Best. (1) What can a
lawyer learn from these insights into our internal geography? And
(2) is there anything he could give psychologists in return?
(1) The book starts with what reads like a legal case history. A
man is rushed to a hospital in the throes of a heart attack. The doc-
tor needs to decide quickly whether the victim should be treated
as a low-risk or a high-risk patient. Only in the latter case does he
receive expensive care. Assume the doctor has read the book and
applies the heuristic reported therein. The doctor tests systolic
blood pressure first. If it is below 91, the patient is immediately
treated as high risk. If not, the doctor checks the patient’s age. A
patient under 62.5 years is classified as low risk. For older patients
the doctor searches for a third cue, sinus tachycardia. If it is pres-
ent, the patient gets full and immediate treatment. If not, the pa-
tient is once and forever treated as low risk. Let this be our pa-
tient, and assume that he dies from heart disease on the next day.
His relatives sue the hospital for malpractice. They point to a host
of other diagnostic means that are state of the medical art. Does
the hospital nonetheless have a chance to win in court?
The answer depends on the standard of health care. It would be
of no use for the hospital to recall what the book reports on the
limitations of the individual mind. At least not insofar as these lim-
itations can be overcome by technology, other specialists, antici-
patory training or better organisation. Within this framework, time
pressure might count. And if, in that legal order, cost-benefit analy-
sis may be applied to questions of life and death, decision costs
might be an argument. The hospital would be in a stronger posi-
tion if the doctor had to choose among several patients who looked
similarly ill at the outset. But the attorney of the hospital would
focus on another argument: other hospitals that tested all the sci-
entifically available cues made on average less accurate choices.
Is the law hindered from using this knowledge? There are two
major obstacles. Going to court is a form of third party settlement.
This third party needs reliable information on the facts of the case.
In cases of alleged malpractice, this information is not easy to col-
lect, and even more difficult to prove. Information economics
speaks about nonverifiable information. Standard court practice
overcomes the problem by formal rules of consent, and by relying
on state of the art treatment. If the doctor proved both, he would
normally not be liable. This strategy is difficult to transfer to
heuristics, for they perform well precisely because they are not
general, but issue-specific or even situation specific. They exploit
local knowledge. Local knowledge is often unverifiable. And the
general reliability of a search and decision tool is hard to prove, if
its very essence is to be “ecologically rational,” not general. One
way out might be an ex ante contract that explicitly empowers the
doctor to use those heuristics that are approved by a formalized
doctors’ community.
The second obstacle stems from the fact that the courts are part
of government. What they do must appear legitimate. More tra-
ditional forms of rationality easily produce what political scientists
call “output legitimacy.” The term refers to a form of legitimacy
that does not rely on acts of empowerment by the electorate, but
on the fact that government ostensibly improves welfare, which is
why court decisions must have reasons. That heuristics may do
better than formal rationality is a highly counter-intuitive finding,
and it is provocative in that it destroys the illusion of full rational-
ity. If the courts accept decisions based on heuristics, they have to
confront the parties with the fact that they live in an insecure
world. Put more precisely: heuristics will only have a fair chance
in court if people learn that they can trust heuristics at least as
much as they now believe they can trust formal rationality.
(2) Heuristics are not the sole form of reasoning to overcome
the limitations of formal rationality. Heuristics should rather be
tested against the other forms of applied rationality, not against
utopian scientific models. Some of the legal experiences with ap-
plied rationality may be worth considering for psychologists. Ap-
plied rationality is not for Robinson Crusoe, but for a world pre-
viously shaped by institutions, be they formal legal rules, social
norms, personal ties, cultural and historical embeddedness, or
common beliefs. The stronger institutions narrow the situation
down, the longer the illusion of formal rationality can be main-
tained at relatively low cost.
The way a lawyer is trained to find his decisions is not formal
rationality, but also not heuristics. One might call it holistic deci-
sion making. It relies strongly on common sense and judgment
(Urteilsvermoegen). The lawyer starts by relatively formal and
general rules. But if his reading of the facts before him makes him
doubt the wisdom of the rule, a rich toolbox allows him to take
tailor-made steps aside. The further he leaves the general rule be-
hind, the stronger his reasons must be. And the single courtroom
is part of the legal system. The single unusual case can therefore
set a learning process for the legal system into motion.
The picture becomes even richer if we look at the social func-
tion of legal rules. In the great majority of cases, legal rules are
simply obeyed. Often the parties do not even know that there is a
formal rule. The rule is mirrored in social norms or simple rou-
tines. But the formal legal system is always present in the back-
ground. Each party has at any time the right to trigger its applica-
tion. One can interpret this as different levels of rationalisation,
depending on the controversial character of the case, or the re-
sources a party wants to invest into its settlement.
How good are fast and frugal inference
heuristics in case of limited knowledge?
Edgar Erdfelder and Martin Brandt
Department of Psychology, University of Bonn, D-53117 Bonn, Germany.
{erdfelder; brandt}@uni-bonn.de www.psychologie.uni-bonn.de/~erdfel
–
e
Abstract: Gigerenzer and his collaborators have shown that the Take the
Best heuristic (TTB) approximates optimal decision behavior for many
inference problems. We studied the effect of incomplete cue knowledge
on the quality of this approximation. Bayesian algorithms clearly outper-
formed TTB in case of partial cue knowledge, especially when the validity
of the recognition cue is assumed to be low.
Gigerenzer et al.’s Simple heuristics that make us smart provides
a powerful demonstration of Simon’s (1956a) satisficing principle:
Human inference mechanisms can be both simple and accurate.
A class of reasoning heuristics characterized by speed and frugal-
ity is shown to perform very efficiently in a variety of areas and
across a wide range of inference problems. The most prominent
example is the Take the Best (TTB) rule of decision making under
uncertainty, discussed in more than half of the chapters of the
book. TTB uses the principle of one-reason decision making in an
apparently simplistic step-by-step manner. In fact, had we not
read the pioneering article by Gigerenzer and Goldstein (1996a)
prior to thinking about the effectiveness of TTB, we would most
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 747
likely have sided with those believing that TTB is easily outper-
formed by alternative inference rules.
What struck us even more than the good performance of TTB
compared to more costly decision heuristics are the results of
Martignon and Laskey’s (Ch. 8) comparisons to Bayesian algo-
rithms. The computationally intensive “profile memorization
method” (PMM) defines the optimum that can be achieved
for cue-based inferences under uncertainty. Let a and b denote
any two of n objects. For each object, m binary cue values C
1
,
C
2
, . . . , C
m
are given, and the task is to predict which of the
two objects scores higher on a criterion variable X. Then PMM
predicts X
a
. X
b
if
Thus, if there are d # n different cue profiles, then d?(d 2 1)/2
conditional probabilities need to be computed (or estimated from
a sample). In contrast, TTB does not even need the m cue validi-
ties to determine the sequence of steps in the decision tree; their
rank order is sufficient.
A Bayesian algorithm more similar to TTB in terms of frugality
is the “Naive Bayes” (NB) rule. NB assumes conditional indepen-
dence of cue values given the criterion values. If this assumption
holds, then the PMM decision rule reduces to the NB rule: Pre-
dict X
a
. X
b
if the product
If the independence assumption is violated then, in general, L
NB
(a, b) differs from L
PMM
(a, b) and NB is just an approximation to
PMM that has the advantage of requiring less parameters for the
prediction task.
Despite its frugality, TTB comes close to the PMM benchmarks
in almost all inference tasks summarized in Table 8-1 (p. 182), and
it performs as well as and sometimes even better than the NB rule.
For example, for the city population task previously analyzed by
Gigerenzer and Goldstein (1996a), the percentages of correct de-
cisions for TTB, NB, and PMM are 74.2%, 74.0%, and 80.1%, re-
spectively.
We were interested in the boundary conditions that must
be met to guarantee that TTB approximates optimal decision
behavior so closely. This is a topic in some chapters of the book,
and the message of the authors is clear: It is certainly possible
to conceive inference problems in which TTB compares unfa-
vorably with PMM, NB, and alternative decision heuristics. For
example, TTB runs into difficulties if a large number of cues (m)
is used to rank a small number of objects (n) and if the cue va-
lidities are approximately equal (see Chs. 5 and 6). However, in-
ference problems characterized by these attributes appear to be
“artificial” in the sense that they do not conform to the struc-
ture of inference problems that are typical of real-world set-
tings.
Is it permissible to argue that the more an inference problem
resembles real-world problems, the more TTB approximates
optimal decision behavior? To answer this question, we ran an-
other competition between TTB and Bayesian algorithms, this
time considering the more realistic case of limited knowledge.
A simple way of incorporating incomplete knowledge into
Bayesian algorithms is to compute expected probabilities when-
ever some of the cue values are missing. For example, if we need
to compute P(X
a
. X
b
u(C
1
(a) 5 ?, C
2
(a) 5 0), (C
1
(b) 5 0, C
2
(b)
5 1), where “1” means a cue is present, “0” it is absent, and “?”
cue value is unknown, then we use the conditional expected
value
P(X
a
. X
b
u(C
1
(a) 5 1, C
2
(a) 5 0), (C
1
(b) 5 0, C
2
(b) 5 1))
?P(C
1
(a) 5 1u(C
2
(a) 5 0), (C
1
(b) 5 0, C
2
(b) 5 1))
1 P(X
a
. X
b
u(C
1
(a) 5 0, C
2
(a) 5 0), (C
1
(b) 5 0, C
2
(b) 5 1))
(3)
?P(C
1
(a) 5 0u(C
2
(a) 5 0), (C
1
(b) 5 0, C
2
(b) 5 1)).
We employed this principle in a computer simulation of the city
population inference task. In each simulation run, 90, 80, 50, and
25% of the cue values were randomly deleted from the profiles.
Table 1 summarizes the results for the case that all n 5 83 Ger-
man cities are recognized. As expected, the TTB scores match the
results reported by Gigerenzer and Goldstein (1996a, p. 656).
Somewhat unexpectedly, however, TTB performs best in the un-
realistic case of perfect cue knowledge. If cue knowledge is not
perfect, NB outperforms TTB quite clearly. Similarly, the relative
performance of TTB with respect to PMM is slightly worse if 75%
rather than 100% of the cue values are known.
Figure 1 illustrates how these results generalize to more realis-
tic scenarios where not all of the cities are recognized and only
50% of the cue values are known. Obviously, the disadvantage of
TTB with respect to the Bayesian algorithms depends heavily on
the validity of the recognition cue which is always evaluated first
in TTB. If the recognition cue validity is .80, then TTB is almost
as efficient as Bayesian procedures (Fig. 1a). However, if the
recognition cue is not correlated with the criterion – a realistic as-
sumption for several inference problems discussed in the
book – then TTB performs worse the smaller the number of cities
recognized (Fig. 1b).
We conclude that TTB has no built-in mechanism that makes it
suitable for all types of real-world inference problems. Rather,
TTB and other fast and frugal heuristics need to be comple-
mented by meta-mechanisms that determine the choice among
the heuristics and their variants. Gigerenzer et al. (1999) hold a
similar position (pp. 364–65). We are thus looking forward to fu-
ture research that helps surmount the remaining problems.
ACKNOWLEDGMENT
The preparation of this work was supported by grants ER 224/1-1 and ER
224/1-2 of the Deutsche Forschungsgemeinschaft. Correspondence should
be addressed to Edgar Erdfelder, Psychologisches Institut, Universität Bonn,
Römerstraße 164, D-53117 Bonn, Germany. erdfelder@uni-bonn.de.
Commentary/Todd & Gigerenzer: Simple heuristics
748 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
(2)
Lab
PX X C a C b
PX X C a C b
abj j
abj j
j
m
NB
(,) :
|(),()
|(),()
.=
>
()
≤
()
>
=
∏
1
1
Table 1 (Erdfelder & Brandt). Percent correct inferences
of the Take-the-Best heuristic and two Bayesian decision
algorithms (PMM Bayes, Naive Bayes) for the city population
inference task given different degrees of cue knowledge
% cues known Take the Best Naive Bayes PMM Bayes
0% 50.0% 50.0% 50.0%
10% 55.4% 58.7% 58.9%
20% 59.4% 63.1% 63.7%
50% 66.8% 69.5% 71.9%
75% 70.9% 72.2% 76.6%
100% 74.2% 74.0% 80.1%
Lab
PMM
(,) :=
PX X C a C a C a C b C b C b
PX X C a C a C a C b C b C b
ab m m
ab m m
| ( ), ( ),..., ( ) , ( ), ( ),..., ( )
| ( ), ( ),..., ( ) , ( ), ( ),..., ( )
.
>
()()
()
≤
()()
()
>
12 12
12 12
1
(1)
Simple heuristics: From one infinite
regress to another?
Aidan Feeney
Department of Psychology, University of Durham, Science Laboratories,
Durham DH1 3LE, England.
aidan.feeney@durham.ac.uk
http://psynts.dur.ac.uk/staff/feeney.html
Abstract: Gigerenzer, Todd, and the ABC Research Group argue that op-
timisation under constraints leads to an infinite regress due to decisions
about how much information to consider when deciding. In certain cases,
however, their fast and frugal heuristics lead instead to an endless series
of decisions about how best to decide.
Gigerenzer, Todd, and the ABC Research Group’s alternative ap-
proach to decision making is based upon a dissatisfaction with the
notions of unbounded rationality and rationality as optimisation
under constraints. They claim that whilst the notion of unbounded
rationality is not informed by psychological considerations, opti-
misation under constraints seeks to respect the limitations of in-
formation processors, but in a manner which leads to an infinite
regress. Specifically, when an information processor is making a
decision, the optimisation under constraints approach requires
him/her to further decide whether the benefits of considering
more information relevant to that decision are outweighed by the
costs of so doing. As such a cost/benefit analysis must be per-
formed every time a decision is made, the decision making process
becomes endless.
Gigerenzer et al.’s alternative is to specify a range of fast and
frugal heuristics which, they claim, underlie decision making.
Their stated goals (Gigerenzer et al. 1999, p. 362) are as follows:
1. To see how good fast and frugal heuristics are when com-
pared to decision mechanisms adhering to traditional notions of
rationality.
2. To investigate the conditions under which fast and frugal
heuristics work in the real environment.
3. To demonstrate that people and animals use these fast and
frugal heuristics.
As the authors admit (p. 362), they are undoubtedly much
closer to achieving their first two aims than they are to achieving
the third. Before their third objective can be reached however,
Gigerenzer et al. must attempt to answer a further question: How
do decision makers decide how to decide?
Applying the fast and frugal analysis seems least objection-
able in cases where the algorithm used to make a decision is pre-
determined (by evolution or by a programmer, etc.). In principle,
fast and frugal heuristics seem nonproblematic for phenomena
such as a parent bird’s decisions about provisioning or some of the
relatively automatic processes involved in, for example, memory
retrieval (all that remains is a demonstration that animals and hu-
mans do employ them). Their application is nonproblematic in
these cases because, given certain environmental conditions, there
is likely to be only one way in which, for example, an individual
bird will feed its young. The relevant heuristic is pre-programmed
so, as there exists only one decision method for that decision un-
der those conditions, there is no confusion about which method
to apply.
Now consider the example used by Rieskamp and Hoffrage
(Ch. 7, p. 141). They ask the reader to consider Mr. K., who is try-
ing to figure out how his friends (Mr. Speed and Mr. Slow) make
investment decisions. Here decision methods requiring more pro-
cessing resources than do the fastest and most frugal of the fast
and frugal heuristics are treated as alternative strategies that peo-
ple are more likely to use in the absence of time pressure. This
sounds suspiciously like the kind of situation that could, poten-
tially, lead to an infinite regress. The decision maker is free to de-
cide between a range of decision-making strategies, leaving him/
her to make decisions about how to make decisions ad infinitum.
Rieskamp and Hoffrage’s only attempt to explain why the the-
ory does not predict an infinite regress is the following: “Based on
an individual’s prior experience of decision making, a particular
situation could prompt her or him to use a particular decision
strategy” (p. 147). This explanation seems inadequate. For one
thing, part of our advantage over other species is our ability to
make decisions in situations for which prior experience has not
prepared us. For example, Wason’s abstract indicative selection
has recently been characterised as a decision-making task rather
than as a problem best thought of as requiring deductive inference
(Evans & Over 1996; Oaksford & Chater 1994). It is certainly a
task requiring decisions (which card or cards should be selected
in order to test the experimental rule) for which the naïve partic-
ipant’s prior experience is unlikely to have prepared him. Given
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 749
Figure 1 (Erdfelder & Brandt). Percent correct inferences of the Take the Best heuristic and two Bayesian decision algorithms (PMM
Bayes, Naive Bayes) for the city population inference task with 50% cue knowledge. Performance is plotted as a function of the number
of cities recognized. Figure 1a (left) refers to a recognition cue validity of .80, Figure 1b (right) to a recognition cue validity of .50.
such a lack of preparedness one might expect participants, when
selecting cards, to rely wholly on the inappropriate application of
heuristics successful in superficially similar domains. Indeed,
there is substantial evidence that this may be the case (see Evans
et al. 1993 for a review). However, more recent evidence (Feeney
& Handley, in press) suggests that, at least under certain experi-
mental conditions, participants will reason deductively on the ab-
stract selection task. It is not clear how prior experience might ex-
plain such differential use of heuristic and deductive strategies on
Wason’s task.
Rieskamp and Hoffrage contrast their “prior experience” solu-
tion with the view that limited time and limited knowledge con-
straints are supplementary criteria evaluated in the course of mak-
ing a decision. The implication seems to be that evaluating these
supplementary criteria whilst making a decision leads to an infi-
nite regress, whereas an appeal to prior experience does not. As
we have seen, prior experience cannot be relied upon to prepare
people for certain situations, such as attempting Wason’s selection
task, where decisions are called for. Yet it has been shown that un-
der different experimental conditions, people may use different
strategies to make these decisions. Of course, this is not to claim
that Rieskamp and Hoffrage are incorrect in claiming that very of-
ten, prior experience will guide the strategy we select to make a
decision.
Unfortunately, Gigerenzer et al.’s analysis may lead to an infi-
nite regress when a decision maker faces an unfamiliar decision
situation and is free to adopt one of a number of decision strate-
gies or decision heuristics. Given that Gigerenzer et al.’s central
complaint about the optimisation under constraints view of ratio-
nality is that it leads to an infinite regress, it is ironic that unless
their own account can be supplemented with metacognitive prin-
ciples it must be adjudged merely to have replaced one infinite
regress with another.
ACKNOWLEDGMENT
The author would like to thank David Over for helpful comments on this
commentary.
Against an uncritical sense of adaptiveness
Steve Fuller
Department of Sociology, University of Warwick, Coventry, CV4 7AL, United
Kingdom.
s.w.fuller@warwick.ac.uk
Abstract: The “adaptive toolbox” model of the mind is much too uncriti-
cal, even as a model of bounded rationality. There is no place for a “meta-
rationality” that questions the shape of the decision-making environments
themselves. Thus, using the ABC Group’s “fast and frugal heuristics,” one
could justify all sorts of conformist behavior as rational. Telling in this re-
gard is their appeal to the philosophical distinction between coherence
and correspondence theories of truth.
Despite its popular evolutionary resonances, the word “adaptive”
normally makes rationality theorists reach for their wallets, since
adaptive conceptions of rationality usually deliver much less than
they promise. Here I do not mean that they lack the rigor, preci-
sion, and systematicity of the standard conceptions. This is already
granted by Gigerenzer, Todd, and the ABC Research Group (1999)
as the price the theorist must pay for a model of rationality that ex-
plains how subjects achieve their goals under the time and resource
constraints of realistic decision-making environments. I am also
happy to grant them this point (cf. Fuller 1985). My concern is that
the “adaptive toolbox” lacks any provision for meta-rationality, or
metacognition more generally, other than as an iterated version of
the first-order mental processes that the ABC Group have identi-
fied.
Symptomatic of the problem, as well as a sense of the stakes, is
the discussion of the trade-off between what Gigerenzer et al. call
“generality” and “specificity” of a particular heuristic’s adaptive-
ness (1999, p. 18). Always writing with an eye toward the history
of philosophy, they associate these two dimensions with, respec-
tively, the coherence and correspondence theories of truth. Al-
though such connections give their model a richness often lacking
in contemporary psychology, they also invite unintended queries.
It is clear what the ABC Group mean by the distinction. To a
first approximation, their “fast and frugal” heuristics “correspond”
to the particular environments that a subject regularly encounters.
But these environments cannot be so numerous and diverse that
they create computational problems for the subjects; otherwise
their adaptiveness would be undermined. In this context, “coher-
ence” refers to the meta-level ability to economize over environ-
ments, so that some heuristics are applied in several environments
whose first-order differences do not matter at a more abstract
level of analysis.
Yet philosophers have come to recognize that correspondence
and coherence are not theories of truth in the same sense.
Whereas correspondence is meant to provide a definition of truth,
coherence offers a criterion of truth. The distinction is not trivial
in the present context. Part of what philosophers have tried to cap-
ture by this division of labor is that a match between word (or
thought) and deed (or fact) is not sufficient as a mark of truth,
since people may respond in a manner that is appropriate to their
experience, but their experience may provide only limited access
to a larger reality. A vivid case in point is Eichmann, the Nazi dis-
patcher who attempted to absolve himself of guilt for sending peo-
ple to concentration camps by claiming he was simply doing the
best he could to get the trains to their destinations. No doubt he
operated with fast and frugal heuristics, but presumably one
would say something was missing at the meta-level.
The point of regarding coherence as primarily a criterion, and
not a definition, of truth is that it forces people to consider
whether they have adopted the right standpoint from which to
make a decision. This Eichmann did not do. In terms the ABC
Group might understand: Have subjects been allowed to alter
their decision-making environments in ways that would give them
a more comprehensive sense of the issues over which they must
pronounce? After all, a model of bounded rationality worth its salt
must account for the fact that any decision taken has conse-
quences, not only for the task at hand but also for a variety of other
environments. One’s rationality, then, should be judged, at least in
part, by the ability to anticipate these environments in the deci-
sion taken.
At a more conceptual level, it is clear that the ABC Group re-
gard validation rather differently from the standard philosophical
models to which they make rhetorical appeal. For philosophers,
correspondence to reality is the ultimate goal of any cognitive ac-
tivity, but coherence with a wide range of experience provides in-
termittent short-term checks on the pursuit of this goal. By re-
garding coherence-correspondence in such means-ends terms,
philosophers aim to delay the kind of locally adaptive responses
that allowed Ptolemaic astronomy to flourish without serious
questioning for 1,500 years. Philosophers assume that if a suffi-
ciently broad range of decision-making environments are consid-
ered together, coherence will not be immediately forthcoming;
rather, a reorientation to reality will be needed to accord the di-
vergent experiences associated with these environments the epis-
temic value they deserve.
All of this appears alien to the ABC Group’s approach. If any-
thing, they seem to regard coherence as simply facilitating corre-
spondence to environments that subjects treat as given. Where is
the space for deliberation over alternative goals against which one
must trade off in the decision-making environments in which sub-
jects find themselves? Where is the space for subjects to resist the
stereotyped decision-making environments that have often led to
the victimization of minority groups and, more generally, to an il-
lusory sense that repeated media exposure about a kind of situa-
tion places one in an informed state about it? It is a credit to his
honesty (if nothing else), that Alfred Schutz (1964) bit the bullet
and argued that people should discount media exposure in favor
Commentary/Todd & Gigerenzer: Simple heuristics
750 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
of personal cumulative experience. But this also led him to distrust
public opinion polls and mass democratic votes as reliable indica-
tors of normatively acceptable social policies.
For all their talk of “social” and “ecological” rationality, the ABC
Group are conspicuously silent on the normative implications of
their research. It would be easy to epitomize their findings as im-
plying that people with a conventional awareness of the social en-
vironments in which they act should trust their gut feelings when
making decisions. The concept of “adaptive preference forma-
tion,” popularized by Leon Festinger (1957), seems to ring no
alarms for them. Consequently, they do not consider how prior
successes in one’s own (or others’) decision-making environments
might reinforce certain responses that, in a more reflective setting,
might come to be doubted and perhaps even reversed. Certainly,
their chapter on the latently positive virtues of “hindsight bias” do
not inspire confidence (Gigerenzer et al. 1999, Ch. 9).
Is less knowledge better than more?
Alvin I. Goldman
Department of Philosophy, University of Arizona, Tucson, AZ 85721-0027.
goldman@u.arizona.edu w3.arizona.edu/~phil/faculty/goldman.html
Abstract: When a distinction is drawn between “total” knowledge and
“problem-specific” knowledge, it is seen that successful users of the recog-
nition heuristic have more problem-specific knowledge than people un-
able to exploit this heuristic. So it is not ignorance that makes them smart,
but knowledge.
Gigerenzer et al. (1999) present a fascinating case for the accuracy
of fast and frugal heuristics. In Chapter 2, “The recognition heuris-
tic: How ignorance makes us smart,” Goldstein and Gigerenzer
contend that (in certain cases) the recognition heuristic (RH) en-
ables comparatively ignorant people to get correct answers to
questions more often than knowledgeable people. This finding,
they claim, is paradoxical: “The recognition heuristic can thus lead
to a paradoxical situation where those who know more exhibit
lower inferential accuracy than those who know less” (Gigerenzer
et al. 1999: pp. 45–46). Does RH really imply that comparatively
ignorant people fare better than comparatively knowledgeable
ones in certain cases? Yes and no; it depends on how one concep-
tualizes comparative knowledgeability.
In a Goldstein-Gigerenzer thought experiment (later substan-
tiated by experimental work), the Scottish MacAlister brothers
take a quiz composed of two-alternative questions about the pop-
ulation sizes of the 50 largest German cities. The youngest brother
recognizes none of these cities, the middle brother recognizes 25
of them, and the eldest brother recognizes all 50. Because the
middle brother recognizes some cities but not others, he can
sometimes apply RH, where RH consists in the following rule: “If
one of two objects is recognized and the other is not, then infer
that the recognized object has the higher value” (p. 41). In the pres-
ent case the “higher value” is the larger population size. So when
the middle brother is presented with a city that he recognizes and
a city that he does not, he can apply RH and infer that the recog-
nized city has a larger population than the unrecognized one. By
assumption, he will be right on 80% of these choices. The older
MacAlister brother has no opportunity to use RH, because he rec-
ognizes all 50 of the cities. Goldstein and Gigerenzer assume that
when a brother recognizes both cities in a pair, there is a 60%
chance of making the correct choice. Thus, it turns out that the
middle brother scores better on the quiz than the older brother,
despite the fact that, as Goldstein and Gigerenzer put it, the older
brother knows more.
Is this a good way to describe the comparative knowledge states
of the older and middle brothers? Let us distinguish two bodies
of knowledge: total knowledge and problem-specific knowledge.
Plausibly, the older brother has more total knowledge about German
cities than the middle brother; but does he have more problem-
specific knowledge? On the contrary, I suggest, the middle brother
has more problem-specific knowledge; so there is nothing “para-
doxical” about the fact that the middle brother performs better on
the quiz. It is not unambiguously true of the middle brother, as
Goldstein and Gigerenzer claim, that ignorance “makes him smart.”
Yes, he is comparatively ignorant in total knowledge of German
cities, but he is not comparatively ignorant on the crucial dimen-
sion of problem-specific knowledge.
Consider an analogous case. Mr. Savvy knows a lot about poli-
tics. Concerning the current Senatorial campaign, he knows the
voting records of each candidate, he knows who has contributed
to their campaigns, and so forth. Mr. Kinny has much less knowl-
edge on such matters. So Savvy certainly has more total political
knowledge than Kinny. It does not follow, however, that Savvy has
more problem-specific knowledge on every question concerning
the Senatorial race. Even such a crucial question as “Which can-
didate would do a better job vis-à-vis your interests?” might be
one on which Kinny has superior problem-specific knowledge
than Savvy. Suppose, as Kinny’s name suggests, that he has a
well-informed cousin who always knows which of several candi-
dates is best suited to his own interests, and the cousin also has the
same interests as Kinny himself. So as long as Kinny knows which
candidate is favored by his cousin, he will select the correct an-
swer to the question, “Which candidate would do a better job vis-
à-vis my (Kinny’s) interests?” (In Goldman 1999, Ch. 10, I call this
sort of question the “core voter question.”) In recent years politi-
cal scientists have pointed out that there are shortcuts that voters
can use to make crucial political choices, even when their general
political knowledge is thin. Kinny’s holding the (true) opinion that
his cousin knows who is best is such a shortcut. Indeed, it is an in-
valuable piece of knowledge for the task at hand, one that Savvy
may well lack.
Return now to the German cities problem. When the middle
brother gets a test item in which he recognizes exactly one of the
two named cities, he acquires the information that this city is more
recognizable to him than the other. As it happens, this is an ex-
tremely reliable or diagnostic cue of the relative population sizes
of the cities. If, as Goldstein and Gigerenzer assume, he also be-
lieves that a recognized city has a larger population than an un-
recognized one, then these two items of belief constitute very sub-
stantial problem-specific knowledge. The older brother has no
comparable amount of problem-specific knowledge. From the
point of view of problem-specific knowledge, then, the brothers
are misdescribed as a case in which ignorance makes the middle
brother smart. What he knows makes him smart, not what he is ig-
norant of. More precisely, his ignorance of certain things – the
names of certain German cities – creates a highly diagnostic fact
that he knows, namely, that one city is more recognizable (for him)
than the other. No comparably useful fact is known to his older
brother. So although the older brother has more total knowledge,
he has less problem-specific knowledge.
I do not take issue with any substantive claims or findings of
Goldstein and Gigerenzer, only with the spin they put on their
findings. RH can be exploited only when a person knows the true
direction of correlation between recognition and the criterion. In
the cities case, he must know (truly believe) that recognition cor-
relates with greater population. When this kind of knowledge is
lacking, RH cannot be exploited. Suppose he is asked which of two
German cities has greater average annual rainfall. Even if there is
a (positive or negative) correlation between recognition and rain-
fall, he won’t be able to exploit this correlation if he lacks an ac-
curate belief about it. Goldstein and Gigerenzer do not neglect
this issue. They cast interesting light on the ways someone can es-
timate the correlation between recognition and the criterion
(1999: pp. 41–43). But they fail to emphasize that only with a (tol-
erably) accurate estimate of this sort will applications of RH suc-
ceed. For this important reason, knowledge rather than ignorance
is responsible for inferential accuracy. There is no need to rush
away from the Goldstein-Gigerenzer chapter to advise our chil-
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 751
dren or our students that the new way to get smart is to stop read-
ing books or drop out of school. Knowledge of relevant premises,
not ignorance, is still the best way to acquire further knowledge
through inference.
Heuristics in technoscientific thinking
Michael E. Gorman
School of Engineering and Applied Science, University of Virginia,
Charlottesville, VA 22903-2442
meg3c@virginia.edu
repo-nt.tcc.virginia.edu
Abstract: This review of Gigerenzer, Todd, and the ABC Research
Group’s Simple heuristics that make us smart focuses on the role of heuris-
tics in discovery, invention, and hypothesis-testing and concludes with a
comment on the role of heuristics in population growth.
In this commentary, I will explore the role of heuristics in techno-
scientific thinking, suggesting future research.
Scientific discovery.
Herbert Simon and a group of colleagues
developed computational simulations of scientific discovery that
relied on a hierarchy of heuristics, from very general or weak ones
to domain-specific ones. The simplest of the discovery programs,
BACON.1, simulated the discovery of Kepler’s third law by look-
ing for relationships between two columns of data, one corre-
sponding to a planet’s distance from the sun, the other its orbital
period (Bradshaw 1983). The program’s three heuristics:
1. If two terms increase together, compute ratio.
2. If one term increases as another decreases, compute prod-
uct.
3. If one term is a constant, stop.
Given the data nicely arranged in columns, these heuristics will
derive Kepler’s third law. Simon and his colleagues termed this an
instance of data-driven discovery. Gigerenzer et al. (1999) argue
that heuristics save human beings from having to have complex
representations of problem domains. All of Kepler’s struggles to
find a way to represent the planetary orbits might be unneces-
sary – all he had to do was apply a few simple heuristics.
But the importance of problem representation is cueing the
right heuristics. No one but Kepler would have looked for this
kind of relationship. He had earlier developed a mental model of
the solar system in which the five Pythagorean perfect solids fit
into the orbital spaces between the six planets. This pattern did
not fit the data Kepler obtained from Tycho Brahe, but Kepler
knew there had to be a fundamental geometrical harmony that
linked the period and revolution of the planets around the sun. A
heuristics-based approach can help us understand how Kepler
might have discovered the pattern, but we also need to understand
how he represented the problem in a way that made the heuris-
tics useful.
Kulkarni and Simon (1998) did a computational simulation of
the discovery of the Ornithine cycle, involving multiple levels and
types of heuristics. To establish ecological validity, they used the
fine-grained analysis of the historian Larry Holmes. Unlike Kep-
ler, Krebs did not have to come up with a unique problem repre-
sentation; the problem of urea synthesis was a key reverse-salient
in chemistry at the time.
Gigerenzer et al. need to pay more attention to the way in which
problems and solutions come from other people. An alternative to
recognizing a solution is recognizing who is most likely to know
the solution. Could “Take the Best” apply to a heuristic search for
expertise?
For Krebs, the key was a special tissue-slicing technique he
learned from his mentor, Otto Warburg. This hands-on skill was
Krebs’s “secret weapon.” These hands-on skills are at least partly
tacit, because they have to be learned through careful appren-
ticeship and practice, not simply through verbal explanation. To
what extent are heuristics tacit as well?
In his experimental notebook on February 21, 1876, Alexander
Graham Bell announced that he was going to follow the analogy
of nature and build a telephone based on the human ear. “Follow
the analogy of nature” is a common heuristic used by inventors
(Gorman 1998), but using it depends on having a good mental
model of the source of the analogy. Bell had built devices that gave
him hands-on tacit knowledge of the workings of the human ear,
so his use of the nature heuristic was his “secret weapon.”
To what extent are heuristics tacit? Is there value in making
them explicit, as Bell tried to do?
Confirmation bias.
In Chapter 11, p. 235, Berretty, Todd, and
Martignon discuss the categorization by elimination (CBE)
heuristic. In 1960, Peter Wason discussed how participants failed
to eliminate hypotheses on the 2–4–6 task. Wason’s finding
sparked a literature on confirmation bias (Gorman 1992), the gist
of which is that people do not ordinarily eliminate hypotheses
when confronted with negative evidence. [See Stanovich & West:
“Individual Differences in Reasoning” BBS 23(5) 2000.]
Klayman and Ha (1987) tried to separate positive and negative
test heuristics from confirmation. In the case of Bell, for example,
most of his experiments were directed towards obtaining a posi-
tive signal, but failure to obtain the hoped-for result usually meant
a problem with the experimental apparatus, not a disconfirmation
(Gorman 1995). Falsification is useful in a late stage of problem-
solving when the possibility of error is low. Would the same be true
for CBE on a complex, multi-dimensional classification where ev-
idence had to be gathered over time? Could CBE be used to di-
rect the search for additional evidence?
Population growth.
In Chapter 14, p. 309, Davis and Todd dis-
cuss heuristics for parental investment. In humans, the heuristic
with the greatest global consequences may be the one that deter-
mines how many children to have. The greater the risk of losing a
child, the more children humans want. Instead of investing heav-
ily in one child, this is a “spread the risk” heuristic; in large parts
of the world, people feel they have little control over disease, war,
famine, and other factors that increase the risk of child mortality.
In more affluent societies with low child mortality and educated,
empowered women, parents invest in fewer offspring (Sen 1994).
The role of heuristics in population growth is a promising area for
future research. [See also Vining: “Social versus Reproductive
Success” BBS 9(1) 1986.”]
Evolution, learning, games,
and simple heuristics
Peter Hammerstein
Innovationskolleg Theoretische Biologie, Humboldt-Universität zu Berlin,
12247 Berlin, Germany
p.hammerstein@itb.biologie.hu-berlin.de
Abstract: Humans are incapable of acting as utility maximisers. In con-
trast, the evolutionary process had considerable time and computational
power to select optimal heuristics from a set of alternatives. To view evo-
lution as the optimising agent has revolutionised game theory. Gigerenzer
and his co-workers can help us understand the circumstances under which
evolution and learning achieve optimisation and Nash equilibria.
Gigerenzer and his co-workers present an impressive study
(Gigerenzer et al. 1999) of how human decision making is guided
by fast and simple procedures. They also theorise about the adap-
tive nature of these procedures and demonstrate that simple
heuristics can even be superior to statistical methods, such as mul-
tiple regression analysis, if only one makes appropriate assump-
tions about the environments in which decisions are made. This
seems to indicate that in the environments under consideration
the “heuristic that makes us smart” is better than many alterna-
tives. The authors thus implicitly invoke optimality considerations,
at least for a constrained set of alternative procedures. At first sight
Commentary/Todd & Gigerenzer: Simple heuristics
752 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
this may appear inconsistent with some of their statements in
which they suggest that we should dismiss optimality considera-
tions in the study of decision making. My comment aims at show-
ing how this inconsistency can be resolved, and why optimality still
has a place in decision theory even if one assumes like the authors
that humans do not possess sufficient mental tools to actually solve
optimisation problems in their daily lives.
I agree with them that considering humans as utility maximis-
ers is like entering the world of science fiction. We know too well
that most humans cannot deal properly with probabilities and that
the task of computing conditional expectations is too difficult even
for professional mathematicians when they have to decide quickly.
Businessmen are perhaps making more money than mathemati-
cians but again this is not due to their talents in optimisation. For
example, in many auctions it can be observed that the bidders who
actually get the object that is put up for auction are those who
overestimate the value of this object and pay more for it than it is
worth to them. This phenomenon is known as the “winner’s curse.”
Rational decision makers would anticipate the winner’s curse but
experiments dealing with this phenomenon show that humans
easily step into the pitfall set up by the auctioneer.
In contrast, suppose that the process of biological evolution
would select bidding strategies for auctions that take place gener-
ation after generation in a population in which strategies are ge-
netically inherited. The maladaptive winner’s curse phenomenon
would then disappear! In other words, evolution and not the hu-
man mind has an optimising tendency. Our fast and frugal heuris-
tics are probably better than many alternative procedures because
they have been subject to Darwinian evolution.
The history of game theory can be used to further illustrate this
point. John Nash invented the central game-theoretic solution
concept which is now named after him. In a Nash equilibrium,
every player uses a strategy that maximises this player’s payoff,
given that all the others use their equilibrium strategies. A fast but
not frugal way of justifying this concept is to make the assumption
that “every player knows that every player knows that everybody
in the game is rational.” Of course, this is an absurd assumption.
Why then has it been used for decades? A cynical answer to this
question would be that this assumption created an ideal “play-
ground” and many positions for mathematicians, enabling them to
do work of apparently great importance without ever having to
bother much about empirical findings. Another answer would be
that people in the field did not really trust rationality reasoning
and had vague ideas about alternative foundations of the Nash
equilibrium in mind.
Modern evolutionary game theory demonstrates nicely that
such alternative foundations are possible as long as one invokes
evolution or learning as those processes that actually make the
choice of strategy. The first major step in this direction was made
by Maynard Smith and Price and in the biological literature fol-
lowing their work. More recently, economists, such as Weibull,
have also adopted evolutionary game theory. Even Nash himself
had interpretations along the lines of evolutionary game theory in
mind. In his Ph.D. thesis he already introduced the “mass action
interpretation” of the Nash equilibrium. This passage of his thesis
did not show up in any of Nash’s publications. Ironically, theorems
about mathematical existence of Nash equilibria seemed to be
more acceptable for publication than conceptual arguments about
why these equilibria are of any importance. Had Nash not re-
ceived the Nobel award, forcing some people to think about lauda-
tory speeches, we would still not know about his mass action in-
terpretation.
Seeing this partially unfortunate history of conceptual thinking
in game theory it appears to me that the book by Gigerenzer et al.
is an important step in exactly the direction of research that has
been ignored for too long. However, one should not throw out the
baby with the bath water. Evolution certainly has an optimising
tendency if one makes reasonable assumptions about the space of
alternative mental mechanisms from which natural selection
“picks a winner.” This is where evolutionary biology and psychol-
ogy mutually depend on one another. Biology provides the back-
ground about the optimising process and psychology can help to
understand what the space of strategies is that evolution acts upon.
Not only evolution but also learning can optimise and produce
Nash equilibria but it does so less reliably. For example, the liter-
ature on learning direction theory, which is partially cited in the
book, shows that unlike evolution, learning does not cause the
winner’s curse phenomenon to disappear in experiments where
people have a chance to get experience at auctions.
Why do people not learn the optimal behaviour in this case?
Probably because fast and too simple mental procedures set the
conditions for how to change bidding tendencies according to ex-
perience from previous rounds of the same experiment. Once these
tendencies are inappropriately specified, the resulting learning pro-
cedure fails to act as an optimising agent. This shows that even in
the context of learning one has to think about the effects of sim-
ple heuristics. I suggest placing more emphasis on this problem in
future work of the ABC group. Needless to say that it seems like
a very promising task for both biologists and psychologists to elab-
orate on the ideas that Gigerenzer and his co-workers have put to-
gether in their seminal contribution to decision theory with em-
pirical content.
On the descriptive validity and prescriptive
utility of fast and frugal models
Clare Harries
1
and Mandeep K. Dhami
2
1
Department of Psychology, University College London, London WC1E6BT,
United Kingdom;
2
Department of Psychology, City University, London EC1V
0HB, United Kingdom.
clare.harries@ucl.ac.uk
www.psychol.ucl.ac.uk/clare/self.html m.k.dhami@city.ac.uk
Abstract: Simple heuristics and regression models make different as-
sumptions about behaviour. Both the environment and judgment can be
described as fast and frugal. We do not know whether humans are suc-
cessful when being fast and frugal. We must assess both global accuracy
and the costs of Type I and II errors. These may be “smart heuristics that
make researchers look simple.”
Are humans really fast and frugal? Should humans be fast and fru-
gal? Human judgment may be described on a number of dimen-
sions such as the amount of information used and how it is inte-
grated. The choice of a model dictates how these dimensions are
characterised, irrespective of the data. For example, regression
models in judgment and decision-making research are linear and
compensatory, and researchers have assumed that humans are,
too (Cooksey 1996). The fast and frugal models proposed by
Gigerenzer, Todd, and the ABC Research Group (1999) use few
cues and are often noncompensatory, assuming humans are, too.
Are humans really using less information in the fast and frugal
model than the regression model? People can chunk information
(e.g., Simon 1979). Regression models are characterised as com-
plex in terms of use of multiple cues, but they often contain few
significant cues (on average three; Brehmer 1994). This chal-
lenges the argument that fast and frugal models are more frugal
than regression models, at least in terms of the number of cues
searched. Unlike standard practice (Tabachnik & Fidell 1996), in
their regression analyses, Gigerenzer et al. retain nonsignificant
cue weights. A fairer test would compare fast and frugal models
against parsimonious regression models.
Regression models have been used to describe the relationship
between judgments and the cues (the judgment system), and the
relationship between outcomes and the cues (the environment
system; Cooksey 1996). In both cases the underlying structure of
the cues is similar (e.g., they are correlated). Fifteen years of ma-
chine learning research demonstrates that fast and frugal models
can describe environments (Dutton & Conroy 1996). It is not sur-
prising that these models should also be good at describing human
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 753
judgment. Both types of models are useful for fitting data per se.
Chapter 7 demonstrates that fast and frugal models are good at
describing human judgment, under conditions of time pressure
with participants neither experienced nor familiar with the choice
task. At other points in the book, results of simulations seem to be
generalised with little justification to humans. However, research
has shown that fast and frugal models are valid descriptions of pro-
fessionals’ judgment behaviour in the legal and medical domains
(Dhami & Ayton 1998; Harries & Dhami 1998). So far we have
learned that the environment and humans can be described as fast
and frugal. We do not yet know whether humans are successful
when being fast and frugal because studies either don’t collect
judgments or don’t include outcomes.
We have doubts about the prescriptive utility of fast and frugal
models. The book argues (at least implicitly) that if fast and frugal
models are good at predicting the environment, then humans
should (and do) use these strategies to make accurate decisions.
However, in many situations global accuracy is not the first con-
cern: the two types of errors (Type I and Type II) are differentially
weighted. In medicine, for example, all tests involve a trade off
between Type I and Type II errors. Researchers developing
machine-learning models in this domain incorporate the costs of
the two types of error (Kukar et al., 1999). In criminal justice, the
opposing concepts of due process and of crime control attempt to
reduce crime whilst minimising different types of error (Type I–
the number of people falsely convicted and Type II–the number
of guilty people acquitted, respectively). It so happens that due
process expects a regression-like behaviour: all available informa-
tion is searched, weighted, and integrated. The fast and frugal
strategy of crime control emphasises information associated with
guilt, encouraging “conveyor belt justice.” Justice is synonymous
with due process, so the judge should behave like a regression
model. Of course, unlike medicine, the socially constructed nature
of criminal justice implies that we could change our notion of jus-
tice to one that reflects fast and frugal behaviour. Before Gigeren-
zer et al. encourage this we recommend that they evaluate mod-
els on other criteria in addition to global accuracy. In sum, the
descriptive success of simple heuristics does not, of itself, imply
their prescriptive utility.
On a differing point, if we do find that fast and frugal models
have prescriptive utility, their potential as cognitive aids or in cog-
nitive feedback vastly outweighs that of regression models (which
have done pretty well; Cooksey 1996). Fast and frugal models are
easy to understand and to apply while regression models are dif-
ficult to use without an aid and without knowing the range of cases
on which they were formed.
In short, we welcome fast and frugal models because they make
us re-think the dimensions of human judgment. The danger is that
they will be automatically adopted as tools to describe human
judgment, like regression models have been for 50 years. All mod-
els are paramorphic not isomorphic. So, we should be wary of
“smart heuristics that make researchers look simple.”
Decision rules in behavioural ecology
Alasdair I. Houston
Centre for Behavioural Biology, School of Biological Sciences, University
of Bristol, Woodland Road, Bristol BS8 1UG, United Kingdom.
a.i.houston@bristol.ac.uk
www.bio.bris.ac.uk/research/behavior/behavior.htm
Abstract: Gigerenzer, Todd, and the ABC Research Group give an inter-
esting account of simple decision rules in a variety of contexts. I agree with
their basic idea that animals use simple rules. In my commentary I con-
centrate on some aspects of their treatment of decision rules in behav-
ioural ecology.
Like Gigerenzer et al. (1999) I believe that animals are likely to
base their decisions on simple rules that are appropriate for a par-
ticular environment (see for example Houston 1987; Houston &
McNamara 1984; 1999; Houston et al. 1982; McNamara & Hous-
ton 1980). I feel, however, that Gigerenzer et al. may have under-
emphasised the use of rules within the context of optimisation.
Some of my concerns can be described in the context of patch-use.
Gigerenzer et al. (1999, Ch. 15, p. 327, Goodie et al.) discuss
the work of Green (1984) concerning when to leave a patch of
food. The optimal solution is given by the marginal value theo-
rem (Charnov 1976): leave when the rate of gain on the current
patch falls to the maximum possible rate of energetic gain g*.
Gigerenzer et al. point out that this result does not tell us how an
animal could know that it was time to leave a patch. The impres-
sion they give is that the animal has to know too much. McNa-
mara and Houston (1985) address this issue. They consider a sim-
ple learning rule that starts with an estimate g
0
for g*. The rule
states that the animal leaves the first patch when the rate on the
patch falls to g
0
. On arrival at the next patch a new estimate g
1
of
the rate g* is calculated on the basis of food obtained and time
taken. This rate is used to decide when to leave the second patch
that is encountered, and on arrival at the next patch a new esti-
mate g
2
is calculated. McNamara and Houston show that such a
rule produces a sequence of estimates g
0
, g
1
, g
2
. . . that tend to
g*. In other words, the rule learns the correct optimal rate. Mc-
Namara and Houston also discuss the problems that arise when
the environment changes. In the context of heuristics, it can be
pointed out that the marginal value theorem can be viewed as a
form of satisficing, with g* acting as an aspiration level. The rule
proposed by McNamara and Houston is a form of satisficing in
which the aspiration level is modified by experience (cf. Simon
1959).
Gigerenzer et al. conclude (1999; p. 341) that Green’s work
“could be, and often has been, viewed as optimizing under con-
straints of information gathering ability, but . . . Green’s analysis
explicitly does not try to optimize.... There are no claims that this
is the best an animal could possibly do.” I disagree with this sug-
gestion that Green’s (1984) work does not involve optimization.
Green considers three sorts of rule: (i) fixed-time rule (ii) giving-
up time rule, and (iii) assessment rule. In each case, Green finds
the best rule (1984; see pp. 33–35). In case (i) Green says “the
best thing to do is to stay until each patch has been exhausted.”
(p. 33). In case (iii) he says (p. 33) “The best rule is found by dy-
namic programming.” In fact Green’s use of dynamic program-
ming in this context involves a recursive estimation of g* that pro-
vides a robust and efficient way of finding optimal behaviour (see
Houston & McNamara 1999 for further discussion).
The use of optimality to investigate rules is not unusual in be-
havioural ecology. This can be thought of as optimization under
constraints, but it does not correspond to the restrictive way in
which this term is defined in Chapter 1 (p. 3; Gigerenzer & Todd).
It is often desirable to gain an idea of how well a rule performs
(see Ch. 13, p. 287, Todd & Miller and Ch. 14, p. 309, Davis &
Todd). This may involve finding an optimal rule. It may also in-
volve finding the optimal behaviour. Finding the optimal behav-
iour enables us to find the optimal performance, which provides
a way in which the performance of rules can be evaluated (Hous-
ton 1987; Houston & McNamara 1984; Houston et al. 1982).
Gigerenzer et al. make a good job of the difficult task of both
explaining the debate on matching versus maximising and putting
operant schedules in a naturalistic setting. I agree with their gen-
eral conclusion that matching is likely to be the consequence of a
rule that evolved through natural selection (see Houston & Mc-
Namara 1988). I would have liked to see a clear statement that
matching per se cannot be the fundamental principle. This follows
from the fact that matching does not uniquely specify behaviour
(e.g., Houston 1983; Houston & McNamara 1981). Gigerenzer et
al. do mention melioration as being able to remove some ambigu-
ities in matching. It does not, however, remove the fundamental
non-uniqueness concerning behaviour on concurrent variable-
interval schedules. Furthermore, it is not clear from Gigerenzer
et al. that biased matching rather than simple matching describes
Commentary/Todd & Gigerenzer: Simple heuristics
754 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
behaviour when an animal can choose between a variable-interval
and a variable-ratio schedule (Williams 1988).
What’s in the adaptive toolbox: Global
heuristics or more elementary components?
Oswald Huber
Department of Psychology, University of Fribourg, CH-1700 Fribourg,
Switzerland.
oswald.huber@unifr.ch
www.unifr.ch/psycho/Allgemeine/Oswald_Huber.htm
Abstract: From the standpoint of decision research, investigating global
heuristics like LEX is not fruitful, because we know already that people
use partial heuristics instead. It is necessary (1) to identify partial heuris-
tics in different tasks, and (2) to investigate rules governing their applica-
tion and especially their combination. Furthermore, research is necessary
into the adequate level of resolution of the elements in the toolbox.
Fast and frugal heuristics in the Gigerenzer, Todd, and the ABC
Research Group (1999) book are assumed to be specialized higher
order cognitive processes that are in the mind’s adaptive toolbox.
If we postulate elements in the toolbox, we have to make assump-
tions about the adequate grain of these elements. As I interpret
the authors, they regard global heuristics like the Lexicographic
heuristic (LEX), Weighted Pros or Elimination-by-Aspects (EBA)
as elements of this toolbox, in the decision making context.
Results of decision theory contradict such an assumption. In
many experiments where decision makers have to choose one of
several alternatives (presented simultaneously), the following very
stable result is observed (cf. e.g., Ford et al. 1989): The decision
process can be divided into two main phases. In the first, people
use, for example, some parts of EBA, not to make the final choice,
but in order to reduce the set of alternatives quickly to a short list.
When they have arrived at a short list they use, in the second
phase, another partial heuristic in order to select the best alterna-
tive. For these alternatives, usually much more information is
processed than for those not in the short list, and in a more alter-
nativewise manner (transition to another attribute of the same al-
ternative). From these results as well as from those obtained with
verbal protocols, we conclude that decision makers do not apply a
complete heuristic like LEX, and so on, but use a part of a heuris-
tic or combine partial components of heuristics.
One such partial heuristic is, for example, Partial EBA, which
is characterized by a sequence of the following two steps:
Step 1: Select a criterion (attribute, dimension . . . ) from set C of
criteria.
Step 2: Eliminate all alternatives from the set A of alternatives
which do not surpass an acceptance level on the selected
criterion.
Global EBA consists of repeated applications of Partial-EBA,
but most often Partial-EBA is combined flexibly with other par-
tial heuristics. If the decision maker faces several alternatives she
may apply Partial-EBA once or twice to reduce the set of alterna-
tives to a more manageable short list, and then use another partial
heuristic to make the final choice.
Thus, from the point of view of decision research, the toolbox
has to contain smaller units than global strategies. The experi-
ments reported by Gigerenzer et al. (1999) do not contradict these
well established results. They were not designed to study the ques-
tion of global heuristics versus components, and are restricted to
the special case of only two alternatives. However, even in cases
with two alternatives we cannot exclude the possibility that peo-
ple combine parts of heuristics (e.g., LEX and the Conjunctive
heuristic).
For research on the elements of the toolbox, this has two con-
sequences:
1. In the context of decision making and judgment, the inves-
tigation of global heuristics is not a fruitful research strategy, be-
cause we already know that people do not use them. It is rather
necessary to identify partial heuristics in different tasks. A variety
of partial heuristics has already been investigated in multi-attribute
decision making (see, e.g., Montgomery & Svenson 1989; Payne
et al. 1993), but we do not know much, for example, about non-
lottery risky decision situations.
2. If we have identified partial heuristics as elements, we need
a theory that explains the rules of the use and the combination of
partial heuristics. Even in multi-attribute decision making we do
not have such a theory, able to model the decision process as a se-
quence of partial heuristics in such a way that the detailed deci-
sion behavior can be predicted. The problem of a theory that ex-
plains the combination of partial components is not treated in the
book.
If we decompose global heuristics into smaller components as
the results of decision research make necessary, the question
arises at which level of decomposition to stop, because the partial
heuristics again can be decomposed, and so on, until elementary
operators are reached. We have to determine which level of reso-
lution is adequate for the elements of the toolbox.
Consider, as an example, Partial EBA as described above as a
sequence of two steps. At one level of resolution we could define
each of the steps 1 and 2 as a basic component of the toolbox. An
advantage of this resolution is frugality, because step 1 could serve
as a component in many partial or even global heuristics (e.g., Par-
tial LEX or Weighted Pros). At another less fine-grained level, we
consider the two steps together as one unit. In my opinion, even
if Partial-EBA is on a coarser level than the level where its two
components are treated as separate units, it is a more adequate ba-
sic element in the toolbox. There are two reasons: (1) In people’s
task representations of a decision situation, probably alternatives
and sets of alternatives play a central role. Therefore, people can
easily form a subgoal to reduce the set of alternatives and search
for an operator to reach that subgoal. In this process, details of
how this operator functions are not relevant to the decision maker.
Thus, partial heuristics are, on the one hand, big enough to ease the
workload on the thinking process. (2) On the other hand, partial
heuristics are small enough to be combined in a flexible manner.
The question of the adequate level of resolution of the elements
of the toolbox is not treated in the book. It is especially important
if we assume that the elements are genetically fixed (because they
have been put into the toolbox by evolution).
ACKNOWLEDGMENT
I am grateful for discussions with Siegfried Macho.
The role of mathematics in heuristic
performance
Paul C. Kainen
Department of Mathematics, Georgetown University, Washington, DC 20057
kainen@math.georgetown.edu
www.math.georgetown.edu/faculty/kainen/
Abstract: A mathematical approach to heuristics is proposed, in contrast
to Gigerenzer et al.’s assertion that laws of logic and probability are of lit-
tle importance. Examples are given of effective heuristics in abstract set-
tings. Other short-comings of the text are discussed, including omissions
in psychophysics and cognitive science. However, the authors’ ecological
view is endorsed.
The book by Gigerenzer, Todd, and the ABC Research Group
(1999) proposes that heuristics enjoy some sort of ecological ra-
tionality. However, the arguments do not seem entirely consistent;
on pp. 18–19, heuristics are taken to be so simple that they apply
to many cases, but complex enough to exploit environmental de-
pendencies.
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 755
Gigerenzer et al. (1999) seem to believe that no formal struc-
ture is needed to understand the remarkable performance of
heuristics. On p. vii, they assert: “The laws of logic and probabil-
ity play little if any role.” I believe that this is false and that, on the
contrary, heuristics derive their power precisely by their utiliza-
tion of mathematical theory. Indeed, heuristics can be clearly seen
in an entirely abstract context. I’ll give two examples that show the
idea (Kainen 1997).
Consider the search for an endpoint in a large tree. This is a
well-defined task and can be implemented via software. If the tree
has n vertices, then the usual algorithm, which merely follows a
path until it finally terminates at an endpoint, will need order-log-
n steps. However, if the tree is selected “at random” from all pos-
sible trees (on the same set of labeled vertices) and if a vertex is
then selected at random, then there is a chance of approximately
1/e (i.e., 0.37 . . . ) that the vertex will be an endpoint. Guessing
40 times, one has a probability of less than (
2
/
3
)
40
of being wrong,
independent of n. Using random choice as a heuristic beats the al-
gorithm by as much as you like once n gets sufficiently large. Since
many situations, for example, the solutions of games, can be cast
in terms of tree search for endpoints, this mathematical result can
be applied to many concrete examples.
Notice that the guessing heuristic allows parallel processing and
makes no demands on sharing information. Moreover, if the data
contains an extra non-tree edge, then the algorithm could be
trapped in a loop but the heuristic will only be influenced slightly
because each extra edge can kill off at most only two of the roughly
n/e vertices which are endpoints in the tree.
Another heuristic, called First Fit Decreasing, has been ana-
lyzed for a resource-allocation problem. It turns out that using two
reasonable strategies together (do the hardest first and just take
the first available resource – i.e., be greedy) will get one to the es-
sentially best possible solution.
While the book includes many examples showing how well
some heuristics do in special test conditions, for example, how we
infer intent from mouse movements on a computer, it does not go
on to consider detailed computations from the perspective of psy-
chophysics. For example, movement attracts human vision, guid-
ing the direction of focal attention, as do other salient features.
Heuristics may be involved because the speed of visual response
and minimum requirements for information pretty much elimi-
nate any conceivable algorithm. Another example may be the
process of linearization so well known in mathematics, which has
turned up in neurophysiological data for speech (Sussman et al.
1998) and also for reaching behaviors (Desmurget et al. 1996). I
wish the book had gone further in these directions, which certainly
seem congruent with the authors’ basic slant.
Heuristic ideas can also be extended to cover issues relevant to
cognitive science – G. Lakoff (1980) and H. Plotkin (1993) come
to mind. These connections ought to be pointed out in future edi-
tions of this work. That physical metaphors fit so well with lin-
guistic and psychological data may be evidence for the “unrea-
sonable effectiveness” of mathematics even in the biological
domain (Kainen 1998).
It would be nice to have an encyclopedia of basic heuristics.
However, this might be a Sisyphean task. As the statistician B.
Efron said, “Good simple ideas are our most precious intellectual
commodity,” but there may be no end to such good ways to orga-
nize knowledge.
The worst aspect of the book is its verbosity. Surely, the story
could be told more succinctly. The authors must have used the
phrase “fast and frugal heuristic” a thousand times. Homer got
away with this trick, but he had a better ear. One might like to hear,
rather, several reports, each of a few pages, on how using a simple
heuristic has led to improvement. For example, here is one I stum-
bled across while working at Bell Laboratories: Distrust software
(or systems) whose name is a third-order acronym.
This useful heuristic revealed a logistical horror story. A pro-
gram had been written to determine the deployment of a new
device which allowed multiple conversations to share the same
transmission facilities. But this powerful multiplexing device was
reduced to only a few percent of its actual capability by an elabo-
rate algorithm – fossilized from birth because of the vast distance
from programmers to factory-floor network environment, as the
acronym indicated. Once the conceptual errors in the program
were recognized, the problem was readdressed (successfully) via
heuristic methods, and that would make another case history.
It would improve the next publication of this group if they could
recount concrete instances like these. Although heuristic concepts
can have some overarching features, the richness of the context is
essential to see them in vivo.
In their preface, Gigerenzer and Todd refer to an interdiscipli-
nary spirit “put[ting] everyone . . . together . . . learning the lan-
guage and the skills of the others.” This type of collaboration is
called transdisciplinary by Ivan Havel, who distinguishes it pre-
cisely by the degree, depth, and longevity of the interactions. The
authors have certainly made a contribution by promoting aware-
ness of heuristic methods. If there is any area in which multiple
research streams are converging, it is right here. Heuristics pro-
vide a vital tool for ongoing problems of science and industry.
Two cheers for bounded rationality
Raanan Lipshitz
Department of Psychology, University of Haifa, Haifa, Israel 31905
raanan@psy.haifa.ac.il
Abstract: Replacing logical coherence by effectiveness as criteria of ra-
tionality, Gigerenzer et al. show that simple heuristics can outperform
comprehensive procedures (e.g., regression analysis) that overload human
limited information processing capacity. Although their work casts long
overdue doubt on the normative status of the Rational Choice Paradigm,
their methodology leaves open its relevance as to how decisions are actu-
ally made.
Hastie (1991, p. 137) wondered whether the field of decision mak-
ing “will ever escape the oppressive yoke of normative ‘Rational’
models” and guessed that the Expected Utility Model will “fade
away gradually as more and more psychologically valid and com-
putationally tractable revisions of the basic formation overlay the
original” (p. 138). Gigerenzer et al.’s work shows that escaping the
“Rational” paradigm requires not a gradual revision of the “origi-
nal,” but radical reformulation of the purpose of psychology and
the nature of rationality.
Following Brunswik’s dictum that psychology is the study of
people in relation to their environment, Gigerenzer et al. (1999)
suggest that “the function of heuristics is not to be coherent.
Rather, their function is to make reasonable, adaptive inferences
about the real social and physical world given limited time and
knowledge” (p. 22). Replacing internal coherence by external cor-
respondence as a criterion for rationality, Gigerenzer et al. man-
age to cast doubt on the normative underpinnings of the rational
paradigm. Despite repeated demonstrations of its poor descrip-
tive validity, the model continues to influence Behavioral Decision
Theory both descriptively (e.g., the operationalization of decision
as choice and of uncertainty as probability estimates), and pre-
scriptively (i.e., guiding evaluation and improvement of decision
quality). This resilience is due, in large part, to Savage (1954), who
suggested that the SEU model can be interpreted as (1) a de-
scription of an actual human decision maker, or (2) a description
of an ideal decision maker who satisfies some “rational” criteria
(e.g., transitivity of preferences). Because most human decision
makers cannot be regarded as ideal, neither the fact that they sys-
tematically deviate from the model nor the fact that they are in-
capable of the comprehensive information processing required by
the model is relevant to its coherence-based normative status.
Uniquely in science, the rational paradigm in the study of decision
making takes lack of descriptive validity as grounds for improving
Commentary/Todd & Gigerenzer: Simple heuristics
756 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
its “suboptimal” subjects instead of its invalid models (Cohen
1993).
Using correspondence in place of coherence, Gigerenzer et al.
use rational methods (regression and Bayesian analyses) as com-
petitors (rather than yardsticks) of simple heuristics which require
a fraction of the information, time, and computational power re-
quired by the former. Their result – that under certain conditions
fast and frugal heuristics win the competition – should dampen
enthusiasm for unrealistic, wasteful, and resource guzzling recipes
epitomized by Janis and Mann’s (1977) prescription:
1. Thoroughly canvass a wide range of alternative courses of ac-
tion;
2. Survey a full range of objectives and values;
3. Carefully weigh all known positive and negative conse-
quences;
4. Search for new information intensively;
5. Reexamine all alternatives and considerations before mak-
ing the decision;
6. Make detailed implementation plans, prepare for potential
contingencies.
The principal contribution of Gigerenzer et al.’s work leads to its
principal weakness. To rigorously refute the normative basis of the
rational paradigm they use simple judgment problems and computer
simulations. It is certainly reasonable to begin with simple tasks and
controlled methodologies before moving on to more complex and
less tractable, but the authors themselves admit that this strategy
leaves the really interesting (and “messy”) questions unanswered:
“[I]f we are also concerned with the principles that guide natural hu-
man and animal behavior, we must . . . [ask] what is the evidence that
humans or animals use specific fast and frugal heuristics?” (p. 23).
An alternative research strategy is to forego traditional stan-
dards of rigor and tackle real-world decision processes in their nat-
uralistic settings (Chi et al. 1982; Klein et al. 1993; Rogoff & Lave,
1984). Two findings and one conclusion from this research seems
particularly pertinent to the question which Gigerenzer et al. leave
unanswered:
1. Recognition does play a major role in decision making, but
not as a mere sense of familiarity. It is a complex (still ill-under-
stood) process of pattern matching which focuses attention on
critical cues and generates goals, expectations, and action alterna-
tives (Klein et al. 1993).
2. Experienced decision makers do use heuristics that save cog-
nitive effort (Cohen et al. 1996; Scribner 1984). These, however,
are highly domain specific and rely on considerable amount of do-
main specific knowledge and cannot be reduced either to “maxi-
mize expected utility” or to “choose the best.”
3. Thus, effective real-wold use of “fast and frugal” heuristics
requires considerable background knowledge, for example, “Which
is the best indicator?” “What is the informational structure of the
environment?” Similar to the Rational paradigm, which they so ef-
fectively undermine, Gigerenzer et al. pay insufficient attention to
the fact that boundedly-rational human decision makers compen-
sate the limited capacity of their short-term memories by the con-
siderable capacities of their long-term memories and learning.
Fast, frugal, and surprisingly
accurate heuristics
R. Duncan Luce
Social Science Plaza, Departments of Cognitive Sciences and Economics,
University of California, Irvine, CA 92697-5100.
rdluce@uci.edu
Abstract: A research program is announced, and initial, exciting progress
described. Many inference problems, poorly modeled by some traditional
approaches, are surprisingly well handled by kinds of simple-minded
Bayesian approximations. Fuller Bayesian approaches are typically more
accurate but rarely are they either fast or frugal. Open issues include cod-
ifying when to use which heuristic and to give detailed evolutionary ex-
planations.
This volume (Gigerenzer et al. 1999) is a preliminary progress
report – and progress it does indeed report – of the Center for
Adaptive Behavior and Cognition (ABC) of the Max Planck Insti-
tute for Human Development in Berlin. Although not identified
as such, it is an edited work with 16 signed chapters that are more
than usually well integrated and coherent. Presumably Gigeren-
zer and Todd are the editors. The theme is that evolution has led
people and other creatures to infer heuristics that are, in an often
repeated phrase, “fast and frugal” and surprisingly effective.
The message seems directed primarily to psychologists inter-
ested in decision theory, but in reality the audience should be far
broader than that. One claim is that our standard arsenal of sta-
tistical methods – those based on the familiar additive expressions
of analysis of variance and linear regression – really seem to rest
on a singularly bad representation of a great deal of reality; this
matters greatly. Virtually all scientific psychologists should heed
this message.
Examples of inference and categorization problems repeatedly
arise that exhibit the following two features. First, each of a num-
ber of observables is correlated with a measure of interest whose
value is not known directly. These observables may or may not be
independent. For example, suppose comparative city size is a mea-
sure of interest and the observables are such things as having a pro-
fessional soccer team, being the home of a university, being a state
capital, and so on. Second, to decide which of two cities is larger,
suppose one simply proceeds through the observables in descend-
ing order of correlation stopping at the first observable that dis-
criminates between the cities: that dictates the choice. Surprisingly,
this “take-the-best” heuristic regularly outperforms a variety of ad-
ditive measures. Because no trade-offs occur, not all of the available
information needs to be examined exhaustively, and very little com-
putation is needed. So the heuristic tends to be fast as well as ac-
curate. This can be seen as one way to implement Herbert Simon’s
(1956a) call for limited search and satisficing in decision making.
Many of the inference problems posed seem to fit more closely
a Bayesian perspective than they do the classical additive trade
offs, and indeed when fast and frugal heuristics are compared in
Chapter 8 (p. 169, Martignon & Laskey) with certain Bayesian
analyses, the latter indeed do somewhat better. But the expense
in time and computation is considerable and the authors believe,
but hardly prove, that evolution has found it effective to trade off
a bit of accuracy for very fast procedures, often a condition for
survival. “Fast and frugal heuristics can have their place in every-
day affairs where time is limited and knowledge is scarce, and
Bayesian tools can be the choice of someone who is in no hurry
and has access to a computer” (p. 186).
Indeed, a major theme of the book is just that: Calculations of
optimal behavior just are not practical for much real world deci-
sion making, and people should not be assumed even to approxi-
mate such calculations. Chapter 13 (p. 287, Todd & Miller) takes
up the problems typified by selecting a secretary or a mate, where
each party is dealing with a somewhat unknown pool of alterna-
tives, both must agree on a match, and one cannot return to indi-
viduals previously passed over. The optimal rule is known for a
given, fixed pool size, say 100, and assuming that the candidate se-
lected will accept the offer: Examine 37 of the applicants, the best
of whom establishes an aspiration level, and then select the next
person exceeding that value. The chance of actually finding the
optimal person is also 37% and, on average, 74 people are inter-
viewed. Clearly, this is a costly and far from reliable procedure. In-
deed, should one’s goal be the optimum? Simulations show that a
criterion based on the first 14 has an 83% chance of finding some-
one in the top 10% of the pool.
Another part of the so-called Bayesian revolution are attempts to
take into account people’s preferences over alternatives and uncer-
tainties about the environment giving rise to them. This aspect has
been embodied in subjective expected utility theory and a number
of variants. Although they allude to this line of work, which I sus-
pect they do not much like, they do not approach it directly: “we
have focussed on adaptive goals in terms of correspondence crite-
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 757
ria (e.g., accuracy, speed, and frugality) as opposed to coherence
criteria (e.g., consistency, transitivity, additivity of probabilities) tra-
ditionally used to define rationality. Is any role left for coherence
criteria?” (p. 364, Todd & Gigerenzer). “Models of reasoning need
not forsake rationality for psychological plausibility, nor accuracy
for simplicity. The mind can have it both ways” (p. 365).
A large area is delineated, and it will require many scien-
tists – not just psychologists – and much time to explore and cod-
ify it. First, how does one classify problems and decide upon which
of several possible fast and frugal heuristics to employ? They speak
of having an “adaptive tool box,” and the question is when to use
which tool. Over three quarters of a century of effort has gone into
systematizing experimental design and analysis based on standard
statistics, and something comparable probably will be needed to
show how to proceed more effectively in modeling inference and
classification. Second, how does one decide which tool each par-
ticipant in an empirical study is actually using? This is an issue be-
cause the problems encountered neither automatically nor
uniquely point to a particular analysis, and so it is only reasonable
to expect variation in tool use. And third, how do we test in a non-
tautological fashion the claim that some of these procedures have
been selected for by evolution? As we all are well aware, this is a
very tricky issue, and evolutionary arguments, at least in psychol-
ogy, typically invite a good deal of skepticism and, perhaps, have
been misused in some cases. Should these developments actually
occur, this book will be seen as seminal.
Simple heuristics that make us dumb
Howard Margolis
The Irving B. Harris Graduate School of Public Policy Studies, University of
Chicago, Chicago, IL 60637.
hmarg@uchicago.edu
Abstract: The simple heuristics that may indeed usually make us
smart – or at least smart enough – in contexts of individual choice will
sometimes make us dumb, especially in contexts of social choice. Here
each individual choice (or vote) has little impact on the overall choice, al-
though the overall choice is compounded out of the individual choices. I
use an example (risk aversion) to illustrate the point.
Gigerenzer, Todd, and the ABC Research Group (1999) argue
that simple rule-of-thumb responses will often be strikingly effec-
tive relative to logically better but pragmatically hard to learn and
hard to use responses. Hence, their message: “simple heuristics
can make us smart.” And they are right. But simple heuristics can
also make us dumb. In fact, the very same simple heuristics.
As Gigerenzer et al. (1999) make clear, their simple heuristics
come to be in place because experience in the world has trained
us to rely on them, or sometimes even because experience of our
species in evolutionary time has entrenched the responses genet-
ically. We can expect that entrenched responses will be good
enough to be favored by whatever selection process is operating.
The net effect (the benefits when it works, net of the costs when
it doesn’t) must be positive enough, relative to feasible alterna-
tives, to make sense of how the response comes to be entrenched.
But this argument only works for contexts close to those that fa-
vored the response. Even in just those contexts, the response will
be subject to false alarms. It may be prompted when it is irrelevant
or ineffective, and so does no good while perhaps pre-empting a
less easily prompted response that would actually have worked. But
in contexts remote from those that account for why a response be-
comes entrenched, these ordinarily favorable responses may be far
from good. There is no reason to assume they would continue to
be even moderately reliable in contexts far from their home terri-
tory, and they might even be completely unreliable. In unfamiliar
contexts, the anchor-and-adjust response that guides our intuition
might trigger a simple heuristic that is not at all a good proxy for
what a more considered, more logical analysis would recommend.
I stress here, in particular, the contrast between contexts of in-
dividual choice in commonplace circumstances against contexts of
social choice, where the aggregate effects of individual responses
have large consequences entirely beyond the scope of ordinary ex-
perience. Then, the effect of any one individual choice is socially
microscopic, hence also the motivation for an individual to think
hard about that choice. Indeed, in the individual context, if a par-
ticular response is what a person feels comfortable with, that is
likely to be all we need to know to say that response is a good one,
or at least a good enough one. But in social contexts that very of-
ten is not true at all.
Here is an illustration. Our genetically entrenched propensities
with respect to risk would have evolved over many millennia of
hunter-gatherer experience, where life was commonly at the mar-
gin of subsistence, and where opportunities for effective stockpil-
ing of surplus resources were rare. In such a context, running risks
to make a large gain would indeed be risky. If you succeed, you
may be unable to use what you have gained, and if you fail (when
you are living on the margin of subsistence), there may be no fu-
ture chances at all.
In contrast, such a life would encourage risk taking with respect
to averting losses. If you have little chance to survive a substantial
loss, you might as well take risks that could avert it. So we have a
simple account of why (Kahneman & Tversky 1981) we are ordi-
narily risk-averse with respect to gains but risk-prone in the do-
main of losses. And this yields simple heuristics: with respect to
gains, when in doubt, don’t try it, and the converse with respect to
averting a loss.
But we do not now live on the margin of subsistence, so now
these simple heuristics that make us smart may easily be dumb: es-
pecially so with respect to a social choice that is going to affect large
numbers of individual cases, where (from the law of large num-
bers) maximizing expectation makes far more sense than either risk
aversion or its opposite. But because entrenched responses are (of
course!) hard to change, and especially so because their basis is
likely to be scarcely (or even not at all) noticed, effectively altering
such choices will be socially and politically difficult.
Although space limits preclude developing the point here, I
think a strong case can be made that the consequences of such ef-
fects are not small. One example (but far from the only one), is the
case of new drug approvals in the United States, where there has
been a great disparity between attention paid to the risks of harm-
ful side effects and to the risks of delaying the availability of a med-
icine to patients whose lives might be saved.
Nor can we assume that faulty judgments governed by simple
heuristics will be easily or soon corrected. I ran across one recently
that had persisted among the very best experts for 400 years (Mar-
golis 1998).
I think a bit of old-fashioned advice is warranted here: “If we
may admire the power of ideas when they lead us and inspire us,
so must we learn also their sinister effects when having served
their purpose they oppress us with the dead hand.” (Sir Thomas
Clifford 1913) Same for simple heuristics.
Heuristics all the way up?
Adam Morton
Department of Philosophy, University of Bristol, Bristol BS8 1TB, United
Kingdom
adam.morton@bristol.ac.uk mail.bristol.ac.uk/~plam
Abstract: I investigate whether heuristics similar to those studied by
Gigerenzer and his co-authors can apply to the problem of finding a suit-
able heuristic for a given problem. I argue that not only can heuristics of
a very similar kind apply but they have the added advantage that they need
not incorporate specific trade-off parameters for balancing the different
desiderata of a good decision-procedure.
Assume that most of the claims made by Gigerenzer et al. (1999)
are true, and that each person possesses a toolbox of relatively
Commentary/Todd & Gigerenzer: Simple heuristics
758 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
naive procedures which, when used in suitable environments, give
results almost as good as sophisticated statistical reasoning, for a
fraction of the psychological cost. These procedures will give ex-
tremely bad results when used in the wrong environments. The
simplest example of a bad environment is one where the values of
a quantity to be estimated by the recognition heuristic are in-
versely correlated with the familiarity of the cues. There is thus a
very non-trivial problem of matching heuristics to problems. How
do we know which tool to take from the box?
The matching could be done by some approximation to the sta-
tistical considerations of Chapters 6 and 8. Or it could itself use
some simple heuristics, which in suitable environments gave good
results. Or, it could work in some entirely different way. Let us ex-
plore the second possibility. (The first seems unattractive, given
the general ethos of the project, and although the third might well
be true we can only explore it once we see the limitations of the
second.) We must thus see how, given a problem of decision or es-
timation, we can choose from among a set of available simple pro-
cedures one which will give an accurate-enough and efficient-
enough solution. People do seem to adapt their decision-making
procedures to the circumstances of the problem at hand, as re-
marked in Chapter 6 (Martignon & Hoffrage, p. 140), referring to
Payne et al. (1988; 1993). But the core theory of frugal heuristics
is itself neutral on the procedures by which the right heuristic for
the problem at hand is chosen, as Chapter 16 (p. 364, Todd &
Gigerenzer) explicitly accepts.
When we pose the meta-choice problem we are immediately
faced with a question of incomparability. The choice procedure
is asked simultaneously to optimize accuracy and frugality, with-
out being given a trade-off function between them. This might be
taken to be another dimension of difficulty, and indeed recent
philosophical literature on decision-making often treats incom-
parability as a basic conceptual problem of decision, along with
risk and cooperation (see Chang 1997; Morton 1990). But the
simple heuristics point of view has a very significant card to play.
Frugal heuristics often manage incomparability as a matter of
course.
Suppose, for example, that we are faced with the problem of
choosing a restaurant, where both quality and price are desider-
ata. If we apply a heuristic with a simple stopping rule, such as
Take the Best we can find that we do not need to decide how to
balance the desiderata. We must phrase the stopping rule neu-
trally: stop when you find a characteristic that correlates with ei-
ther of the targets. But then we can simply stop searching when
we find a candidate and a characteristic that is linked either to
good price or good quality. In a series of such choices a balance of
quality and price will be struck, but the form of the balance will
depend on the environment to which the heuristic is applied and
not on any parameter of its definition.
The same can apply with a meta-choice. Suppose we have a
toolbox of heuristics and a database of cases, which would specify
the categorization of a problem, whether one of the heuristics was
applied, and whether it gave a result that was acceptable in terms
of time or accuracy. Then, given a new problem falling into some
category, a person can apply a meta-heuristic that involves a stop-
ping rule as described above to select one that is acceptable either
on the one criterion or the other. The result of applying this
heuristic to this problem then expands the database to make it a
more effective basis for subsequent meta-choices.
The choice of heuristics is unlikely to be made by any rule that
is exactly parallel to any first order heuristic. But some features of
first order heuristics are very attractive as attributes of meta-
choice, in particular the use of a simple stopping rule and the de-
termination of some basic parameters by the environment. This
suggests to me that there is another break to make with a tradi-
tional conception of rationality. We must not only be wary of an
ideal of unlimited cognitive capacity; we must also be suspicious
of ideals of self-containment, according to which all the parame-
ters of a choice procedure are fixed by internal features of cogni-
tion.
What is an ecologically rational heuristic?
Stephen E. Newstead
Department of Psychology, University of Plymouth, Plymouth PL4 8AA
United Kingdom.
s.newstead@plymouth.ac.uk
Abstract: The notion of ecological rationality, although plausible, does not
readily lead to testable predictions. This is illustrated with respect to
heuristics in syllogistic reasoning. Several possible heuristics have been
proposed but ecological rationality does not appear to offer a sensible ra-
tionale for choosing between these.
There is much that I agree with in the book by Gigerenzer, Todd,
and the ABC Research Group. I am sure they are right that many
human judgments are based on heuristics. These heuristics are in-
deed often sensible ways of dealing with the situation in hand, and
are sometimes more effective than logical responding. I find my-
self less convinced by their claim that these heuristics are “eco-
logically rational,” in the sense that they are “adapted to the struc-
ture of an environment” (Gigerenzer et al. 1999, p. 13).
The problem is in translating this claim into operational terms
and using it to make predictions. Any heuristic response will in-
volve responding on the basis of only part of the information pre-
sented or using only limited search. But this claim has value only
if it can predict which aspects of the situation will be selectively
responded to. If the relevant features can be indicated only after
responses are given then the theory has little or no predictive va-
lidity.
Consider, for example, syllogistic reasoning. This is precisely the
kind of artificial reasoning task in which people deviate from the dic-
tates of logic and where heuristics might come into play. There has,
in fact, been no shortage of possible heuristics invoked to explain
syllogistic reasoning errors. Possible contenders include:
Atmosphere: The claim that people base their responses on sur-
face features of the quantifiers – whether these are negative or
positive, and universal or particular (Woodworth & Sells 1935).
Probability: The claim that people use the least informative
premise as the basis for their conclusion (Chater & Oaksford
1999).
Caution: The claim that people choose the response which
commits them to the least general statement (Sells 1936).
Limited processing: The claim that people reach a decision af-
ter constructing just one representation of the premises (New-
stead et al. 1999).
Believability: The claim that people give the conclusion they
find most believable (Evans et al. 1983).
All of these predict reasonably well the responses that people
actually give, and they are not mutually exclusive. The point is that
there seems to be no sensible rationale based on ecological ratio-
nality for predicting which of these biases (if any) would be ex-
pected to operate. Intuitively, both the limited processing and the
believability heuristics might make sense in a variety of other sit-
uations. Limited processing is, of course, one of the heuristics dis-
cussed by Gigerenzer et al.; and responding according to believ-
ability makes sense, as it would in many situations be irrational to
accept an argument that was known to lead to an untrue conclu-
sion. But much the same could be said of probability and caution.
Oaksford and Chater claim that their probability heuristic has con-
siderable generality, and caution could be a sensible heuristic to
adopt in a number of very different situations. Atmosphere seems
to be the only heuristic motivated solely by considerations of the
syllogistic reasoning task, and even this could be seen as a more
general tendency to match responses to surface characteristics of
the information given.
And there’s the rub. For if any of these heuristics can be argued
to be ecologically rational, how can one predict which one will oc-
cur? And if one cannot make a prediction, how can the theory be
tested? It is not enough to see which heuristic best fits the evi-
dence and then claim that this is the most ecologically rational; this
would clearly be circular.
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 759
A further point worth noting with respect to syllogistic reason-
ing is that there is overwhelming evidence that people are capa-
ble of responding according to logic. Studies of belief bias, for ex-
ample, almost invariably find an effect of logic as well as an effect
of believability (see Evans et al. 1983). It is not clear whether in-
dividuals respond partly on the basis of logic and partly on the ba-
sis of belief, or whether there are individual differences in the ten-
dency to respond in these ways. Whichever is the case, this is
clearly a complicating factor in any attempt to explain perfor-
mance in terms of heuristics alone.
None of this implies that Gigerenzer et al. are wrong. On the
contrary, what is needed is for them to develop their theory fur-
ther so that more specific predictions can be put to the test.
Speed, frugality, and the empirical basis
of Take-The-Best
Mike Oaksford
School of Psychology, Cardiff University, Cardiff, CF1 3YG, Wales, United
Kingdom.
oaksford@cardiff.ac.uk www.cardiff.ac.uk/psych/oaksford
Abstract: This commentary questions the claim that Take-The-Best pro-
vides a cognitively more plausible account of cue utilisation in decision
making because it is faster and more frugal than alternative algorithms. It
is also argued that the experimental evidence for Take-The-Best, or non-
integrative algorithms, is weak and appears consistent with people nor-
mally adopting an integrative approach to cue utilisation.
Although I agree with much of Gigerenzer, Todd, and the ABC
Research Group’s approach – indeed, Nick Chater and I believe
it can be extended to classical reasoning tasks such as syllogisms
(Chater & Oaksford 1999) – I argue that their comparison with
other algorithms provides less support for Take-The-Best than
they suggest and that its empirical basis is weak and consistent
with alternative interpretations.
Gigerenzer et al. (1999, Ch. 4, p. 94, Gigerenzer & Goldstein;
Ch. 10, p. 231, Hertwig, Hoffrage & Martignon) cite the results of
an unpublished study (Chater et al. 1999), comparing Take-The-
Best with integrative algorithms such as neural networks and the
generalised context model (GCM). Our interpretation of these re-
sults differs from that of Gigerenzer et al. (1999). They claim that
Take-The-Best is particularly attractive because it is fast (it in-
volves a small number of serial processing steps) and frugal (it
draws on very limited information, because it is non-integrative).
However, neither consideration straightforwardly gives Take-The-
Best an advantage over the available alternatives.
There are two points to consider concerning speed. First, rapid
integration of large amounts of information is believed to occur in
language processing, perception, motor control, and common-
sense reasoning. Hence integrative processing may be fast enough
to account for the relatively slow human responses in the city size
estimation task. the only empirical evidence the authors provide
(Ch. 7, p. 141, Rieskamp & Hoffrage) is that people use non-
integrative algorithms like Take-The-Best only under time pres-
sure. However, most of the decision domains to which Gigerenzer
et al. have directed their modeling efforts (Ch. 5, pp. 99–100,
Czerlinski et al.), do not require decisions to be made under time
pressure. For example, predicting which of two cities has the
higher rate of homelessness is not a decision that people would
normally need to make rapidly. Consequently, the emphasis on
speed as a deciding factor between algorithms may be inappro-
priate.
Second, Gigerenzer et al.’s measure of speed depends on as-
sumptions about the architecture of the cognitive system (Chater
& Oaksford 1990; Oaksford & Chater 1991; 1993; 1995). On a se-
rial architecture, where information is searched in memory at a
constant rate, Take-The-Best would be more rapid than the ac-
counts Chater et al. considered. But in a parallel architecture, pro-
cessing speed will not generally be related to the amount of infor-
mation searched in memory, because large amounts of information
can be searched simultaneously. For example, both the learning
and application of multiple regression can be implemented in par-
allel using a connectionist network with a single layer of connec-
tions. This implementation could operate very rapidly – in the
time it takes to propagate activity across one layer of connections
(e.g., Hinton 1989). Similarly in an instance-based architecture,
where instances can be retrieved in parallel, GCM would be the
quickest. Take-The-Best only has a clear advantage over other al-
gorithms if cognitive processes are assumed to be serial. Given the
extensive research programs aimed at establishing the viability of
instance-based and connectionist architectures as general ac-
counts of cognitive architecture (e.g., Kolodner 1993; Rumelhart
et al. 1986), it seems that considerable caution must be attached
to a measure of speed that presupposes a serial architecture.
Gigerenzer et al. (1999) also compare the computational com-
plexity of different algorithms (pp. 183–86). Using this measure
they find that the complexity of Take-The-Best compares favourably
with integrative algorithms. However, Gigerenzer et al. concede
that the relevance of these worst-case sequential analyses to the
presumably highly parallel human implementation is not clear (al-
though the speed up could only be by a constant factor). More-
over, as we now argue there are many cognitive functions that
require the mind/brain to perform rapid, integrative processing.
Take-The-Best is undoubtedly a very frugal algorithm. Rather
than integrating all the information that it is given (all the features
of the cities), it draws on only enough feature values to “break the
tie” between the two cities. But does the frugality of Take-The-
Best make it more cognitively plausible? Comparison with other
domains suggests that it may not.
In other cognitive domains, there is a considerable evidence for
the integration of multiple sources of information. We consider
two examples. First, in speech perception, there is evidence for
rapid integration of different cues, including cues from different
modalities (e.g., Massaro 1987). This integration even appears to
obey law-like regularities (e.g., Morton 1969), which follow from
a Bayesian approach to cue integration (Movellan & Chadderdon
1996), and can be modelled by neural network learning models
(Movellan & McClelland 1995). Second, recent work on sentence
processing has also shown evidence for the rapid integration of
multiple “soft” constraints of many different kinds (MacDonald et
al. 1994; Taraban & McClelland 1988).
Two points from these examples are relevant to the cognitive
plausibility of Take-The-Best. First, the ability to integrate large
amounts of information may be cognitively quite natural. Conse-
quently, it cannot be taken for granted that the non-frugality of
connectionist or exemplar-based models should count against
their cognitive plausibility. Second, the processes involved require
rich and rapid information integration, which cannot be handled
by a non-integrative algorithm such as Take-The-Best. Thus Take-
The-Best may be at a disadvantage with respect to the generality
of its cognitive performance.
A possible objection is that evidence for rapid integration of
large amounts of information in perceptual and linguistic domains
does not necessarily carry over to the reasoning involved in a
judgment task, such as deciding which of two cities is the larger.
Perhaps here retrieval from memory is slow and sequential, and
hence rapid information integration cannot occur. However, the
empirical results that Gigerenzer et al. report (Ch. 7) seem to show
performance consistent with Take-The-Best only when people are
under time pressure. But, as we suggested above, the judgments
used in Gigerenzer et al.’s experiment do not normally need to be
made rapidly. Consequently, the authors’ data are consistent with
the view that under normal conditions, that is, no time pressure,
participants wait until an integrative strategy can be used. That is,
for the particular judgments that Gigerenzer et al. consider, it is
more natural for participants to adopt an integrative strategy; they
use a non-integrative strategy only when they do not have the time
to access more cues.
Commentary/Todd & Gigerenzer: Simple heuristics
760 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
In sum, whether Take-The-Best is fast, is architecture depen-
dent, and whether frugality is a virtue are questioned by the many
other cognitive functions that require fast, parallel, and integra-
tive approaches. Moreover, the weak empirical basis for Take-
The-Best seems consistent with people normally adopting an in-
tegrative approach (albeit with limited cues).
Sub-optimal reasons for rejecting optimality
David R.Shanks and David Lagnado
Department of Psychology, University College London, London WC1E 6BT
United Kingdom.
{d.shanks; d.lagnado}@ucl.ac.uk
www.psychol.ucl.ac.uk/david.shanks/Shanks.html.
Abstract: Although we welcome Gigerenzer, Todd, and the ABC Re-
search Group’s shift of emphasis from “coherence” to “correspondence”
criteria, their rejection of optimality in human decision making is prema-
ture: In many situations, experts can achieve near-optimal performance.
Moreover, this competence does not require implausible computing
power. The models Gigerenzer et al. evaluate fail to account for many of
the most robust properties of human decision making, including examples
of optimality.
A paradox in the rationale for fast and frugal algorithms.
There
is a curious paradox in Gigerenzer et al.’s argument for the role of
fast and frugal algorithms in human decision-making (Gigerenzer et
al. 1999). They suggest that psychologists have been led astray by
focusing on behavior from an optimization perspective and they
imply that optimization models are implausible, intractable, and
require demonic capacities. Instead, they urge us to explore fast
and frugal algorithms. Yet they admit on p. 237 that categorization
performance can often be optimal, but if that is the case, then surely
the case for fast and frugal algorithms – which will almost certainly
never achieve this level of performance – evaporates?
To evaluate Gigerenzer et al.’s case for minimal complexity in
cognitive processes it is critical to determine whether decision
making is truly optimal. The jury is still out on this issue, of course,
but what is indisputable is that near-optimal performance can be
achieved by experts in many realms including categorization (An-
derson 1991; Ashby & Maddox 1992) and choice (Binmore 1991;
Davis et al. 1993).
Gigerenzer et al. repeatedly ridicule what they take to be “op-
timal” theories (e.g., multiple linear regression, MLR) on the
grounds that they require unrealistic amounts of computation
(e.g., p. 76), but this is a highly misleading claim. Contrary to the
impression made by Gigerenzer et al., it is possible to find a re-
gression solution in minimal time without doing any computa-
tion at all. Imagine a set of points each represented by a peg on
a two-dimensional board (the solution also works in principle in
n dimensions). Then attach a long thin rod by a set of elastic
bands to the pegs. By minimizing the allocation of tension across
the elastic bands, the rod will align exactly according to the re-
gression equation. As another example, consider the well-known
Travelling Salesman problem in which the shortest route must
be computed that visits each of a number (N) of cities exactly
once. Despite its computational complexity (the computing time
needed to solve this problem increases faster than any power of
N), near-optimal solutions can be achieved by parallel neural
networks in the blink of an eye (Hopfield & Tank 1985). What
objection is there to the view that the human cognitive system
approximates optimality by use of parallel constraint-satisfaction
processes?
It is also troubling that Gigerenzer et al. take multiple linear re-
gression (MLR) as one of their benchmark models throughout the
book. Humans can learn highly nonlinear judgment rules in a va-
riety of domains (Ashby & Maddox 1992; Ceci & Liker 1986) so
MLR is simply not an appropriate model. If TTB (Take The Best)
and CBE (categorization by elimination) approximately match the
performance of MLR and if human experts significantly outper-
form MLR then the obvious conclusion is that TTB and CBE are
inadequate models of human performance.
Implausibility of the CBE model.
We believe that the candidate
fast-and-frugal model for categorization which Gigerenzer et al.
present, the CBE model, is wholly inadequate for human perfor-
mance. First, it is unable to predict one of the benchmark phe-
nomena of categorization, namely the ubiquitous “exemplar ef-
fect,” that is, the finding that classification of a test item is affected
by its similarity to specific study items, all else held constant (e.g.,
Whittlesea 1987). Even in the case of medical diagnosis, decision-
making in situations very like the heart-attack problem Gigeren-
zer et al. describe is known to be strongly influenced by memory
for specific prior cases (Brooks et al. 1991). The recognition
heuristic is not adequate to explain this effect because it concerns
the relative similarity of previous cases, not the absolute presence
versus absence of a previous case. If a heavy involvement of mem-
ory in simple decision tasks seems to characterize human perfor-
mance accurately, then plainly models which ignore this feature
must be inadequate.
Second, there is strong evidence against deterministic response
rules of the sort embodied in Gigerenzer et al.’s fast-and-frugal
algorithms (Friedman & Massaro 1998): for instance, Kalish and
Kruschke (1997) found that such rules were rarely used even in a
one-dimensional classification problem. Thirdly, CBE is not a
model of learning: it says nothing about how cue validities and re-
sponse assignments are learned. When compared with other cur-
rent models of categorization such as exemplar, connectionist, and
decision-bound models, which suffer none of these drawbacks,
the CBE model begins to look seriously inadequate.
Methodology of testing the models.
By taking a tiny domain of
application (and one which is artificial and highly constrained),
Gigerenzer et al. find that the CBE model performs competently
and conclude that much of categorization is based on the applica-
tion of such algorithms. Yet they mostly do not actually fit the
model to human data. The data in Tables 5-4, 11-1, and so on, are
for objective classifications, not actual human behavior. It is hard
to see how a model’s ability to classify objects appropriately ac-
cording to an objective standard provides any evidence that hu-
mans classify in the same way as the model.
Even in the cases they describe, the models often seriously un-
derperform other models such as a neural network (Table 11-1).
Compared to the more standard approach in this field, in which
researchers fit large sets of data and obtain log-likelihood mea-
sures of fit, the analyses in Chapters 5 and 11 are very rudimen-
tary. Gigerenzer et al. report percent correct data, which is known
to be a very poor measure of model performance, and use very
small datasets, which are certain to be highly nondiscriminating.
The difference between the CBE model and a neural network
(e.g., up to 9% in Table 11.1) is vast by the standards of catego-
rization research: for instance, Nosofsky (1987) was able to distin-
guish to a statistically-significant degree between two models
which differed by 1% in their percentages of correct choices.
Melioration as a fast-and-frugal mechanism.
The algorithms
explored by Gigerenzer et al. (TTB, CBE, etc.) share the common
feature that when a cue is selected and that cue discriminates be-
tween the choice alternatives, a response is emitted which de-
pends solely on the value of that cue. Gigerenzer et al. (Ch. 15, p.
327, Goodie et al.) consider the application of such models to the
simplest possible choice situation in which a repeated choice is
made between two alternatives in an unchanging context. The
prototypical version of such a situation is an animal operant choice
task in which, say, a food reinforcer is delivered according to one
schedule for left-lever responses and according to an independent
schedule for right-lever responses. As Gigerenzer et al. point out
(p. 343), fast-and-frugal algorithms predict choice of the alterna-
tive with the highest value or reinforcement rate. Although this
may seem like a sensible prediction, human choice does not con-
form to such a “momentary-maximization” or “melioration” process.
In situations in which such a myopic process does not maximize
overall reinforcement rate, people are quite capable of adopting
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 761
better response strategies. A well-known example is the Harvard
Game (Herrnstein 1997) in which one response alternative (say,
right) always pays more at any moment than the other (left), but
where overall reinforcement rate is maximized by allocating all re-
sponses to left. People’s behavior is often seen to approach opti-
mality under such conditions (Herrnstein et al. 1993; R. Tunney
& D. Shanks, unpublished data). Yet again we have an example of
humans’ ability to achieve near optimal levels of performance, ex-
actly as the “demonic” theory of rational choice predicts.
The selection problem.
Gigerenzer et al. say very little about
how individual heuristics are selected for application to specific
problem domains. Such meta-level decisions will typically require
some prior knowledge about the structure of the environment
(e.g., whether it is non-compensatory, J-shaped, etc.), which may
add substantially to the overall processing costs of a fast and fru-
gal model. This would reduce its advantage over those models that
can learn about the environment and have general applicability
(thus cutting out the metadecision stage). In the majority of the
simulations in the book, one particular heuristic is pre-selected to
operate in a specific environment. More rigorous tests would
place a complete fast and frugal system (different heuristics plus
metadecision heuristics) in a variety of different environments,
and compare its performance against an alternative general-
purpose learning model.
The precision/accuracy trade-off.
On a more positive note, we
welcome Gigerenzer et al.’s shift of emphasis from “coherence” to
“correspondence” criteria. This is an important step towards a
more complete understanding of rationality, and removes some of
the obstacles placed by the heuristics-and-biases school. In addi-
tion to the examples cited in the book, the inadequacy of coher-
ence criteria has been demonstrated in various experiments in
which people trade the probability of being correct for increased
precision in their judgments (Yaniv & Foster 1995), thereby sac-
rificing probabilistic coherence for a possible gain in informational
content. It is not clear, however, how readily this fits into the fast
and frugal picture. Computing a trade-off between precision and
accuracy would appear to place additional processing demands on
the decision maker, contrary to the spirit of speed and frugality.
We believe that this problem is resolvable by identifying the
appropriate correspondence criterion, and the cognitive mecha-
nisms attuned to this criterion. Recent work in human causal in-
duction (López et al. 1998) suggests that predictive judgments are
mediated by associative mechanisms sensitive to real-world statis-
tical contingencies. Furthermore, it can be shown that networks
sensitive to such a measure automatically compute a precision/ac-
curacy trade-off. This suggests, contra Gigerenzer et al., that al-
though the mechanisms underlying our mental algorithms may be
simple, the computations which they embody need not be.
Fast and frugal heuristics:What about
unfriendly environments?
James Shanteau and Rickey P.Thomas
Department of Psychology, Kansas State University, Manhattan, KS 66506-
5302
{shanteau; thomas}@ksu.edu www.ksu.edu/isbr/shanteau.htm
Abstract: Simple heuristics that make us smart offers an impressive com-
pilation of work that demonstrates fast and frugal (one-reason) heuristics
can be simple, adaptive, and accurate. However, many decision environ-
ments differ from those explored in the book. We conducted a Monte
Carlo simulation that shows one-reason strategies are accurate in
“friendly” environments, but less accurate in “unfriendly” environments
characterized by negative cue intercorrelations, that is, tradeoffs.
Gigerenzer, Todd, and the ABC Research Group’s book offers an
impressive compilation of theoretical and empirical work on how
one-reason decision making can be both efficient and accurate in
appropriate environments (Gigerenzer et al. 1999). The interac-
tion between mind and environment is central to the book (see
Gigerenzer & Todd, Ch. 1). Simon’s “bounded rationality” con-
cerns the mind side of the interaction, that is, how the human
mind operates with limited computational capacity. “Ecological
rationality” concerns the environment side of the interaction,
namely, how decision strategies implemented by the mind are
adapted to the environment. The findings in the book demon-
strate convincingly that fast and frugal (F&F) heuristics can be
simple, adaptive, and accurate.
The environments examined are sampled from real-world do-
mains and share four important properties; choices are based (1)
on judgments of estimation/inference (2) between two alterna-
tives (3) with dichotomous cues (4) where cue intercorrelations
are positive. Such simple environments are an obvious place to be-
gin in a research program.
Many decision environments, however, possess different prop-
erties than those explored here (as recognized by Todd & Gigeren-
zer, Ch. 16). For instance, choice is often based on (1) preferences
(2) between more than two alternatives (3) with continuous cues
(4) in “unfriendly” environments. “Friendly” environments (of the
sort analyzed in this book) have intercorrelations that are positive
for the most valid cues. Rieskamp & Hoffrage (Ch. 7) are aware
of findings that suggest negative cue intercorrelations may signif-
icantly influence the decision process. We argue that unfriendly
environments must be considered when evaluating decision rules.
In many multiattribute problems cues are negatively correlated,
which implies the need to make tradeoffs (Stillwell et al. 1981).
For example, consumer decisions require a tradeoff between
price and quality, that is, an increase in quality (a good thing) can
lead to a price increase (a bad thing). Note that reverse scoring of
cues does not eliminate the tradeoff. In an unfriendly world, no
alternative exists that simultaneously maximizes all attribute di-
mensions (McClelland 1978). Decision-makers often make cas-
caded (multistage) choices, in which alternatives are successively
eliminated if they fail to meet certain minimal requirements
(Todd & Miller, Ch. 13). Such exclusion stages can dramatically
change cue intercorrelations. McClelland (1978) proves analyti-
cally that multiattribute cues are necessarily negatively correlated
for non-dominated alternatives. Johnson et al. (1989) further ar-
gue that negative cue intercorrelations arise in consumer deci-
sions whenever the market/consumer eliminates dominated al-
ternatives from consideration.
Does it matter whether environments are friendly or un-
friendly? The following simulation study was designed to provide
answers.
We compared three decision strategies in a Monte-Carlo simu-
lation: Lexicographic (LEX) strategy (Coombs 1974), Dawes’s
equal-weight (EQ) rule (Dawes & Corrigan 1974), and Multiat-
tribute utility (MAU) with Rank-Sum weights (Stillwell et al.
1981). LEX (a one-reason decision strategy) selects the alternative
with the highest utility for the most valid cue – a generalization of
Take The Best (Rieskamp & Hoffrage, Ch. 7). EQ serves as a non-
normative alternative and MAU (RS weights) serves as a norma-
tive alternative.
The decision strategies were evaluated for choices in three en-
vironments: friendly, neutral, and unfriendly. All decision envi-
ronments consist of two cues and three alternatives. The cues are
continuous bivariate normal with cue intercorrelations of .75
(friendly), 0 (neutral), and 2.75 (unfriendly). Five thousand deci-
sion problems were simulated for each environment. All results
were compared to the optimal weighted additive difference
(WAD) model using true weights. The entries in Table 1 are mean
selection accuracy, that is, the average proportion of times the de-
cision strategy selects the same alternative as WAD (true weights).
The accuracy results for all decision strategies decrease as the
environment changes from friendly to neutral to unfriendly. Just
as the authors contend, a one-reason strategy (LEX) performs as
well as other strategies in friendly environments (Martignon &
Hoffrage, Ch. 6; Todd & Gigerenzer, Ch. 16). However, the se-
lection accuracy of LEX is less in unfriendly environments.
Commentary/Todd & Gigerenzer: Simple heuristics
762 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
From other simulations, we have found the selection accuracy
of LEX generally decreases in unfriendly environments as (1) the
steepness of the tradeoff increases, (2) the number of important
cues increases, and (3) the number of alternatives increases.
Moreover in some unfriendly environments, the selection accu-
racy of LEX is lower than a random choice process.
We believe our findings are supported by common sense; one
good reason is not adequate for making decisions when there are
tradeoffs. When consumers buy a VCR, for instance, they do not
automatically go with the lowest price because the selected model
is likely to be of inferior quality. As Keeney and Raiffa (1993) note,
LEX is “naively simple” and “will rarely pass a test of reasonable-
ness” (pp. 77–78).
A related problem is that one-reason heuristics are not descrip-
tive of expertise. Experts generally work in complex environments
involving multiattribute decisions with multiple tradeoffs, that is,
negative cue intercorrelations. They typically follow a hierarchical
process, with different stages of decision making. Although a one-
reason rule may describe the final stage, one cannot conclude the
entire process consists of such simple processes (Phelps & Shan-
teau 1976).
In conclusion, one-reason decision making works well in the en-
vironments assumed in the book – two alternative estimation (or
inference) tasks where the cues are dichotomous and positively in-
tercorrelated (for examples, see Czerlinski et al., Ch. 5). Our sim-
ulations show that F&F rules also perform well when choices are
based on preference and the cues are continuous, as long as the
environment is friendly. One-reason decision making, however,
does not perform well in unfriendly environments (characterized
by tradeoffs) when there are more than two alternatives. Future
research is needed to determine how well modified (multistage)
F&F rules might do in such environments, for example, using
elimination and satisficing heuristics (Hertwig et al., Ch. 10;
Berretty et al., Ch. 11; Todd & Gigerenzer, Ch. 16). We look for-
ward to learning of the results from Gigerenzer, Todd, and the
ABC Research Group.
ACKNOWLEDGMENT
Preparation of this paper was supported in part, by Grant 98-G-026 from
the Federal Aviation Administration, Department of Transportation.
Heuristics and development:
Getting even smarter
Gregg E. A. Solomon
Decision Management Group and Department of Brain and Cognitive
Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139.
geas@psyche.mit.edu
Abstract: There are parallels between Gigerenzer et al.’s emphasis on the
rationality of adults’ reasoning in terms of simple heuristics and develop-
mental researchers’ emphasis on the rationality of children’s reasoning in
terms of intuitive theories. Indeed, just as children become better at us-
ing their theories, so might some people, experts, become better at using
simple heuristics.
Gigerenzer, Todd, and the ABC Research Group (1999) present a
welcome counter to the prevailing interpretation of human deci-
sion making: Left to our own devices, we tend to be irrational. The
issues raised in the debate over the extent to which people observe
the rules of logic recalls the debate in cognitive development con-
cerning the extent to which children observe the rules of logic and
how they become better thinkers.
The traditional, staunchly Piagetian, interpretation is that
young children’s reasoning does not adhere to the rules of formal
logic. Development, on such a view, can be described as the ac-
quisition of increasingly more powerful, domain-general reason-
ing structures. Just as the adult rationality literature has focused
on robust and compelling phenomena, the Piagetian research tra-
dition has yielded a collection of striking failures of logic. Not sur-
prisingly, the conception of the young child implicit in many sci-
ence education curricula in Euro-America is that of a thinker
incapable of formal logical reasoning. Consequently, for many of
these curricula, the preliminary goal is to teach children how to
think logically (e.g., Lawson & Thompson 1988). But the attempt
to improve children’s understanding of science through tuition in
the principles of logic has not been terribly successful (Bruer
1983). The literature on judgment errors would similarly indicate
that even adults who have been trained in logic and probability are
not immune to such errors, suggesting a lack of transfer of abstract
logical principles to real-world decision making.
In recent years, cognitive science has broken with the concept
of the child as a fundamentally different kind of thinker (e.g.,
Carey 1985). Many researchers have come to describe them as
possessing powerful intuitive or framework theories that guide
their understanding of the world about them (Wellman & Gelman
1992). Gigerenzer and Todd share this notion that we can have dis-
positions to reason within particular domains in terms of specific
principles, and that such privileged ways of reasoning are trig-
gered by specific cues. An integral part of the framework theory
is still an account of how children’s thinking develops, of how they
get better at making predictions about the world. The educational
implications of this characterization of cognitive development are
an emphasis on teaching facts, as well as on addressing the frame-
works in which children interpret their new facts.
Gigerenzer et al.’s model, unfortunately, gives development
short shrift. This is not to say that their ABC research program
precludes a developmental component. Far from it; their lack of
attention to educational implications of heuristics is more likely a
consequence of their (delightfully perverse) emphasis on demon-
strations of superior novice performance. There is again a paral-
lel in the framework theory literature. Many developmental re-
searchers, in their rush to demonstrate the brilliant rationality of
little children, have done so at the expense of a recognition of dif-
ferences between children’s early theories and the target adult
theories. So too do the ABC researchers pay little attention to pos-
sible expert/novice differences. If there are such things as experts
(granting that there is no single kind of expertise), then there is a
place in this research program for the study of development.
What, if anything, do experts do that novices do not in their use
of heuristics? Borrowing again from the debate in cognitive de-
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 763
Table 1 (Shanteau & Thomas). Average selection accuracy
of three decision strategies in friendly, neutral,
and unfriendly decision environments
Strategy
Environment LEX EQ RS
Friendly 0.90 0.93 0.96
Neutral 0.80 0.84 0.90
Unfriendly 0.76 0.70 0.84
Note. The average selection accuracy estimates are based on
comparisons with WAD across five true weight vectors ({.50, .50},
{.60, .40}, {.70, .30}, {.80, .20}, and {.90, .10}).
velopment, we might expect two broad courses of development:
continuous and discontinuous. It can be argued that young chil-
dren reason about particular phenomena (e.g., folk-psychology) in
qualitatively the same ways as adults do, but their predictions of-
ten differ simply because they do not know as much as adults do.
Do experts in a particular domain use the same heuristics as do
novices, but merely use them better, more efficiently? For exam-
ple, surely the Take The Best heuristic yields improved perfor-
mance when employed by individuals with more experience on
which to base their estimations of which cues have been more suc-
cessful.
By contrast, there are other domains of thought in which chil-
dren’s theories would appear to undergo conceptual change. For
example, young children may respond to cues in “living things”
that lead them to reason in a manner more appropriate to folk-
psychology than folkbiology (see Carey 1985). Children arguably
come to interrelate concepts concerning living things in a qualita-
tively different manner; there is a change in which cues are rec-
ognized as centrally important. Similarly, it may be that experts
and novices alike invoke heuristics in a particular domain, but they
could differ immensely in their choices of search, stop, or decision
making strategies. Indeed, novices, given their relative ignorance,
might tend to rely on default dispositions to recognize particular
cues in specific domains, whereas experts might be driven by ex-
plicit theories to attend to particular cues and in terms of particu-
lar heuristics (e.g., in the domain of wine tasting, see Solomon
1997). The expert strategies might be more ecologically rational,
more suited to the particular environmental structures, but
novices might not know enough to realize this (not unreasonably,
in the case of wine tasting, novices’ decision strategies would ap-
pear more suited to making predictions about beverages in gen-
eral rather than wines in particular). Finally, it remains to be seen
to what extent novices (and children) can be trained in more effi-
cient use of heuristics. At the very least, the nature of such inter-
ventions ought to reflect an attention to the nature of the specific
differences between experts and novices, rather than a general at-
tention to logical ability.
Damn it, I still don’t know what to do!
Robert J. Sternberg
Department of Psychology, Yale University, New Haven, CT 06520-8205.
robert.sternberg@yale.edu www.yale.edu/rjsternberg
Abstract: The simple heuristics described in this book are ingenious but
are unlikely to be optimally helpful in real-world, consequential, high-
stakes decision making, such as mate and job selection. I discuss why the
heuristics may not always provide people with such decisions to make with
as much enlightenment as they would wish.
Simple heuristics that make us smart (Gigerenzer et al. 1999) is a
wonderful, ingenious, and even brilliant book. I found it one of the
most interesting psychology books I have read in quite a while. It
is a milestone that helps move human decision-making research
into a new post-Kahneman-and-Tversky era.
I was delighted to receive the book when I did, because it ar-
rived when I was (and still am) in the throes of a very difficult,
high-stakes decision – whether to remain at the institution where
I am currently teaching or to accept another job offer. Much as I
enjoyed reading the book, when I finished it, I threw up my hands
and said to myself, “Damn it, I still don’t know what to decide.”
Why?
Stakes in decision making.
Most (although certainly not all) of
the decisions described in the book are for very low stakes. How
much do I care whether San Diego has more inhabitants than San
Antonio, how much houses cost in Erie, Pennsylvania, how fertile
395 Arctic char are, or how much oxygen is absorbed by cow ma-
nure? In making these decisions, I would happily go for any of the
one-reason heuristics for decision making. But I would be much
more reluctant to do so when an important life decision is at stake.
Although the kinds of problems used by Gigerenzer, Todd, and
their colleagues are several steps up from poker chips, most of
them are still a step down from consequential life decisions.
Some of the decisions described in the book are potentially con-
sequential, such as investing in the stock market, choosing a mate,
and investing in children. Whether most people will feel comfort-
able investing solely on the basis of name recognition of compa-
nies remains to be seen. But I found the advice on mate-selection
decisions and parental investment less than useful. Why?
What are the attributes and what are their weights?
Issues with
regard to mate selection are described in terms of a dowry prob-
lem, where one is trying to select the mate who will produce the
highest dowry. This decision and others in the chapter differ from
real mate-selection decisions, however, in that the attributes in-
volved are clearly specified and unidimensional. But in real-life
mate selection, at least for many people, there is no obvious at-
tribute, such as a dowry, that can be readily quantified and ex-
pressed unidimensionally. Often it is not even clear what the at-
tributes are, or if they are identified, which ones should matter at
all.
The chapter repeatedly refers to one mate choice being better
than another or in the top such-and-such percent, but much of the
problem is figuring out the attributes to use to decide who is bet-
ter than whom. And having figured out the attributes, one still
needs to figure out their weights. These issues, discussed in so
much detail for the less consequential decisions, are bypassed for
this kind of more consequential decision.
Multiple interests.
The chapter on mate selection as well as that
on parental investment are especially interesting because they
touch on a further issue that characterizes real-life high-stakes de-
cisions but that does not characterize most of the decisions con-
sidered in this book. In everyday life, many interests are involved.
In truth, mate selection does not just involve the self and the part-
ner. It usually also involves interests of parents, friends, members
of reference groups, and so forth. A career decision, too, often in-
volves many different parties, as do union-management negotia-
tions, international negotiations, and the like.
Gigerenzer et al. deserve credit for looking at many decision-
making contexts. But many of the contexts are rather different
from the decisions that truly matter in one’s life.
What is missing.
Other issues such as those mentioned above
could be raised, but my goal is not to be exhaustive but rather to
make a more general point. The kind of decision making described
here, in many cases, is reminiscent of the kinds of problem solv-
ing found on conventional tests of mental abilities. The items
clearly measure important skills, but perhaps not those that will
matter most to who succeeds in real-life decision making or prob-
lem solving so that colleagues, spouses, and friends unaware of test
or task scores will label the person as “smart.”
Consequential real-world decision making and problem solving
are often different in kind from the decision making and problem
solving represented by low-stakes problems that to participants
may seem contrived. Our own data suggest that there is little or
no correlation between performance on the two kinds of tasks
(Sternberg et al. 2000). Even the real-world tasks studied, such as
mate selection and parental investment, are not studied in a way
that is likely to be maximally helpful to people facing serious
everyday constraints. For example, it is not at all clear that parents
can or will “rely on simple rules to guide their investment in their
children” (p. 309), or that we would label as “smart” parents who
do so.
One book later, I am still stuck as to my employment decision.
I could try just counting the top two considerations, if I could fig-
ure out what they are or even should be. But that is much of the
problem. Wonderful though the book may be, I suspect that many
others seeking decision rules for the high-stakes decisions they en-
counter in their lives will not find that the rules in this book will
make their decisions all that easy. Damn.
Commentary/Todd & Gigerenzer: Simple heuristics
764 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
ACKNOWLEDGMENT
Preparation of this report was supported by Grant R206R950001 from the
U.S. Department of Education, Office of Educational Research and Im-
provement. Such financial support does not constitute agreement with or
support for any of the statements made in this article.
Smart people who make
simple heuristics work
Annika Wallin and Peter Gärdenfors
Lund University Cognitive Science, Kungshuset, Lundagård, 222 22 Sweden.
{annika.wallin; peter.gardenfors}@lucs.lu.se
www.lucs.lu.se/People/{Annika.Wallin; Peter.Gardenfors@lucs.lu.se
Abstract: To evaluate the success of simple heuristics we need to know
more about how a relevant heuristic is chosen and how we learn which
cues are relevant. These meta-abilities are at the core of ecological ratio-
nality, rather than the individual heuristics.
Gigerenzer, Todd, and the ABC Research Group (1999) focus on
simple heuristics for decisions instead of optimization procedures
that presume unbounded rationality. We agree that this is an im-
portant step toward an understanding of the cognitive processes
underlying human (and animal) decision making. However, Gi-
gerenzer et al. mainly explain the success of simple heuristics as
an exploitation of the structure of our natural environment. We
wish to add that it is not the simple heuristics in themselves that
make us smart. Knowing how to choose the right heuristic in the
right context and how to select relevant cues is just as important
in the decision process (regardless of whether theses choices are
conscious or unconscious). In brief, we are smart enough to make
simple heuristics work and before we can evaluate the role of sim-
ple heuristics, we must know more about how people choose to
apply a particular heuristic in a given decision situation.
A heuristic must be applied in a context where it can reliably
utilize the world’s natural structure. For instance, the recognition
heuristic is most sensibly used when there is a (causal) connection
between the fact that we recognize something, and whatever fac-
tor it is we are trying to determine. In the examples presented, the
environmental criteria presumed by the heuristics are fulfilled by
the selection of examples. However, there are plenty of real world
situations where this is not the case. If these heuristics are applied
in such situations, they may not be as successful as Gigerenzer et
al. claim. To repair this, one must add to the description of the
heuristics how they take advantage of the environmental structure
through our ability to find and understand certain regularities.
In order to apply most heuristics successfully, it is also neces-
sary to know the value of the cues that are utilized. Another fea-
ture of Gigerenzer et al.’s examples is that knowledge concerning
the relevant cues is accessible to the decision maker. The selection
and ecological ordering of cues had already been made in the con-
text the examples came from (mostly statistical textbooks). The
ecological rationality of a heuristic such as Take The Best cannot
be evaluated until we know more about how the cues are selected.
The value of a cue is judged by its ecological validity, which
Gigerenzer et al. define as the proportion of correct predictions
generated by the cue. Knowledge about the ecological validity of
different cues is necessary for successful application of several of
the heuristics studied by Gigerenzer et al. However, in a practical
decision situation, agents must select the cues themselves and
have no guarantee that the most relevant ones have been found.
In such a situation, there is often no way of knowing whether the
best decision was made. Hence there is a double difficulty in de-
termining the validity of the cues.
We believe that ecological validity should be seen as only a sec-
ondary effect of the fact that a decision maker aims at forming hy-
pothesis about causal connections between the cues and the deci-
sion variable. The causal reasoning involved in this process may
better explain how the decision makers act than the statistical cor-
relations that are used in Take The Best and the other heuristics.
Unfortunately, Gigerenzer et al. do not discuss this kind of causal
reasoning (Glymour 1998; Gopnik 1998).
Even if we stick to the ecological validity studied by Gigerenzer
et al., it will be important to know how humans learn the correla-
tions. One reassuring finding is that humans are very good at de-
tecting covariations between multiple variables (Billman & Heit
1988; Holland et al. 1986). (But we don’t know how we do it.) This
capacity is helpful in finding the relevant cues to be used by a
heuristic. The ability can be seen as a more general version of
“ecological validity” and it may thus be used to support Gigeren-
zer et al.’s arguments.
Another aspect of the role of the experience of the agent is that
the agent has some meta-knowledge about the decision situation
and its context which influences the attitude of uncertainty to the
decision. If the type of situation is well-known, the agent may be
confident in applying a particular heuristic (since it has worked
well before). But the agent may also be aware of her own lack of
relevant knowledge and thereby choose a different (less risk-
prone) heuristic. The uncertainty pertaining to a particular deci-
sion situation will also lead the agent to greater attentiveness con-
cerning which cues are relevant in that kind of situation.
We have focused on two problems that have been neglected by
Gigerenzer et al.: How the decision maker chooses the relevant
heuristics and how the decision maker learns which cues are most
relevant. We believe that these meta-abilities constitute the core
of ecological rationality, rather than the specific heuristics that are
used (whether simple or not). In other words, the important ques-
tion concerning the role of heuristics is not whether the simple
heuristics do their work, but rather whether we as humans possess
the right expertise to use a heuristic principle successfully, and
how we acquire that expertise.
From Simon’s scissors for rationality
to ABC’s adaptive toolbox
X.T.Wang
Psychology Department, University of South Dakota, Vermillion, SD 57069.
xtwang@usd.edu
Abstract: The smartness of simple heuristics depends upon their fit to the
structure of task environments. Being fast and frugal becomes psycholog-
ically demanding when a decision goal is bounded by the risk distribution
in a task environment. The lack of clear goals and prioritized cues in a de-
cision problem may lead to the use of simple but irrational heuristics. Fu-
ture research should focus more on how people use and integrate simple
heuristics in the face of goal conflict under risk.
1. A scissors missing one blade.
Bounded rationality, accord-
ing to Herbert Simon, is shaped by a scissors whose two blades are
“the structure of task environments and the computational capac-
ities of the actor” (1990, p. 7). However, an overview of the stud-
ies of human reasoning and decision making shows an unbalanced
achievement. We have gained a great deal of knowledge about hu-
man computational capacities over the last several decades, but
have learned little about the roles of the structure of task envi-
ronments played in human rationality.
Although persistent judgmental errors and decision biases have
been demonstrated in cognitive studies, biologists, anthropolo-
gists, and ecologists have shown that even young monkeys are
adept at inferring causality, transitivity, and reciprocity in social re-
lations (e.g., Cheney & Seyfarth 1985) and foraging birds and bees
are rational in making risky choices between a low variance food
source and a high variance one based on their bodily energy bud-
get (e.g., Real & Caraco 1986; Stephens & Krebs 1986). This pic-
ture of “rational bees and irrational humans” challenges the Lapla-
cian notion of unbounded rationality and calls for attention to the
Commentary/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 765
mapping between our mental structure and the structure of evo-
lutionary, ecological, and social environments.
In answering such a call, Gigerenzer et al. (1999) provide us
with a toolbox of fast and frugal heuristics designed to work in dif-
ferent task environments. The book offers a ground-breaking syn-
thesis of Simon’s concept of satisficing (e.g., 1956a; 1990) and
Brunswik’s concept of vicarious functioning (e.g., 1940) with ap-
pealing theoretical ideas, thorough computer simulations and
initial empirical testing. This team work of the ABC (Adaptive
Behavior and Cognition) group represents a major advance in un-
derstanding human rationality under real-world constraints.
2. Satisficing goal setting and cue ranking.
The smartness of
simple heuristics depends on their fit to the structure of task envi-
ronments. A lack of these constraints in task environments would
devastate the search process for cues. An important issue raised by
the book concerns the priority structure of decision cues. The pro-
posed simple heuristics are primarily procedural heuristics deal-
ing with the selection and integration of cues. However, these fast
and frugal heuristics would not work effectively if one did not know
the priority ranking of relevant cues. Thus, how to sort out valid
cue ranking in a task environment, particularly when risks are in-
volved, becomes essential for the success of simple heuristics. Al-
though cue ranking determines the use of simple heuristics, goal
setting in a task affects the ranking of relevant cues.
The functional values of fast and frugal heuristics can be viewed
in a framework of goal setting and problem solving in which a de-
cision maker is expected to maximize the opportunity of reaching a
task-specific goal (see also, Lopes 1987). Being fast and fru-
gal becomes psychologically demanding when a decision goal is
bounded by the risk distribution in a task environment. The simple
heuristics become even more useful when the risk factors are taken
into account. Under risk, one needs not only consider a task-spe-
cific goal but also a task specific minimum requirement (e.g., to get
x amount of y before the deadline z). In such a situation, to search
for a satisficing solution under task constraints is to maximize the
likelihood of reaching a goal and minimize the likelihood of falling
below a minimum requirement at the same time. In contrast to the
normative concept of maximizing expected utility values, a choice
alternative yielding the highest expected value may not have a risk-
variance distribution that satisfies the task constraints as measured
by both the goal level and minimum requirement.
Goals not only define the relevance of decision cues but also de-
fine psychological accounting in making decisions. For instance,
as demonstrated by Tversky and Kahneman (1981), one is more
likely to buy a theater ticket for $10 after losing a $10 bill than to
buy a ticket again after losing a $10 ticket. Presumably, the loss of
a $10 bill is a goal-irrelevant event and thus a small loss in an in-
dividual’s overall wealth. In contrast, the loss of a $10 ticket is re-
lated to the goal of seeing a play and thus a larger loss in the ac-
count that is set up along with the goal.
On the other hand, the lack of clear goals and prioritized cues
in a decision problem may lead to the use of simple but irrational
heuristics. To illustrate the point consider the framing effect dem-
onstrated in the Asian disease problem by Tversky and Kahneman
(1981). The observed reversal in risk preference as a result of ways
in which a choice problem is presented violates the descriptive in-
variance principle of normatively defined rationality. As a matter
of fact, this irrational reversal in risk preference can be attributed
to the use of a simple heuristic which directs the decision maker
to be risk-averse when choice outcomes are framed positively, but
risk-seeking when the same outcomes are framed negatively.
Our studies (Wang 1996a; 1996b) suggest that the use of such
simple but dumb heuristics is a result of the lack of clear task goals.
This irrational framing effect disappears when the problem is pre-
sented in a kinship context or when the group size of endangered
lives is reduced to a single- to two-digit number which approxi-
mates a typical group size throughout most of human evolution.
The kinship cue and group size cue have made a sure outcome of
saving one-third of endangered lives unacceptable and forced the
decision makers to choose the gamble option irrespective of the
hedonic cues of verbal framing. Consistent with the Take-The-
Best heuristic, subjects’ risky choice is determined by the most
dominant decision cue whose presence overwhelms the secondary
cue of outcome framing. Kinship, group size, and other social and
biological concepts may help us understand goal setting and cue
ranking in social decisions. Relying on valid cue ranking, fast and
frugal heuristics are no longer quick and dirty expediencies but
adaptive mental tools for solving problems of information search
and goal conflict at risk.
Heuristics refound
William C.Wimsatt
Department of Philosophy and Committee on Evolutionary Biology, The
University of Chicago, Chicago, IL 60637.
w-wimsatt@uchicago.edu
Abstract: Gigerenzer et al.’s is an extremely important book. The ecolog-
ical validity of the key heuristics is strengthened by their relation to
ubiquitous Poisson processes. The recognition heuristic is also used in con-
specific cueing processes in ecology. Three additional classes of problem-
solving heuristics are proposed for further study: families based on near-
decomposability analysis, exaptive construction of functional structures,
and robustness.
This is an extremely important book. It could precipitate a second
wave of interest in bounded rationality – delivering the revolution
begun by Herbert Simon in the late 1940s with his “satisficing”
model of decision making. Gigerenzer, Todd, and the ABC Re-
search Group (1999) argue the natural affinity of their “fast and
frugal” heuristics to new developments in social cognition; Simon’s
model came out of a study of corporate decision making in ad-
ministrative structures – decisions which are both satisficed and
distributed. Ecological rationality also figures in Simon’s original
work, and even more centrally in the present work. With its new
tools, results, perspectives, and diverse applications, this book
should give significant direction to that new wave, while confirm-
ing the original deep insights of Simon’s first wave.
This is an amicus curae brief for this new program from a long-
time devotee and user of Simon’s work. Most central are the strik-
ing experimental results and simulations with the “recognition”
and “take the best” heuristics, and their “ecological” analyses to
determine the conditions under which they should be expected to
work well, and when they should break down. These chapters are
extremely well done. The robustness, economy, and simplicity of
the heuristics under these conditions make them important, but
the crisp analysis of their limits is also a methodological paradigm
for future workers. The varied applications in Chapters 9 through
14 only begin to suggest the fruitfulness of this new paradigm. One
of my favorites is the chapter on hindsight bias (Ch. 9). It is a pow-
erful argument for the “fast and frugal” approach in that it yields
such a revealing account of this ubiquitous and seemingly unre-
lated phenomenon – making it a signature of such methods.
The ecological rationality of these procedures noted in Chapter
10 deserves particular emphasis: the J-shaped distributions re-
quired for the robustness of these procedures should themselves
be extremely robust: they are produced by power laws (empha-
sized by physicist Per Bak) and more generally by Poisson pro-
cesses, which are ubiquitous in nature. Poisson distributions for
objects and processes in nature do not guarantee Poisson dis-
tributions for cue validities (what else is required?), but are very
suggestive, and worth more attention. If this connection can be
fleshed out, it would be hard to imagine a more robust way of an-
choring these procedures in a stochastic world.
The recognition heuristic is both inevitable and advantageous
in another ecological situation: so called “conspecific cueing.”
Colonizing species or organisms with wide ranges may cover large
amounts of territory in search of food, nest sites, or other re-
sources. Because they would leave unsuitable areas quickly and
Commentary/Todd & Gigerenzer: Simple heuristics
766 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
spend more time in suitable ones, the presence of a conspecific,
when rare, is a good indicator of the suitability of an area. And
most species already have and need means for recognizing con-
specifics for mating, territory defense, migration, and other ends.
Many use specific marking behaviors to indicate their presence,
and can detect the age, sex, and other characteristics of other
markers (Kiester 1979; Stamps 1987).
But there are other problem areas which could be fruitfully
searched for “fast and frugal” strategies. The three classes of
heuristics below are effective, simplifying, and extremely widely
used. They would benefit from a similar analysis.
The first, “near-decomposability” heuristics, also received pi-
oneering elaborations by Simon. They are at the core of reduc-
tionistic and “analytic” problem-solving methods in all areas (Si-
mon 1996; Simon & Ando 1961; Wimsatt 2000a). One approaches
a problem by trying to break it into sub-problems which can be
solved independently and whose solutions can then be strung to-
gether as a solution, or the first try at one, for a more complex
problem. It is crucial in the analysis of complex systems and the
synthesis of composite systems, but also in planning for and exe-
cuting any complex task – either an extended task by an individ-
ual or a coordinated plan (e.g., for hunting) by a group of individ-
uals. Not all complex problems are solvable in this way (there may
be complex interactions between subsystems which cannot be
treated in this quasi-modular fashion), but the architecture of our
own artifacts is likely skewed in this direction as a result of our own
cognitive methods.
The second are “exaptive” heuristics. Gould and Vrba (1982) note
that many things classified as adaptations were not originally cre-
ated for the ends they now serve. Evolution, human engineering,
science, and culture all systematically reuse constructs in new con-
texts that drive their elaboration in new directions. It is simply eas-
ier to take something which you already have and can make do
(perhaps with simple modifications) for the new task. And it is exap-
tations all the way down. As a result, one cannot understand the
functional organization of any complex system without considering
its history. And some deep problems – the Y2K fiasco – can be
traced to early trivial decisions whose consequences propagated so
widely that their correction is immensely costly (Wimsatt 2000b).
A third class of “robustness” strategies use multiple presump-
tively independent means to locate something, triangulate on its
properties, cross-check and calibrate the means of access, and
more generally decide what is real and trustworthy and what is
fleeting and artifactual. These strategies are widely used in our
perceptual systems, and in scientific inference (Wimsatt 2000a).
Authors’ Response
How can we open up the adaptive toolbox?
Peter M.Todd, Gerd Gigerenzer, and the ABC
Research Group
Center for Adaptive Behavior and Cognition, Max Planck Institute for Human
Development, 14195 Berlin, Germany
{ptodd; gigerenzer}@mpib-berlin.mpg.de
www.mpib-berlin.mpg.de/abc
Abstract: The adaptive toolbox is an evolutionarily inspired vision
of the mechanisms of cognition, including simple decision making
heuristics for specific problem domains. In Simple heuristics we
showed how different heuristics in the adaptive toolbox could be
constructed for different tasks, and how they could achieve eco-
logical rationality (being accurate and robust) by exploiting the
structure of information in the environment. Our commentators
have raised a number of important challenges for further extend-
ing the study of ecological rationality. Here we summarize those
challenges and discuss how they are being met along three theo-
retical and three empirical fronts: Where do heuristics come
from? How are heuristics selected from the adaptive toolbox?
How can environment structure be characterized? How can we
study which heuristics people use? What is the evidence for fast
and frugal heuristics? And what criteria should be used to evalu-
ate the performance of heuristics?
In Simple heuristics that make us smart (Gigerenzer et al.
1999), we introduced the main concepts for studying the
cognitive mechanisms that make up the adaptive toolbox:
the idea of simple heuristics whose building blocks are pre-
cisely specified (simple rules for search, stopping, and de-
cision), the way heuristics achieve ecological rationality by
exploiting the structure of information in the environment,
and how they can be accurate and robust through being fast
and frugal. The adaptive toolbox is inspired by a Darwinian
vision of decision making in humans, animals, and artificial
agents. First, just as evolution does not follow a grand plan
but results in a patchwork of solutions for specific prob-
lems, so the toolbox is structured as a collection of mecha-
nisms that each do a particular job. Second, just as evolu-
tion produces adaptations that are bound to their particular
context, the heuristics in the adaptive toolbox are not good
or bad, rational or irrational, per se, but only relative to a
particular environment. From these two features springs
the potential power of simple heuristics: They can perform
astonishingly well when used in a suitable environment.
The vision of the adaptive toolbox conflicts with several
beautiful ideals, which some of the commentators share ex-
plicitly or implicitly. These ideals have their origins in a long
philosophical tradition in which humans are recreated in
the image of an omniscient God, or in a secularized version
thereof, Laplace’s superintelligence. The principles under-
lying the adaptive toolbox also have a long pedigree, from
Darwin to Herbert Simon. We therefore begin by stating a
few of the idealistic assumptions taken at face value by some
of our commentators, and the opposing principles underly-
ing the adaptive toolbox:
1. More information is always better. One-reason deci-
sion making is granted by Sternberg for everyday affairs
but not for “consequential” decisions, conveying the im-
plicit assumption that you are always better off using as
much information as possible when time allows. The ideal
that more information is always better is, however, mis-
leading. Rather, in order to make sound decisions in an
uncertain world, one must ignore some of the available in-
formation. The reason is that not all of the information
available about one situation is useful for making judgments
about another – a strategy that used all the available infor-
mation would fall prey to overfitting and be unable to make
robust generalizations. The trick – the job of frugal heuris-
tics – is to ignore the proper pieces of information. Engel
points out that frugality also conflicts with legal systems,
which (like bureaucracies) often run on the defensive vision
that more is always better.
2. Optimization is always better. Shanks & Lagnado
imply that because human behavior can be optimal, fast and
frugal heuristics, which do not optimize, cannot account
for it. But the distinction must not be blurred between op-
timizing processes (e.g., computing the maximum of some
function such as expected utility), which heuristics do
not employ, and optimal outcomes, which heuristics can
Response/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 767
nonetheless reach. Moreover, using optimization does not
guarantee an optimal outcome for a given situation, be-
cause the choice of optimizing process must often be made
based on uncertain simplifying assumptions. Similarly, the
optimal strategy in a particular domain will usually not gen-
eralize to being optimal in a different domain, because of
the particular assumptions on which optimization must be
based. The considerations of speed, simplicity, robustness,
and psychological plausibility can add to make heuristics a
better choice in particular situations.
3. Complex environments demand complex reasoning
strategies. Allen suggests that social environments, being
“responsive” rather than “passive,” are so complex and
quixotic that they require demonic reasoning abilities (cf.
the Machiavellian intelligence hypothesis on the social evo-
lution of intelligence; Whiten & Byrne 1997), or at least the
application of logic and probability theory. In particular, the
assumption is that if you do not reason logically, you can be
exploited by others. But simple social exchange rules (e.g.,
cheater detection; see Cosmides & Tooby 1992) can coor-
dinate social interactions without logical reasoning. Con-
versely, following logic can make one predictable and hence
open to exploitation (Frank 1988), making “illogical” pro-
tean behavior more adaptive in many situations (Driver &
Humphries 1988).
4. Search can be ignored. Oaksford argues that infor-
mation is usually integrated in decision making by pointing
to examples (such as speech perception and sentence pro-
cessing) where the necessary information is available si-
multaneously, obviating search. But integration seems less
universal when one recognizes that many decision situa-
tions require cues to be searched for, whether internally in
memory or externally in the world. In such cases, there is
evidence for fast and frugal mechanisms that stop informa-
tion search as soon as possible, coupled with decision rules
that do not integrate information (see sect. 5). (This may
also apply in some of the language processing examples that
Oaksford draws upon, according to optimality theory’s lex-
icographic search for rules; see Prince & Smolensky 1997.)
By ignoring the need for search, we can easily overlook
those situations in which information is not integrated – one
of the territories of simple heuristics.
Simple heuristics is a progress report of our first three
years of studying the adaptive toolbox. As many of the com-
mentators agreed, there is a need for a new alternative to
rational choice theory and other demonic visions of deci-
sion making in fields ranging from primatology, to cognitive
psychology, to philosophy, and we are grateful to the com-
mentators for pointing out the important open questions in
this program and suggesting some possible answers. We
have organized this reply around six open questions raised
by the commentators. The three major theoretical questions
are: Where do heuristics come from? How are heuristics se-
lected from the adaptive toolbox? How can environment
structure be characterized? The three methodological and
empirical questions are: How can we study which heuristics
people use? What is the evidence for fast and frugal heuris-
tics? What criteria should be used to evaluate the perfor-
mance of heuristics?
Before we address these pressing questions, we want to
clarify one issue. We called the book “Simple heuristics that
make us smart” rather than “Simple heuristics make us
smart” for a good reason. We do not believe, and do not
want to be misconstrued as saying, that the set of simple
heuristics and the set of things that make us smart are iden-
tical. Not every reasoning task is tackled using simple
heuristics – some may indeed call for lengthy deliberation
or help from involved calculations. Conversely, not every
simple strategy is smart. Thus, the key question organizing
the overall study of the adaptive toolbox is that of ecologi-
cal rationality: Which structures of environments can a
heuristic exploit to be smart?
R1. Where do heuristics come from?
Several commentators have called for clarification about
the origins of heuristics. There are three ways to answer this
question, which are not mutually exclusive: heuristics can
arise through evolution, individual and social learning, and
recombination of building blocks in the adaptive toolbox.
R1.1. Evolution of heuristics
Ecologically and evolutionarily informed theories of cogni-
tion, are approved by Baguley & Robertson but they ex-
press concern over how the adaptive toolbox comes to be
stocked with heuristics. The book, they say, sometimes
leaves the reader with the impression that natural selection
is the only process capable of adding a new tool to the tool-
box, whereas humans are innately equipped to learn certain
classes of heuristics. We certainly did not want to give the
impression that evolution and learning would be mutually
exclusive. Whatever the evolved genetic code of a species
is, it usually enables its members to learn, and to learn some
things faster than others.
For some important adaptive tasks, for instance where
trial-and-error learning would have overly high costs, there
would be strong selective advantages in coming into the
world with at least some heuristics already wired into the
nervous system. In Simple heuristics, we pointed out a few
examples for heuristics that seem to be wired into animals.
For instance, the recognition heuristic is used by wild Nor-
way rats when they choose between foods (Ch. 2), and fe-
male guppies follow a lexicographic strategy like Take The
Best when choosing between males as mates (Ch. 4). A
growing literature deals with heuristics used by animals that
are appropriate to their particular environment, as Hous-
ton points out. This includes distributed intelligence, such
as the simple rules that honey bees use when selecting a lo-
cation for a new hive (e.g., Seeley 2000).
Hammerstein makes the distinction between an opti-
mizing process and an optimal outcome very clear. He dis-
cusses the view generally held in biology of how decision
mechanisms including simple heuristics can arise through
the optimizing process of evolution (often in conjunction
with evolved learning mechanisms). This does not imply
that the heuristics themselves (nor specific learning mech-
anisms) are optimizing, that is, that they are calculating the
maximum or minimum of a function. But they will tend to
be the best alternative in the set of possible strategies from
which evolution could select (that is, usually the one clos-
est to producing the optimal outcome). As Hammerstein
says, biology meets psychology at this point, because inves-
tigations of psychologically plausible – and ecologically ra-
tional – decision mechanisms are necessary to delineate the
set of alternatives that evolutionary selection could have op-
erated on in particular domains.
Response/Todd & Gigerenzer: Simple heuristics
768 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
Hammerstein also reminds us that the absence of opti-
mality in observed behavior does not imply that evolution
had no role in building the heuristics involved; instead, a
heuristic that was evolved for adaptive use in one environ-
ment may be misapplied in another. An example is decision
heuristics that appropriately neglect base rate information
in some circumstances (such as in changing environments;
see Goodie & Todd, submitted), but which are tripped up
by this simplicity in other situations (for instance ignoring
base rates when they are stable and useful). Here again psy-
chologists can work together with biologists to understand
behavior that might otherwise be relegated to the category
of irrational biases.
R1.2. Learning and development of heuristics
R1.2.1. Individual learning. Certain classes of heuristics
can be learned, state Baguley & Robertson. Certainly
people can learn new problem-solving techniques, but
there is a distinction to be drawn between adding a new
component to the adaptive toolbox and learning to use the
tools already there in new ways (parallel to Wimsatt’s evo-
lutionary example of exaptations as borrowed adaptations).
Solomon’s commentary is useful in this regard: he points
out that since Piaget, the search for domain-general princi-
ples of reasoning and decision-making in children – and the
cataloging of their “failures of logic” – has been eclipsed by
interest in domain-specific reasoning principles that chil-
dren use in particular contexts or environments. Two gen-
eral conclusions that can be drawn from the developmen-
tal literature to which Solomon refers are (1) that young
children, and even infants, apply different reasoning prin-
ciples in different problem domains (the infant’s adaptive
toolbox already contains multiple tools), and (2) that chil-
dren know when and how to apply these tools from a very
early age (see, e.g., Baillargeon 1986; Csibra et al. 1999;
Spelke 1990).
Solomon distinguishes two kinds of developmental
change that map onto the distinction mentioned above be-
tween adding new tools and using old tools in new ways:
change in the core “theories,” concepts, or reasoning prin-
ciples deployed in a particular domain – what might be
called the tools in the adaptive toolbox (see, e.g., Carey
1985; Gopnik & Meltzoff 1997) – and change in “expertise”
with age, that is, changes in the stores of data upon which
particular tools can be brought to bear, or in how and when
the tools are used. An important area to be explored is thus
the developmental trajectories of different domain-specific
heuristics. For example, Klayman (1985) showed that 12-
year-olds tend to use more frugal strategies in complex
search tasks than adults, though many of the strategies used
by adults are present by age 12.
Simple heuristics did not much address individual learn-
ing and development. But this does not mean that the no-
tion of the adaptive toolbox should be seen as irrelevant for
developmental researchers. On the contrary, as Solomon
points out, the adaptive toolbox perspective raises a set spe-
cific developmental questions: What heuristics come pre-
loaded into the adaptive toolbox? Which ones drop out over
time, which are added, and which are modified? Can the
change in heuristic use over time be matched to changes in
the environment facing growing children? What heuristic
principles for search do children use (e.g., random search,
ordered search), when do they stop search, and how do they
arrive at a decision? And how do children acquire new
heuristics?
R1.2.2. Social learning. Primatologists Barrett & Henzi
wonder whether fast and frugal heuristics are the result of
our primate heritage, or even a specifically human form of
reasoning not available to other primate species. Although
such an extreme position is almost certainly untenable
(as Houston indicates, biologists have long been satisfied
with the idea that animals of all phyla use simple decision-
making rules), humans probably are extreme in our reliance
on social learning of heuristics. This enables much more
rapid increase in the contents of the adaptive toolbox and
provides a foundation for culture.
Gorman points out that there are many domains of hu-
man endeavor, including scientific discovery, where heuris-
tics can be obtained from other individuals, but wonders
whether heuristics might be applicable in the search for
whom to borrow from as well. In this line, Goldman also de-
scribes how the decisions themselves (not just the strategies)
can be obtained from others: For instance, it can make sense
to copy someone with similar political views but more infor-
mation about the candidates, and just vote for whomever she
chooses. There is a growing body of work, primarily cover-
ing other species, that explores the simple mechanisms that
can be used for these sorts of social information exchange
(Noble & Todd, in press). This research has focused on the
ways that imitation-like behavior can be achieved without
the necessity of the imitator modeling the intentions and ac-
tions of the imitated individual; indeed, what looks like imi-
tation can often be the result of one agent merely following
another around and being prompted by the same environ-
mental cues. Explicit language-based instruction and infor-
mation exchange in humans is obviously more involved than
this, but the processes underlying whom to listen to – for in-
stance, how to find experts, as Gorman says, or core voters,
in Goldman’s example – may well be guided by fast and fru-
gal mechanisms. Important links to existing research in so-
cial psychology and sociology can be made here.
As Gorman discusses, scientific discovery and theory-
building is a special case of social information exchange,
where the environment is the cultural one of other scien-
tists and existing theories. He addresses the role of heuris-
tics in discovery, in particular heuristics for guessing laws
from data as in the tradition of the computer program
BACON. While we have not included this topic in Simple
heuristics, some of us have analyzed heuristic processes in
scientific discovery in earlier work, focussing on heuristics
for finding analogies. For instance, the tools-to-theories
heuristic (Gigerenzer 1991; 1994) applies to cases where
new theories are inspired not by new data (as is usually
thought to be the case), but rather by new research tools,
such as statistical methods (Gigerenzer & Murray 1987) or
computers (Gigerenzer & Goldstein 1996b). This heuristic
differs from those implemented in the BACON tradition in
that it does not model discovery as an inductive process, but
as a projection of laboratory practice into theories of mind
(e.g., Neyman-Pearson’s hypothesis testing methods inspir-
ing Tanner and Swets’ 1954 theory of signal detectability).
R1.3. Construction of heuristics from building blocks
In Simple heuristics we discuss how heuristics can be built
from simpler components, whether these are building
Response/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 769
blocks for guiding information search, stopping search, and
making a decision, or whole heuristics combined into com-
posite decision mechanisms. An example of the latter com-
bination is the use of the recognition heuristic as the first
step in Take The Best. We expect such nested heuristics
themselves to be used in environments to which they are
matched, so that for instance the recognition heuristic/Take
The Best combination would not be employed in an en-
vironment where recognition validity is too low (see the
discussion of Erdfelder & Brandt’s simulations in sect.
R2.3).
Indeed, Huber feels that the contents of the adap-
tive toolbox are more likely to be what he calls “partial”
heuristics than the whole or “global” heuristics usually pro-
posed – that is, he thinks most decision making is based on
using (parts of) one heuristic first, and then switching to
another. He argues that “the investigation of global heuris-
tics is not a fruitful research strategy, because we know al-
ready that people do not use them.” But in arguing this
way, Huber overgeneralizes from the artificial lottery prob-
lems of risky choice that many decision experiments rely
on. The fact that more than 90% of the participants in the
studies reported in Chapter 2 made inferences following
the recognition heuristic, and that 65% of the participants
in another study made inferences following Take The Best
(Bröder, in press; Experiment 4) are just two examples
contradicting Huber’s bold assertion. Furthermore, Hu-
ber’s assertion that people use partial rather than global
heuristics sets up a false opposition: both can sit comfort-
ably in the adaptive toolbox. As mentioned above, heuris-
tics are composed of building blocks, and heuristics them-
selves can be combined to form new heuristics. The
possibility of combining parts into new strategies is central
to the toolbox metaphor, but not to the related image of the
mind as a Swiss army knife (Cosmides & Tooby 1992). Both
views emphasize the existence of many domain-specific
strategies (rather than a single general-purpose calculus);
but the toolbox highlights the possibility of recombining
tools and nesting heuristics.
For instance, in an environment where a person has an
intuition about the ranking of cues based on validity, she
can use Take The Best and search for cues in that order;
but in another environment where cue validities are un-
available, the search rule can be changed accordingly to
build a different heuristic that works with less knowledge,
such as Take the Last. Similarly, if a decision is highly con-
sequential, different building blocks may be combined.
Consider Sternberg’s dilemma whether to accept an offer
from a rival university or stay at Yale. Here, search for in-
formation is likely to be prolonged – that is, a different
stopping rule may be used, such as finding all the possible
relevant cues within a two-month decision period. This ex-
tended search, however, may lead to the question of how
to make a trade-off between the reasons found, such as the
intellectual quality of a department and the tears of one’s
children who do not want to move. Not all things have a
common denominator (see Morton’s discussion of incom-
parability). As a consequence, an extended search may still
be combined with a quick and simple decision rule, rely-
ing on the most important cue instead of exchanging all
cues into a common currency and weighting and combin-
ing them. Maybe Sternberg can let us know how he made
up his mind.
R1.4. Learning of Cues
It is not enough to ask where heuristics come from; we must
also address the question of how to find the relevant cues,
as Wallin & Gärdenfors point out. In general, the same
sorts of possibilities exist for an organism to determine what
cues to use as what heuristic to use. First, cues can be ge-
netically encoded, as in the human reliance on bitterness as
a cue to unpalatability. Second, appropriate cues can be
learned through individual experience. Third, cues can be
picked up socially, for instance by copying the decision
strategies of others.
Knowing the appropriate cues to use in an environment
and the direction of their association with a decision vari-
able may be all that a heuristic has to go on, but this can be
enough. The sufficiency of this minimum knowledge stands
in contrast to Wang’s comment that “these fast and frugal
heuristics would not work effectively if one did not know
the priority ranking of relevant cues.” Here is a misunder-
standing that it is important to clear up: Not all heuristics
need a ranking of cues according to their validity. Some do,
such as Take The Best and Categorization by Elimination,
while others do not, such as Take The Last and Minimalist.
To repeat, the minimal knowledge needed for cue-based in-
ference is only which cues to use and the direction in which
each cue points, for instance, whether having a soccer team
in the major league indicates that the associated city has a
large or small population (Ch. 4). This direction can be es-
timated by simply counting within a small learning sample.
The Minimalist heuristic in fact knows nothing more
than this, and thus has no idea about which cues are better
predictors than others. Consequently, the only building
block for search that Minimalist can use is to look up cues
in random order. In contrast to Wang’s intuition, we found
that Minimalist can compete well with other algorithms in
terms of accuracy, particularly when knowledge is scarce
(Chs. 4 and 5). A truly minimal amount of learning (or in-
herited knowledge) can thus be adequate to get a simple
heuristic off the ground in a new domain. With a little more
learning, frugal methods for ranking cues according to es-
timates of their validity can be used (Chs. 4 and 6). Note
that these methods do not necessarily result in the “opti-
mal” ranking of cues, but yield an ordering that is good
enough and robust enough to generalize to new situations.
R2. How are heuristics selected
from the adaptive toolbox?
This question has been asked by many commentators (e.g.,
Cooper, Luce, Wallin & Gärdenfors), and Morton has
proposed an answer. In Simple heuristics, we spent little
more than one page (pp. 32–33) on the issue of heuristic
selection; here, with the help of our commentators, we can
deal with this question a bit more systematically.
R2.1. How pressing is the problem
of heuristic selection?
First, we should point out that heuristic selection may not
always be a problem. As Feeney indicates, there are situa-
tions in which the need for selecting a heuristic does not
even arise, for example when the use of a particular heuris-
tic has been hardwired in a domain-specific (but possibly
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770 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
environmentally contingent) way. When there is more than
one available heuristic, the choice set of possibilities may
still be small. One reason for this is that the heuristics in the
adaptive toolbox are designed for specific tasks – like screw-
drivers and wrenches, they are not universal tools. This
specificity goes a long way to reduce the selection problem.
For instance, when a task calls for estimating a quantitative
variable, the QuickEst heuristic is a candidate, but others
such as Take The Last and Categorization by Elimination,
designed for choice and categorization tasks, will not be in
the choice set. A second factor that reduces the set of pos-
sible heuristics to choose between is the presence or ab-
sence of particular knowledge on the part of the decision
maker. For instance, Take The Last and Take The Best are
both designed for the same type of choice task, but if a per-
son has no intuition about which of several cues should be
checked first (i.e., no validity-based ranking of the cues; see
sect. R1.4), then Take The Best cannot be used.
R2.2. Fast and frugal selection of heuristics
Even after these task- and knowledge-specific reductions of
the choice set, there may still remain a number of heuris-
tics that are applicable for a given situation. How then can
we choose between them? Morton suggests an answer con-
sistent with the notion of an adaptive toolbox: a meta-
heuristic which chooses between heuristics using the same
principles as the fast and frugal heuristics themselves. For
instance, just as Take The Best looks up cues in a particular
(validity-based) order, a meta-heuristic can try heuristics in
a particular (e.g., success-based) order. Furthermore, just
as the cue order that Take The Best follows is not arrived at
by optimizing computations – and is good enough rather
than optimal – the ordering of heuristics is not achieved by
optimizing calculations either, but by using simple and ro-
bust criteria, such as past success. The process of ordering
itself can be modeled by a simple reinforcement learning
mechanism like that described by Erev and Roth (2000).
Morton’s solution avoids what Feeney fears: an infinite
regress of meta- and meta-meta-strategies that would be
needed to compute the best of all heuristics and all meta-
heuristics for each situation given all constraints (as in op-
timization under constraints). As soon as one dispenses with
the ideal of finding the very best heuristics for each situa-
tion, the infinite regress that would burden an optimization
approach does not arise.
Thus, Cooper’s and Feeney’s further worry that the
meta-heuristics will not pick the best heuristic to use could
certainly be true. But the whole point of the adaptive toolbox
approach is not aiming at optimization. We must not let op-
timal requirements sneak in at the meta-level either. More-
over, because there is often more than one heuristic that can
perform well in a particular situation – the flat maximum
phenomenon – the choice between them may not always be
critical, certainly not worth pondering an eternity over.
R2.3. How environments can select heuristics
According to Cooper, we have not specified the conditions
that select particular heuristics. It is fair to say that most
heuristic-relevant conditions must still be discovered, but
we and others (e.g., Payne et al. 1993) have already filled in
some examples. For instance, there are two conditions that
are necessary and sufficient to make the recognition heuris-
tic useful: recognition must be correlated with a criterion
(e.g., recognition of city names is correlated with their size),
and recognition must be partial (e.g., a person has heard of
some objects in the test set, but not all). More formally, this
means that the recognition validity a is larger than .5 and
the number n of recognized objects is 0 , n , N, where N
is the total number of objects. Note that these variables, a,
n, and N, can be empirically measured – they are not free
parameters for data fitting.
When these conditions do not hold, using the recogni-
tion heuristic is not appropriate. Erdfelder & Brandt, for
instance, overlooked the first condition and thereby mis-
applied the recognition heuristic. They tested Take The
Best with the recognition heuristic as the initial step in a
situation with a5.5 (i.e., recognition validity at chance
level). In this case, the recognition heuristic is not a useful
tool, and Take The Best would have to proceed without it.
Their procedure is like testing a car with winter tires when
there is no snow. Nevertheless, their approach puts a fin-
ger on one unresolved question. Just as a driver in Maine
faces the question when to put on winter tires, an agent
who uses the Take The Best, Take The Last, or Minimalist
heuristic needs to face the question of when to use recog-
nition as the initial step. The recognition validity needs to
be larger than chance, but how much? Is this decided on
an absolute threshold, such as .6 or .7, or relative to what a
person knows about the domain, that is, the knowledge va-
lidity b? There seems to be no empirical data to answer this
question. Note that this threshold problem only arises in
situations where objects about which an agent has not
heard (e.g., new products) are compared with objects about
which she has heard and knows some further facts. If no
other facts are known about the recognized object, then the
threshold question does not matter – when there is noth-
ing else to go on, just rely on recognition, whatever its va-
lidity is.
In contrast, one condition that might seem important for
the applicability of the recognition heuristic is actually irre-
levant. Goldman says that “only with a (tolerably) accurate
estimate” of the recognition validity will applications of the
recognition heuristic succeed. This is not necessary – the
recognition heuristic can work very well without any quan-
titative estimate of the recognition validity. The decision-
maker just has to get the direction right. Goldman also sug-
gests that the less-is-more effect in the example of the three
brothers (Ch. 2, pp. 45–46) would be due to the fact that
the middle brother knows about the validity of recognition
while the eldest does not. As Figure 2-3 shows, however,
the less-is-more effect occurs not only when one compares
the middle with the eldest brother, but also when one com-
pares the middle with other potential brothers (points on
the curve) to the left of the eldest. Thus, the less-is-more
effect occurs even when the agent who knows more about
the objects also has the “substantial problem-specific know-
ledge,” that is, the intuition that recognition predicts the
criterion. Less is more.
Margolis raises the fear that environments may prompt
the use of a heuristic that proves maladaptive, especially
with genetically entrenched – evolved – heuristics that are
resistant to modification via learning. His argument is that
when environments change in a significant way (e.g., from
scarce to abundant resources), heuristics adapted to past
Response/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 771
conditions may prove harmful in the new state of affairs.
This discrepancy can become amplified when one looks be-
yond the individual to aggregate social choice. Margolis’s
reasoning here is akin to that of Robert Ornstein and Paul
Ehrlich’s New world, new mind (1989). In this book, the ar-
gument is made that the human mind fails to comprehend
the modern world, because we are more impressed by
unique events and dramatic changes than by the more
threatening slow-motion disasters such as the greenhouse
effect, AIDS, and dwindling natural resources. The evi-
dence for this view, however, is contested, as a widely pub-
licized wager between Paul Ehrlich and the economist Ju-
lian L. Simon illustrates (Tierney 1990). In 1980, Ehrlich
bet that the prices of five metals (which he selected) would
go up within ten years because of the exploitation and ex-
hausting of natural resources; Simon bet that they would go
down because of human innovation. Simon won. Similarly,
the maladaptively entrenched heuristics Margolis points to
may be replaced by new more appropriate heuristics ac-
quired through individual or social innovation and learning.
R3. How can environment structure
be characterized?
The structures of environments are essential for under-
standing cognition and behavior in terms of adaptation, be-
cause adaptations are shaped by (past) environments. Fast
and frugal heuristics that are matched to particular envi-
ronmental structures allow organisms to be ecologically ra-
tional. To understand their performance, one needs con-
ceptual languages both for the design of heuristics (e.g.,
rules for search, stopping, and decision) and for the struc-
ture of environments. The two classic behaviorist-inspired
approaches to studying the structure of environments,
Egon Brunswik’s search for environmental or ecological
texture and J. J. Gibson’s search for invariants in the visual
environment, paid little attention to heuristics or anything
else going on in the mind, and therefore did not analyze the
match between heuristics and environments (see Gigeren-
zer 2000). More recently, rational analysis (Anderson 1990;
see also Chater), Hutchins’s (1995) study of artifacts (e.g.,
maps, navigation instruments), and Norman’s (1993) work
on things that make us smart, among other research direc-
tions, epitomize a growing emphasis on the importance of
environmental structure.
In Simple heuristics, we investigated the following types
of environment structures and analyzed the degree to
which specific heuristics can exploit them: environments in
which lack of recognition is informative (Ch. 2); noncom-
pensatory information (Ch. 6); scarce information (Ch. 6);
J-shaped distributions (Ch. 10); and decreasing choice sets
(Ch. 13). (Note that we are concerned here with the struc-
ture of the environment as it is known by the decision
maker, which of course is strongly tied to the “objective” en-
vironment structure.) Clearly, this is only a beginning. We
are happy that several commentators have added to the cat-
alog of environment structures under investigation.
R3.1. Cost-benefit structure of the environment
Commentator Allen suggests that heuristics may not be
used in situations in which the cost of being wrong exceeds
the benefit of being right. In such cases, he expects people
will aim to maximize their chance of producing correct re-
sponses, and therefore abandon simple heuristics for more
normative or deliberative approaches. Sternberg suggests
that heuristics can be used to good advantage in a range of
everyday decisions but are inappropriate for consequen-
tial (i.e., important) real-world decisions, and Harries &
Dhami voice similar but more prescriptive concerns for le-
gal and medical contexts. All this sounds plausible, but what
is the evidence? As a test of this plausible view, Bullock and
Todd (1999) manipulated what they called the significance
structure of an environment – the costs and benefits of hits,
misses, false alarms, and correct rejections in a choice task.
Against expectations, they found that lexicographic strate-
gies can work well even in high-cost environments. They
demonstrated this for artificial agents foraging in a simu-
lated environment composed of edible and poisonous mush-
rooms. When ingesting a poisonous mushroom is not fatal,
the best lexicographic strategies for this environment use as
few cues as possible, in an order that allows a small number
of bad mushrooms to be eaten in the interest of not reject-
ing too many good mushrooms. When poisonous mush-
rooms are lethal, lexicographic strategies can still be used
to make appropriate decisions, but they process the cues in
a different order to ensure that all poisonous mushrooms
are passed by.
One feature of consequential decisions is that they fre-
quently have to be justified. Often a consequential decision
is reached very quickly, but much further time in the deci-
sion process is spent trying to justify and support the choice.
Such cases illustrate that consequential environments may
call for long and unfrugal search that is nonetheless com-
bined with fast and frugal decision making, as discussed in
section 1.3 (see also Rieskamp & Hoffrage 2000; Ch. 7).
R3.2. Friendly versus unfriendly environments
The cues in an environment (as the decision maker knows
it) can all be positively correlated, or a subset of them can
be negatively correlated. Shanteau & Thomas call the
first type of environment “friendly” and the second type
“unfriendly.” We welcome Shanteau & Thomas’s work to
extend the understanding of the ecological rationality of
heuristics to this type of environment structure. They have
found that unfriendly environments contain tradeoffs that
present a challenge to fast and frugal heuristics, particularly
those that employ one-reason decision making. One way of
meeting this challenge is to combine partial heuristics (as
Huber discusses), starting with an elimination strategy to
remove options with unacceptable tradeoffs, and proceed-
ing to a lexicographic strategy to process the remaining op-
tions.
More specifically, Shanteau & Thomas state that the
performance of the LEX heuristic decreases in unfriendly
environments as the number of cues increases. But it is im-
portant to realize that there is a fundamental asymmetry be-
tween friendly and unfriendly environments. An environ-
ment with many cues can be extremely friendly, but not
extremely unfriendly. That is, all correlations between cues
can be positive, but not all can be negative. To see the point,
imagine two cues which are correlated at r 521; a third
cue which is negatively correlated with one of the first
two cues must be positively correlated with the other. In
other words, unfriendly environments will have pockets of
friendly cues, and the more cues the decision maker as-
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772 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
sesses, the bigger those friendly groups will be. How heuris-
tics can exploit these pockets is a question that should be
explored.
We also want to point out the importance of perfor-
mance measures used to compare strategies in these and
other environments (see also sect. R6). Shanteau &
Thomas measure the performance of their strategies
against a weighted additive difference (WAD) model as the
gold standard, as in earlier work on preferences by Payne
et al. (1993). In Simple heuristics, in contrast, we have used
real-world criteria – from attractiveness judgments to
school drop-out rates – as the gold standard. This corre-
sponds to the difference between preferences (where
there is no external criterion) and inferences (where there
is one). This choice has consequences. When WAD is em-
ployed as the performance standard (rather than an exter-
nal criterion), a simple heuristic such as a lexicographic
strategy can never be more accurate than WAD, by defin-
ition. But when real-world criteria are introduced, heuris-
tics can outperform WAD, as we have shown in Chapters
4 and 5. Specifically, the gold standard is likely to be out-
performed when the task of an agent is prediction (e.g.,
cross-validation) rather than mere data fitting. Thus, we
are curious to know how accurate lexicographic heuristics
are in unfriendly environments when they have to predict
features of the environment (rather than match the out-
puts of a WAD model). Preliminary results obtained by the
ABC Research Group indicate that in unfriendly environ-
ments, Take The Best can be more accurate than Dawes’s
rule (consistent with Shanteau & Thomas), but can also
match or slightly outperform what we call Franklin’s rule,
a weighted additive model.
R3.3. Conspecifics are the environment
One important field for the study of the adaptive toolbox
is social rationality, the investigation of cognitive mecha-
nisms for dealing with an environment consisting of con-
specifics. We agree with Barrett & Henzi that extending
the simple heuristics research program further into the so-
cial domain is an important next step. This would help
bring psychology and game theory together (as Hammer-
stein calls for) and emphasize the importance for social
psychology of interactive strategies – the heuristics indi-
viduals actually employ to deal with others. We have begun
to explore the ways in which people and animals can use
simple rules to process information they gain by observing
the behavior of conspecifics (Noble & Todd, in press; see
also Wimsatt’s example linking the recognition heuristic
with “conspecific cueing” in species where the rare sight of
another conspecific is a good cue for the presence of re-
sources). Allen and Barrett & Henzi raise the possibility
that in the social realm, with selection for increasingly so-
phisticated Machiavellian behavior, simple heuristics may
eventually fall prey to exploitation by more complex strate-
gies. As mentioned earlier, however, the general assump-
tion that increasingly complex environments can only be
tamed by increasingly complex strategies is doubtful.
Counterexamples are simple social heuristics such as Tit-
For-Tat and its relatives, the “automaticity” of everyday life
(Bargh & Chartrand 1999) and the advantage of simple and
transparent rules in businesses and legal systems as op-
posed to cancerous growing bureaucracies (Engel 1994;
Epstein 1995).
R3.4. Poisson processes
In Chapter 10, Hertwig et al. showed how the QuickEst
heuristic can exploit J-shaped distributions in environ-
ments. But which environments have such structure? Wim-
satt points out that J-distributions are likely to be very com-
monplace because they are produced by power laws, and
more generally by Poisson processes, which are ubiquitous
in the natural world. For instance, he directs us to the work
of Bak (1996) who explains seemingly disparate phenom-
ena including the formation of landscapes, the regularity of
catastrophic events such as earthquakes, and the behavior
of economic systems as manifestations of one principle,
self-organized criticality, which produces power-law distri-
butions. Whether or not one agrees with this view, Bak’s
work points to the questions of what kind of mechanisms
and processes produce environmental structures. Linking
an understanding of the processes that generate environ-
ment structure to the mechanisms that people and other
animals use to understand them is an exciting challenge.
R3.5. Causal cues versus surface cues
What kind of environmental cues do heuristics use? Wallin
& Gärdenfors propose that “ecological validity should be
seen as only a secondary effect of the fact that a decision
maker aims at forming hypotheses about causal connections
between the cues and the decision variable.” The implica-
tion is that causally related cues should be sought rather
than merely ecologically valid cues. We disagree with rele-
gating ecological validity to this secondary role. Causal vari-
ables may well be used as cues, if available. However, we
suspect that it may be easier to assess and monitor ecolog-
ically valid cues that are covarying at the surface level with
the decision variable (e.g., because both are caused by the
same underlying process) rather than cues that are causally
linked to the decision variable. Moreover, several causal
cues may need to be taken into account to reach a decision,
when only one surface-level concomitant cue might suffice.
For instance, consider a baseball or cricket player who tries
to catch a ball. If the player tried to compute the spot where
the ball would land by relying on causal variables alone, he
would have to estimate the initial velocity, initial speed,
spin, air resistance, direction and intensity of wind, and a
myriad of other causal factors, and then apply the proper
mathematics to integrate all this information. Real players,
in contrast, seem to rely on one-reason decision making,
and the one reason is not a causal cue. It is the angle of gaze,
that is, the angle that their eyes have to keep to stay directed
at the ball. The simple heuristic is to start running and to
adjust running speed so that the angle of gaze is constant
(or within a certain range, see McLeod & Dienes 1996).
This gaze heuristic illustrates that a smart heuristic can ig-
nore all causal factors, and gain accuracy through its fru-
gality.
R4. How can we study which heuristics
people use?
Obtaining empirical evidence for the use of particular
heuristics demands careful methodology, because of chal-
lenges such as the flat maximum phenomenon (Ch. 7).
Cooper doubts whether this is even possible, feeling that
we have presented an unfalsifiable theory of decision mak-
Response/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 773
ing, akin to the heuristics-and-biases program of Kahneman
and Tversky. This is incorrect – here is an example. One of
the strongest tests of a heuristic is obtained when it makes
a bold and new prediction. Consider the recognition heuris-
tic, which predicts the counterintuitive less-is-more effect
– that is, once a person has a critical degree of knowledge,
more knowledge will produce less accurate inferences. The
necessary and sufficient condition for the less-is-more ef-
fect is that a person’s recognition validity is larger than her
knowledge validity (i.e., a.b, where both are empirically
measurable variables, and no free parameters are involved;
see Ch. 2). Thus, if one experimentally induces (or empiri-
cally observes) this condition, then people who use the
recognition heuristic will exhibit the less-is-more effect. If
the effect is not seen, then the hypothesis that participants
use the recognition heuristic in this situation is falsified.
This less-is-more effect has not been repeatedly experi-
mentally demonstrated (Goldstein & Gigerenzer, in press ).
There are also simpler ways to test whether people use the
recognition heuristic that do not involve such bold
predictions (e.g., setting up conditions as in sect. R2.3). In
general, testing hypotheses about heuristics calls for a
methodology that differs from the dominant approach in
experimental psychology: the comparison of group-means
by null hypothesis testing.
Hypothesis testing in much of experimental psychology
follows a standard paradigm: vary an independent variable,
or a few, and test whether the resulting group means in a
dependent variable differ significantly from the null hy-
pothesis (“chance”). This paradigm, applied to the study of
reasoning strategies or heuristics, has two dramatic flaws.
First, no hypotheses about mental strategies, nor their pre-
dictions, are specified, only a null hypothesis. Second, the
means analyzed are aggregated across participants. Doing
this, one assumes a priori that people will not use different
heuristics, and researchers will hardly detect them if they
do. The flaws of this methodology are well documented
(e.g., Gigerenzer 1993).
The metaphor of the adaptive toolbox, in contrast, en-
courages a methodology that is sensitive to the existence of
multiple heuristics and individual differences in their use.
Such a methodology can consist of (1) specifying multiple
candidate heuristics, (2) deriving the predictions for each
heuristic on the experimental tasks, and (3) testing each par-
ticipant’s judgments against the predictions of each heuris-
tic (e.g., Ch. 7; Gigerenzer & Hoffrage 1995). The result
may be that 60% of the participants use heuristic A, 20%
use heuristic B, 10% use C, and the rest use idiosyncratic
strategies or cannot be categorized. Note that this method-
ology avoids averaging across individuals, which is unjusti-
fied when multiple strategies are in use in a population – a
situation that we have found to be the rule rather than
the exception. This methodology is particularly important
when one analyzes ontogenetic development in heuristic
use, as Solomon proposes. In earlier work, some of us have
identified half a dozen heuristics children use for estimat-
ing size, for instance of chocolate bars (Gigerenzer &
Richter 1990). These heuristics changed systematically
with age, with the most frequent ones in young children
dropping out later while others were added. At each age,
from pre-schooler to adult, there was not one strategy used
across individuals, but several.
This methodology is all too rarely used. For instance, in
the BBS target article on individual differences in reason-
ing by Stanovich and West (2000), no models of reasoning
heuristics were formulated, no competing predictions de-
rived, and the analysis of individual differences was per-
formed exclusively on whether participants’ judgments de-
viated from some norm. This procedure can obscure
evidence for the use of particular heuristics, for instance
when one leads to behavior close to the norm in some situ-
ations but far from the norm in others and thus appears in-
consistent (Hoffrage 2000). Unless a set of hypotheses for
participants’ strategies is formulated in the first place, there
is little hope of identifying individual differences in heuris-
tic use.
Thus, the methodology of the adaptive toolbox encour-
ages precise predictions, including predictions of individual
differences in performance based on individual differences
in knowledge, and, in some lucky cases, bold and counter-
intuitive predictions. For instance, the recognition heuris-
tic makes precise predictions of choices for each pair of ob-
jects, predicts systematic individual differences in choice
on the basis of individual differences in recognition, and
even indicates when the less-is-more effect might be ob-
served. Each of these predictions can be, and has been, ex-
perimentally tested.
Chater discusses how rational analysis (Anderson 1990)
can complement the study of fast and frugal heuristics: It
can provide a framework to evaluate the performance of
simple heuristics. (Rational analysis is thus related to the
use of optimality models in biology as Houston discusses.)
We agree. The two programs approach the first step in the
above methodology – specifying multiple candidate heuris-
tics – from two different ends. Rational analysis starts by
trying to find the optimal solution to some particular prob-
lem, and then begins whittling that down through successive
simplifications – all mathematically derivable and testable
– until finally a psychologically plausible mechanism is
found. In contrast, the program of fast and frugal heuristics
starts with building blocks that people may actually
use – like recognition, or forming aspiration levels – and
looks at how these can be combined into good enough so-
lutions.
R5. What is the evidence for fast
and frugal heuristics?
It is widely accepted that animals use simple heuristics
(more commonly called “rules of thumb”) that are success-
ful and well-adapted to their particular environments, as
Houston points out and as we discuss in Chapters 13, 14,
and 15. Here we focus on the more contentious human
case. Cooper and Harries & Dhami claim that there is lit-
tle or no evidence that humans use simple heuristics. How-
ever, Chapters 2, 7, and 9 of Simple heuristics do provide
just such empirical evidence. Nevertheless, we agree that
more evidence is needed, and we are happy to report here
some of the efforts in this direction.
We are not the first to find evidence that people employ
limited search, fast stopping rules, elimination heuristics,
or one-reason decision making. For example, it has long
been known that people often look up only one or two rel-
evant cues, avoid searching for conflicting evidence, ignore
dependencies between cues, and use non-compensatory
strategies (e.g., Einhorn 1970; Einhorn & Hogarth 1981,
p. 71; Fishburn 1988; Hogarth 1987; Payne et al. 1993; Shep-
Response/Todd & Gigerenzer: Simple heuristics
774 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
ard 1967). But these “limitations” have been tossed too
quickly into the box of human irrationality. For instance, ig-
noring cue dependencies is usually suspected as a “failure”
of the human mind. But we have found that in suitable en-
vironments, one-reason decision heuristics that ignore all
dependencies can be more accurate than linear strategies
that carefully estimate the dependencies (Ch. 5). It may
thus be profitable to return to and reinterpret some of the
important results of earlier decision making research in the
light of the ecological rationality perspective.
Since the publication of Simple heuristics, further tests
of fast and frugal decision mechanisms have been per-
formed. Bröder (in press, Experiment 4) used an ingenious
experimental design to test whether people use Take The
Best. He showed that when participants have to search for
costly information, 65% of all participants were classified as
using Take The Best. In contrast, less than 10% could be
classified as using Dawes’s rule, a simple linear model with
unit weights. Further evidence has also been found for the
earlier hypothesis of Payne et al. (1993) that lexicographic
strategies are employed when time is short (Rieskamp &
Hoffrage 2000). Finally, Harries & Dhami conclude from
their work with English magistrates and other experts that
fast and frugal heuristics could underlie some decisions in
legal and medical domains, even when they are prescribed
against by the stated goals of those professions.
Some heuristics can produce intransitive judgments.
Allen notes that we did not provide evidence that people in
fact make such inconsistent judgments, and the lack of such
evidence can be taken as a strike against the use of particu-
lar heuristics. However, Lages et al. (2000) have now gath-
ered experimental evidence for intransitivities: When peo-
ple make comparisons of population size between pairs of
cities (the example to which Allen refers), the total set of
judgments contains about 10% of the maximum possible
number of intransitive triples, that is, cases where people
inferred that city A is larger than B, B is larger than C, but
C is larger than A.
The reason this is important is that specific rules for
search and stopping predict characteristic patterns of in-
transitivities, as illustrated in Gigerenzer and Goldstein
(1996a, p. 664). Thus, at an individual level we can predict
particular patterns of intransitivities associated with the use
of particular heuristics, and then we can compare these pre-
dictions with the patterns actually observed. Lages et al.
(2000) have derived the theoretically predicted patterns in
detail, and have found that people’s patterns of intransitiv-
ities are consistent with the use of the Take The Last heuris-
tic. Allen further asks whether people show signs of dis-
comfort when they produce intransitivities. Indeed, some
participants said they were afraid of producing intransitivi-
ties. But they did not show discomfort when they actually
made intransitive judgments, because they made several
hundred pair comparisons and did not notice when intran-
sitivities crept in. As Chapter 9 shows, memory of earlier
judgments is limited and often even updated in hindsight,
which could further erode an individual’s recognition of his
own intransitive judgments.
Furthermore, the common assumption that consistency
per se is always better has been challenged by these find-
ings. Consistency does not guarantee correspondence. For
instance, the Take The Last heuristic, which occasionally
produces systematic intransitivities, can generate more ac-
curate judgments than linear strategies (such as Dawes’s
rule, see Ch. 4) which do not. Lages et al. (2000) report that
in about one third of all pairs of participants, the one who
generated more intransitivities was also more accurate.
Finally, Kainen echoes our call for examples of heuris-
tics in other fields, such as perception and language pro-
cessing, and provides examples of heuristics from engi-
neering and other applied fields that he would like to see
collected and tested – but one must be clear about how ex-
amples of these artificial mechanisms can be used to eluci-
date the workings of human or animal minds. Lipshitz sees
more progress to be made in tackling the heuristics under-
lying naturalistic real-world decision making, of the sort
that Klein (1998) investigates.
R6. What criteria should be used to evaluate
the performance of heuristics?
The choice of criteria for evaluating the performance of
heuristics lies at the heart of the rationality debate. Our fo-
cus on multiple correspondence criteria – such as making
decisions that are fast, frugal, and accurate – rather than on
internal coherence has drawn the attention of many com-
mentators. We are happy to spark a discussion of suitable
criteria for evaluating cognitive strategies, because this
topic has been overlooked for too long. As an example,
decades’ worth of textbooks in social and cognitive psy-
chology have overflowed with demonstrations that people
misunderstand syllogisms, violate first-order logic, and ig-
nore laws of probability, with little or no consideration of
whether these actually are the proper criteria for evaluat-
ing human reasoning strategies. This lack of discussion has
an important consequence for the study of cognition: The
more one focuses on internal coherence as a criterion for
sound reasoning, the less one can see the correspondence
between heuristics and their environment, that is, their
ecological rationality.
R6.1. Correspondence versus coherence
A person who states that there is a 95% chance that Elvis is
still alive and a 5% chance that he has gone to his great re-
ward makes a coherent statement (the probabilities add up
to 100%). But as far as we know, the belief does not corre-
spond to the state of the real world. Thus, there can be a ten-
sion between the two ideals of coherence and correspon-
dence, as Allen and Fuller note. The two need not conflict;
a person’s judgments can be coherent, that is, internally con-
sistent, and at the same time correspond well to the outside
world. The ideal of complete coherence among all state-
ments or beliefs of a person, however, can be a demonic fic-
tion because it would require elaborate consistency check-
ing and maintenance mechanisms and may even be
empirically meaningless (Sen 1993). Research on prefer-
ences (as opposed to inferences) invites coherence as a cri-
terion for rationality, because preferences are matters of
taste for which external criteria rarely exist – similarly, there
are only internal, not external, criteria in research on de-
ductive reasoning and mental logic to which Newstead
refers. The decision mechanisms described in Simple
heuristics, however, are intended mainly for inferences, and
here the conflict between coherence and correspondence
can arise. Taking sides in this conflict, Barrett & Henzi
welcome the move to design and test heuristics for real-
Response/Todd & Gigerenzer: Simple heuristics
BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 775
world situations where external correspondence criteria can
reveal their success, as do Shanks & Lagnado, but Allen
expects that it is still worthwhile carrying around the “bag-
gage” of the laws of logic as a standard of good reasoning.
Bermúdez has questioned the justifiability of using fast
and frugal heuristics that are evaluated on the basis of suc-
cess alone. He says that “a workable concept of rationality
must allow us to evaluate the rationality of an action with-
out knowing its outcome.” But basing an evaluation of suc-
cess on the outcome of a decision is exactly what the pro-
cesses of evolution and learning do; and as these are the
processes that led to the decision making mechanisms we
use, we must adopt the same success-oriented perspective
if we want to uncover and understand what is going on in
our heads when we make choices.
R6.2. Choosing a benchmark
To evaluate the performance of heuristics in the real world,
benchmarks are useful. In Simple heuristics, we have em-
ployed a range of benchmarks – linear models, neural net-
works, and Bayesian networks, among others (not just mul-
tiple linear regression, as Shanks & Lagnado imply). The
choice of benchmarks (like the choice of criteria) is not al-
ways straightforward, and for some, particularly benchmark
models with numerous free parameters such as neural net-
works, it typically takes considerable search (e.g., training
and testing) to find a good model for a given situation. Be-
cause this choice can be complicated, we welcome the dis-
cussion that commentators have raised of the benchmarks
we used.
Harries & Dhami, for instance, argue that we should
have used a modified version of multiple regression that ig-
nores all non-significant cue weights, because this pruned
regression would result in a better benchmark. Hertwig,
Hoffrage, and Martignon tested this argument in Chapter
10 (p. 231), with respect to the frugality and accuracy of es-
timation. First, using only the significant weights did not
make multiple regression much more frugal – it only de-
creased the number of cues used from 8 to 7.3 on average.
The QuickEst heuristic, in contrast, used only 2.3 cues on
average. Second, pruning improved the accuracy of regres-
sion only in one (the smallest) of the 10 training sets sub-
stantially, but the fast and frugal QuickEst still remained
more accurate. Similar results were obtained when Dawes’s
rule, a linear strategy with equal weights, was pruned (Ch.
5, p. 112). Thus, Harries & Dhami are right that ignoring
cues can improve the accuracy of linear models and make
them better benchmarks (just as ignoring information can
make heuristics more accurate), but we have found that this
still does not change the overall pattern of comparisons be-
tween the linear models and simple heuristics.
Shanks & Lagnado also stress the problem of choosing
proper benchmarks to evaluate heuristic performance, par-
ticularly challenging our assessment of the Categorization
by Elimination (CBE) heuristic. They want to see more
evaluation of the model in comparison to human data, and
so do we – the problem is that very few experiments have
ever been performed with categories comprising a large
number of cues, the realistic situation for which CBE is in-
tended. Consequently, as we explained in Chapter 11, we
resorted to standard categorization data sets from the ma-
chine learning literature, which contain hundreds to thou-
sands of instances and dozens of cues and are thus neither
“very small” nor “highly non-discriminating” as Shanks &
Lagnado state. But we agree that these tests only allow us
to indicate the general viability of this approach to catego-
rization, and we must extend the model to account for phe-
nomena such as learning and then pit it against further hu-
man data (much of which will have to be obtained from new
experiments; see Berretty 1998). However, the choice of
human data to use as benchmarks is also not without con-
troversy: For instance, Shanks & Lagnado say that CBE
must be able to predict the so-called “exemplar effect,” but
the existence of this effect is still an open question. In ex-
periments showing the exemplar effect, participants were
trained on only a small number of exemplars (e.g., 10 ex-
emplars in Whittlesea 1987, and 30 exemplars in Brooks et
al. 1991). Furthermore, Thomas (1997) has shown that not
all participants used exemplar information in categorization
judgments after learning more realistically sized categories
comprising hundreds of exemplars. Shanks & Lagnado also
argue that CBE’s deterministic response rule is implausi-
ble, but Maddox and Ashby (1993) have shown that hu-
mans respond with less variability than predicted by Luce’s
choice axiom, that is, in a more deterministic fashion than
expected. Thus again we confront the problem of choice of
benchmarks.
R6.3.When fast and frugal heuristics conflict
with established values
Engel, Fuller, and Harries & Dhami have extended the
discussion of performance criteria for heuristics to include
societal and legal values, such as accountability, legitimacy,
and due process. This is an important extension that raises
many fundamental questions. Harries & Dhami ask whether
the use of simple heuristics should be prescribed in situa-
tions where they are successful, and point out the possible
society-level legal implications of fast and frugal judgments.
Engel has previously considered the normative question of
bounded rationality in the law (Engel 1994). In his com-
ment, he makes the question very clear using our introduc-
tory example, the classification of heart-attack patients by
at most three yes-no questions. It is easy to imagine a lawyer
who sues the doctor because he ignored information, fol-
lowing the assumption that more information is always bet-
ter – but which party would be in the right?
We agree with Engel that the philosophy of fast and fru-
gal decision making may conflict with certain interpreta-
tions of the law. The legal system faces a conflict between
the ideals of optimization and bounded rationality similar
to that in cognitive science. There are two ways to react to
a world that is becoming more complex: to strive for per-
fection by designing ever more complex legal rules that gov-
ern every aspect of human behavior, or to stop this growth
and strive for a few simple and robust legal rules, as Epstein
(1995) proposes. Epstein argues that the half dozen rules
he designed would cover 95% of all legal cases. To expect
more complete coverage than this from a legal system, he
says, would be an illusion.
R7. Conclusion
As the range of expertise covered by our commentators
confirms, the study of bounded rationality is a multidisci-
plinary effort, and its results have relevance for all sciences
Response/Todd & Gigerenzer: Simple heuristics
776 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5
that try to understand the behavior of living organisms.
Opening up the adaptive toolbox and figuring out what lies
inside is a challenge that must be addressed from many di-
rections. To the extent that fast and frugal heuristics fill the
toolbox, many fields will have to rethink some of our un-
derlying assumptions of the appropriate representation of
the world, as Luce points out – additive linearity may be,
as he says, “a singularly bad representation of a great deal
of reality; this matters greatly.” To find out, we must extend
our understanding of ecological rationality – how environ-
ment structures and heuristic mechanisms fit together. We
are grateful to the commentators for leading this explo-
ration into new directions.
ACKNOWLEDGMENT
Members of the ABC Research Group who contributed to this re-
sponse were H. Clark Barrett, Patricia M. Berretty, Seth Bullock,
Valerie M. Chase, Jennifer Nerissa Davis, Thomas Dudey, Lau-
rence Fiddick, Daniel G. Goldstein, Adam S. Goodie, Ralph
Hertwig, Ulrich Hoffrage, Monika Keller, Stefan Krauss, Martin
Lages, Barnaby Marsh, Laura Martignon, Jason Noble, Andreas
Ortmann, Jörg Rieskamp, and Christoph Wassner.
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