Axiomatic and ecological rationality: Choosing costs and benefits

Abstract

One important purpose of rationality research is to help individuals improve. There are two main approaches to the task of rendering evaluations of rationality that support guidance: The axiomatic approach evaluates the coherence of behavior according to axiomatic criteria, while ecological rationality evaluates processes according to their expected performance. The first part of the paper considers arguments against the axiomatic and ecological approaches and concludes that neither approach is unserviceable; in particular, each has the flexibility to accept important insights from the other. The second part of the paper characterizes each approach according to the profile of costs and benefits that it accepts, and shows that combining the two approaches in a particular way yields a new approach with a superior cost-benefit profile. This 'hybrid approach' uses axiomatic rationality criteria to evaluate processes that agents might use.

Full text

Erasmus Journal for Philosophy and Economics,
Volume 9, Issue 2,
Autumn 2016, pp. 90-122.
http://ejpe.org/pdf/9-2-art-7.pdf
Axiomatic and ecological rationality:
choosing costs and benefits
Patricia Rich
University of Bristol
Abstract: One important purpose of rationality research is to help indi-
viduals improve. There are two main approaches to the task of rendering
evaluations of rationality that support guidance: the axiomatic approach
evaluates the coherence of behavior according to axiomatic criteria, while
ecological rationality evaluates processes according to their expected per-
formance. The first part of the paper considers arguments against the
axiomatic and ecological approaches and concludes that neither approach
is unserviceable; in particular, each has the flexibility to accept important
insights from the other. The second part of the paper characterizes each
approach according to the profile of costs and benefits that it accepts, and
shows that combining the two approaches in a particular way yields a new
approach with a superior cost-benefit profile. This ‘hybrid approach’ uses
axiomatic rationality criteria to evaluate processes that agents might use.
Keywords: ecological rationality, axiomatic rationality, normativity, heuris-
tics, methodology
JEL Classification: A12, B40, D81
1Introduction
This paper argues that the best approach to normative rationality for the
specific purpose of fostering improvements is a strategic mixture of the
two strongest contenders. The methods of each exploit particular kinds of
information and attain some desiderata at the cost of others; combining
them in a particular way results in a ‘hybrid approach’ that offers a better
cost-benefit package than either alone.
The battles of the so-called ‘rationality wars’ are as multifarious as
they are passionate, with the diversity of goals, methods, and backgrounds
Author’s Note: The author thanks two anonymous referees, Nathan Berg, David
Danks, and Kevin Zollman for extremely helpful written comments on the content
herein. The paper also benefited from discussions with audiences at Carnegie Mellon
University, the University of Bristol, the London School of Economics, and the Zentrum
für Allgemeine Sprachwissenschaft.

Patricia Rich / Axiomatic and ecological rationality
of rationality researchers leaving every position open to attack from some
alternative perspective. At least among well-developed research programs,
we should not expect any of the competing paradigms to be unserviceable
tout court, but rather better or worse for particular purposes and given
particular tools. Each broad program will also have stronger and weaker
subprograms. For these reasons, this paper considers competing general
approaches to normative rationality, and evaluates them with respect to
the specific purpose of guiding individual agents towards greater ratio-
nality.
Specifically, I compare the axiomatic approach (hereafter ‘AA’) with
ecological rationality (hereafter ‘ER’) (see, e.g., Gigerenzer and Selten 1999;
Gigerenzer et al. 2011). Put simply, an AA practitioner defines rational be-
havior in terms of conformity to abstract axioms, while ER defines ratio-
nality in terms of the “match between mind and environment” (Gigeren-
zer et al. 2011, xix). More precisely, “[w]hen a decision procedure is well
matched to an environment, where ‘well matched’ is defined as achieving
good-enough levels on the performance metrics relevant to that environ-
ment, then the pair (decision procedure, environment) is classified as eco-
logically rational” (Berg 2014a, 378). AA is the methodology abstracted
from existing axiomatic theories (ATs), such as AGM belief revision1(Al-
chourrón et al. 1985) and axiomatizations of rational choice; the use of
axioms is the most salient characteristic of these theories, but they have
additional common features that will prove important. In contrast, ER
is a top-down research program that applies its abstract conception of
rationality to multiple types of problems: Gigerenzer and Hertwig run in-
terdisciplinary research centers at the Max Planck Institute with the basic
purpose of developing ER (though not necessarily with a normative focus)
and applying it to choice, inference, and other tasks.
Important related research programs–such as Kahneman and Tver-
sky’s work on heuristics and biases (Kahneman and Tversky 1973; Tversky
and Kahneman 1974; Kahneman 2011)–are not considered as indepen-
dent candidate approaches because their role is to provide descriptive in-
sights rather than new normative criteria. I also evaluate what I take to be
the strongest versions of AA and ER. For one, this means de-emphasizing
those sub-approaches that are most easily and successfully attacked and
remaining agnostic among the defensible ones wherever possible. For this
reason, AA is construed as seeking relatively simple behavioral tests of co-
1AGM is the dominant theory of belief revision, named for its developers: Carlos
Alchourrón, Peter Gärdenfors, and David Makinson. It axiomatizes the concept of belief
revision as the minimal change to a theory or belief set in response to learned, perhaps
incompatible information.
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herence, with emphasis on observability and minimality. In contrast, uses
of axioms that appeal to literal process statements (e.g., “the agent maxi-
mizes expected utility”) make much stronger claims that invite additional
criticism (see, e.g., Simon 1956), and even if behavioral economics can
be given a normative interpretation (cf., Grüne-Yanoff2010; Berg 2003)
its complexity and proliferation of parameters compared to orthodox ra-
tional choice theory makes its normative usefulness highly questionable.
Secondly, I consider the theoretical commitments of each approach and
the best practices that could be carried out within them, rather than the
details of existing practice. This means that I take most seriously ER’s ba-
sic definitions of rationality–which focus on the degree of success to be ex-
pected from using a process, the need to evaluate actual choice and infer-
ence mechanisms, and the importance of speed, efficiency, and accuracy–
rather than the accompanying biological and anti-orthodox rhetoric (see
Hands [2014] for a critical discussion of ER’s normative prospects, includ-
ing the work done by evolutionary and anti-orthodox arguments). While
many examples come from decision theory, the arguments pertain to the
rationality of inferences, probabilistic belief and belief revision, as well as
to the various types of choice problem. Considering general approaches to
normative rationality–rather than individual theories–allows me to draw
conclusions with significance beyond localized disputes (e.g., whether it
is irrational to violate the conjunction rule in the Linda problem [Tver-
sky and Kahneman 1983]; cf., Hertwig and Gigerenzer [1999] and Sturm
[2012]), with relevance for the rationality wars as a whole.
The resultant analysis upholds the view that–contra Berg and Gigeren-
zer (2006) and Berg (2014a)–both the AA and ER approaches have value
and a role to play, even with respect to the specific goal of guiding in-
dividuals. The first step in this argument is to examine arguments that
one of the approaches is completely unserviceable, and rebut them (the
arguments against AA are discussed in section 2, while criticisms of ER
are described and addressed in section 3). Simply put, neither approach
is unserviceable because both are flexible enough to accommodate all of
the features that reasonable people might think matter to rationality. For
one, neither requires that rational individuals use a particular, controver-
sial type of mechanism (either simple or complex); AA involves checking
for the coherence of outcomes and not how they were produced, while
ER’s standard is the performance of the process, so a process that per-
forms poorly will not be judged as rational. Second, both permit agents to
have diverse values matching the diversity actually observed; axioms are
abstract and make no reference to the content of preferences or premises,
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and ER’s criterion of ‘accuracy’ is likewise neutral regarding the content
of the agent’s goals. Finally, both are able to incorporate sensitivity to
features of the environment that legitimately influence people; the AA
proponent is free to endorse different axiom systems for different con-
texts while ER is not committed to a particular way of carving up the
space of contexts with respect to which processes are evaluated. At the
same time, each approach has value because each has a way to produce
concrete evaluations of rationality without dogmatically imposing goals
and values onto people.
Despite this shared agnosticism, practitioners of AA and ER have his-
torically had quite different goals in addressing rationality, and these dif-
ferences are reflected in the methods each uses and the distinct package
of costs and benefits each has chosen (see section 4). Section 4.2 ad-
dresses the requirement of clear rationality tests to be used in evaluating
rationality; in checking the coherence of observed behavior patterns, AA
has a straightforward and relatively objective way to render rationality
judgments, while a major obstacle to the application of ER is that its ra-
tionality criteria are unclear in many cases of interest. Coherence tests are
rather weak, though, and do not lend themselves to suggestions for im-
provement as easily as do ER’s comparisons of concrete processes; Section
4.3 argues that ER has an advantage in that its rationality judgments func-
tion as actionable recommendations. Section 4.4 discusses how each ap-
proach delivers the desideratum of generalizability, but in different ways:
AA judgments generalize across all cases in which agents exhibit the same
behavior, but do not necessarily tell us much about how a particular agent
will perform in other cases. ER judgments only pertain to the specific
context-process pairs that are evaluated, but tell us precisely what per-
formance we should expect when a process is used in a context. Broadly,
then, AA’s use of axioms enables precise, rather scientific judgments on
the basis of readily observable behavior at the cost of those judgments
being circumscribed and relatively weak. In contrast, ER gets to the root
cause of an agent’s performance and the most natural target of recom-
mendations for improvement–the process they use–at the cost of having
to accurately identify such processes and provide defensible criteria for
evaluating them.
Each of these choices could be the more reasonable depending on the
particular setting in which rationality is being evaluated, and especially
on the accessibility of elusive information about agents’ processes, goals,
and so forth. Nonetheless, the costs of each are real and are borne only
because it has seemed necessary to secure the benefits. I submit that we
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can (in many cases) do better: in section 5 I propose a ‘hybrid approach’
that combines AA and ER so as to pay lower costs and reap more ben-
efits than is possible with either alone. This hybrid approach evaluates
processes according to their expected conformity to the relevant axioms,
thus addressing the root cause of agents’ performance while avoiding ER’s
problem of identifying objective standards. While not a panacea, I argue
that the hybrid approach–when applicable–is the best we can do given the
kinds and amounts of information currently available to us. In promoting
a specific method of harnessing the benefits of both AA and ER, I hope
to help advance meta-rationality research beyond the long-standing ar-
guments over the degree to which different views can be reconciled and
show how the approaches’ differences can actually be exploited to our
advantage.
2Objections to the axiomatic approach
2.1 Mechanisms
AA is often criticized (e.g., Simon 1956; van Rooij et al. 2012; Berg and
Gigerenzer 2010), for an alleged commitment to complex mechanisms
such as the maximization of a utility function or the execution of a dif-
ficult computation, but the brief descriptions above suggest that it is ER
that defines rationality according to the process applied to a task, while
AA evaluates the rationality of outcomes. To understand this line of criti-
cism, we must examine some applications of AA and how they have been
interpreted.
As stated, when we apply AA to evaluate an agent’s rationality, eval-
uation proceeds by checking the agent’s behavior (construed loosely to
include choices, inferences, etc.) for conformity to a set of abstract ax-
ioms, which serve as rules of rationality. Which axioms should be used?
Applying AA involves (at least conditionally) endorsing some set of partic-
ular axiomatic theories (ATs), but an AA proponent is under no obligation
to accept any particular AT as normative simply because it purports to
provide axiomatic requirements of rationality. Each AT must be evalu-
ated according to its merits, and the way ATs are typically presented and
defended can give rise to mechanism-based critiques.
The first step in providing an AT is enumerating the axioms them-
selves; these should be abstractly stated, simple, relatively few in number,
and have strong intuitive force (von Neumann and Morgenstern 1953, ch.
1). Yet listing the axioms is not enough; how do we know each of those
axioms should be included, that nothing needs to be added, and that the
system captures (axiomatizes) the intended concept? As von Neumann
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and Morgenstern (1953, ch. 1) write, a system “is usually expected to
achieve some definite aim–some specific theorem or theorems are to be
derivable from the axioms”. In the case of Expected Utility Theory (here-
after ‘EUT’), which originated with those authors, the aim is to provide
axioms for choice that are jointly equivalent to the choices being repre-
sentable as maximizing a numerical utility function (and indeed there are
many ways of doing this; see Gilboa (2009) for discussion of several ax-
iomatizations). Similarly, discussing the axiomatic AGM theory of belief
revision, co-creator Makinson (1985, 350) says that:
When tackling a problem like this–the logical or mathematical un-
derstanding of an intuitive concept or process–there are two general
strategies that tend to present themselves: postulation on the one
hand, and explicit construction on the other. On the former approach,
we seek to formulate a number of postulates, preferably of a more or
less equational nature, that seem plausible for the process, and then
investigate their consequences and interrelations. On the latter ap-
proach, one seeks to formulate explicit definitions or constructions of
the central concepts, and then investigate how far the concepts thus
constructed satisfy various conditions, including in particular those
which on the former approach may have been suggested as postulates.
In the case of belief revision, Grove’s (1988) sphere-based modeling
provides support for the AGM axioms by showing that revising in accor-
dance with those axioms is equivalent to applying a particular minimal
change function to one’s beliefs, given a representation of one’s prior be-
liefs and revision commitments as a (mathematically defined) system of
nested ‘spheres’.
These supporting theorems are known as representation theorems,
and while not all representation theorems introduce process language,2it
seems to arise naturally. For EUT especially, this language is often inter-
preted literally and the theory is criticized for assuming or requiring that
rational agents make choices via the process of calculating the expected
utility of each of their options, and selecting the option with the greatest
expected utility (see, e.g., Simon 1956, 1957; Klein 2001).
Since EUT is sometimes interpreted mechanistically, there is confu-
sion about its theoretical commitments even though the version of EUT
now standard in economics (Mas-Colell et al. 1995, ch. 6) is ‘only as-if’–
i.e., the theory says that people choose as if they maximized a utility
2ATs for which this is not the case are still subject to mechanism-based critiques, and
can still evade those critiques.
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function, not that they actually or should do so. ATs more generally fol-
low this pattern, and awareness of this is reflected in the fact that those
who criticize ATs’ purported mechanisms often criticize them for being
‘only as-if’ as well (Simon 1957, 1956; Gigerenzer et al. 2011). As noted in
the introduction, I aim to evaluate the strongest version of AA, and this
is the version that renders many potential criticisms inapplicable by only
endorsing the weaker ‘only as-if’ claims.3
Nonetheless, even an ‘only as-if’ theory is vulnerable to certain mech-
anism-based objections. Suppose an expected utility theorist (or an AGM
theorist) suspects that an agent makes an axiomatically-rational choice
(or belief revision) because that agent uses a simple heuristic; the theorist
explains or justifies that choice (or revision) by saying that the heuristic
approximates the ideally-rational mechanism of maximizing expected util-
ity (or applying the minimal change function to some set of spheres). This
position does not escape the danger of appealing to implausible mecha-
nisms: van Rooij et al. (2012) argue that the computation that an agent be-
haves ‘as-if’ they performed cannot be explanatory if there is no way that
the agent could have computed it, even approximately. They essentially
prove that if a computation is intractable (i.e., NP hard), we cannot simply
find tractable functions–either one or several–to approximate it, for exam-
ple explaining behavior via a complex calculation and a simple heuristic
that we use in its stead. Since there cannot be fundamental inconsis-
tencies between different levels on which we explain behavior, then, “the
only way to ensure consistency between algorithmic- and computational-
level theories in cognitive science [. . . ] is that computational-level theories
posit functions that are tractably computable” (van Rooij et al. 2012, 482).
The lesson is that the proponent of AA should be quite careful to avoid
appeals to mechanisms that go beyond their conceptual role in represen-
tation theorems and the mathematical power and convenience that they
often provide to a theory. The strongest and least vulnerable version of
AA focuses all normative claims on the axioms as criteria of rationality;
beyond the defensive value of this move, the operationalization of ratio-
nality is one of the chief benefits of AA over ER, as discussed in 4.2. A
more constructive critique of AA takes the importance of mechanisms as
its starting point; such arguments are discussed next, as well as in 4.3 and
4.4.
3See Okasha (2016) for an excellent, clear argument that the behaviorist interpretation
is the only tenable normative interpretation of EUT.
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2.2 Descriptive adequacy
A challenge to any AT must respect the distinction between descriptive
and normative facts–not object to normative claims simply because they
are at odds with what people actually do–and a general challenge to AA
must reflect the theoretical commitments of ATs rather than perhaps
problematic but non-essential views of particular practitioners. The AA
advocate can insist on ‘only as-if’ ATs to evade the mechanism-based cri-
tiques referred to above, but a different variety survives this move. A
compelling argument against ‘only as-if’ theories appeals to naturalism.
Simon and proponents of ER argue that understanding the processes
people actually use to choose, decide, and so forth is critical to under-
standing human rationality. Why would this be true, and why would it
cast doubt on an ‘only as-if’ normative approach? Kitcher (1992) provides
an answer by defending the naturalist position that “prescriptions must
be grounded in facts about how systems like us could attain our epistemic
goals in a world like ours” (63); what people should do depends on their
epistemic goals, cognitive capacities and constraints, and the nature of
their environment. Descriptive facts about human choice and inference
are naturally viewed as important data points in understanding the na-
ture of human rationality, not only because they can help us to determine
what is possible for people (and hence ensure that we respect the ought
implies can principle in the appropriate way) but also because we want to
understand why we perform well, or poorly, when we do. Pursuant to the
“meliorative project” that Kitcher advocates and I take as a starting point,
understanding why someone makes the choices that they do is invaluable
to guiding them towards greater rationality. Kitcher thus emphasizes the
investigation of strategies that may be implemented (see 4.3 for more on
this point). I will even argue in section 4 that such process information is
more valuable than the actual content of agents’ choices, in a way; hence
naturalism provides strong support for ER, which evaluates processes.
This positive argument for ER does not entail that we should reject AA,
though, for several reasons. For one, the value of process information and
the normative status of abstract rules are not incompatible, and in fact I
will argue in section 5 that ATs are well-poised to provide the standards of
rationality against which processes are evaluated. If we do not grant them
this role, alternative normative standards must be found. I will argue that–
especially in the case of choice (as opposed to inference, e.g.)–axiomatic
standards are the only kind of standards that we could justify given our
current knowledge and capacities for understanding descriptive choice,
mainly because axiomatic standards are coherence standards and corre-
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spondence standards for preferential choice are problematic (see section
5 for the elaboration of this point).
The legitimacy of evaluating processes–including simple heuristics–
using axiomatic standards depends on both the ‘only as-if’ interpreta-
tion singled out in 2.1 and the basic coherence I claim for the endeavor.
One might worry that many proponents of ATs will not in fact be happy
to accept that heuristics could be rational and that ER proponents will
likewise resist any attempt to grant normative status to abstract axioms,
the rhetorical enemy. Again, though, the issue is not whether everyone
working within one approach will be immediately willing to incorporate
ideas from the other, or even to grant the other’s value, but instead to
ask whether the approaches in fact have value and what role each is best
suited to play in achieving our goals.
2.3 Relevance of context
A more focused naturalist worry, hinted at above, is that ATs are too
detached from context and agential capabilities because they provide uni-
versal requirements for ideally rational agents (Kitcher 1992). Let’s grant
that the context in which a decision, inference, or belief revision is made
could legitimately impact its outcome, i.e., that it can be rational to be
influenced by contextual features, broadly construed. To give some in-
tuitive Sen-style examples (Sen 1997), one might choose an apple over a
pear in a context in which both are plentiful, but choose the pear in a
context of scarcity in order to leave others their preferred apples; one
might eagerly take the last piece of pizza from the dinner table at home
but move on to celery at an office gathering (when different social norms
are in effect). The context might also determine how carefully I approach
an inference problem and whether I revise my beliefs in response to an-
other’s incompatible assertion or simply dismiss their claim. What is AA’s
best response to the charge that abstract axioms formulated without re-
gard to content or context might fail to account for normatively-relevant
differences between situations?
The standard response in defense of particular ATs is a good start.
The rational choice theorist will note that–since the axioms are abstract–
relevant contextual features should be included as part of the content of
the choice problem. In the example above, the choice is not just between
pizza and celery, or even the last slice of pizza and celery; rather, there is a
choice between the last slice of pizza when this violates no social norms and
celery, and another choice between the last slice of pizza when this may
appear quite rude and celery. It is not inconsistent to choose pizza over
celery in the first but not the second case. The rational choice theorist will
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point out that their theory can accommodate anything that an agent cares
about in this way (Binmore 2009).4
This defense derives from the positive argument in favor of abstract
rules: rules should be formulated and evaluated independently of particu-
lar applications because our intuitions about particular cases can distract
and mislead us. Thus Stalnaker (1998) advocates determining the beliefs
rational agents may have at various stages of a game by applying the AGM
axioms–which provide abstract, general requirements of rational belief
change–rather than reasoning on the basis of the content of the beliefs
that need to be revised (pertaining, e.g., to opponents’ rationality) and
leaving room for our prejudices to influence our verdicts. Similarly, Du-
tilh Novaes (2015) argues that abstract rules of inference were originally
formulated to provide neutral, public standards by which to judge argu-
mentative moves, helping people to distinguish between valid arguments
and arguments with intuitive or appealing conclusions.
A further defense of AA exploits divergence between its rhetoric, its
reality, and its principled commitments. Rhetorically, ATs apply without
regard to context; their generality is emphasized because it is taken to be
a source of potency, for the reasons just given. In reality, a set of axioms
is never intended to apply to all situations; their domains of application
are simply very broad. A version of EUT may apply only to situations of
objectively-quantified ‘risk’ (von Neumann and Morgenstern 1953; Mas-
Colell et al. 1995) or to ‘small worlds’ (Savage 1954) (or situations prof-
itably analyzed as such, which is of course a judgment call). Classical logic
is almost universally assumed within mathematics, but taken to have less
relevance to argumentation or conversation (Grice 1975). Objections to
AGM disappear when the requirements of a revision context are enforced
(Stalnaker 2008). Endorsing an axiom system as providing normative re-
quirements of rationality does involve a commitment to context-neutrality
in one sense–axioms give abstract forms of good reasoning independent
of the content–but this neutrality only ‘kicks in’ once it has been deter-
mined that those axioms apply in the first place. A misapplication of a
particular AT poses no problem for that AT itself, let alone to the ax-
iomatic project as a whole.
One may still object that existing ATs do not apply as broadly is as
claimed, that they have taken abstraction and generality too far, or that
4This is also the rational choice theorist’s best response to complaints that rational
choice assumes agents to be selfish, care only for money, etc. (see Džbánková and
Sir˚uˇ
cek [2015] for a recent example, directed towards economics). Generally, the re-
sponses to this kind of complaint are similar to the responses to the context-based
criticism, and the complaint itself is much less relevant to AA as a whole.
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the existing set of ATs leaves too many contexts of interest unserved by
a normative theory (while some contexts, e.g., of choice, have a confusing
surplus of ATs). Note, however, that these are not theoretical problems
with AA, and future development of axiom systems could (and should)
remedy them.
A small number of ATs have historically been taken to cover most
contexts; yet there is no reason why this must remain the case, as it be-
comes clear that better coverage of the space of potential rationality judg-
ments can be achieved with more ATs. In fact, we can interpret recent
developments within logic in this way: where ‘logic’ once implied ‘classi-
cal logic’, there are now logics to meet every need (an early, well-known
alternative is intuitionistic logic; see Van Dalen [1994] for an overview).
This trend has spread from within the mathematical study of logic to
the use of logic in normative theories of everyday human activities, with
Achourioti et al. (2014) recently arguing for the description of a plurality
of logics where the context of the agent’s goals determines the relevant
norms. Stenning and van Lambalgen’s (2008) work on the interpretation
of conditionals is one example; another is the development of argumen-
tation theory, which seeks to replace classical logic–as a normative theory
of arguments–with alternative systems tailored to common real-life con-
texts (see Zenker [2012] for a survey connecting informal argumentation
theory with developments in formal logic, and Beall and Restall [2006] for
a defense of logical pluralism). For rationality research more generally,
a mapping project–in which ATs are mapped to contexts, and additional,
more specialized axioms are mapped to sub-contexts–could be quite fruit-
ful.
Lastly, AA can again be critiqued via a positive argument in favor of
ER: if humans do well in the world by using heuristics that exploit regular-
ities in the environment, then addressing this directly and understanding
the causes of our success will be valuable (Gigerenzer et al. 2011, intro.).
Again, I stress that finding value in ER does not entail rejecting value
in AA. Using a contextual heuristic–even a very successful one–does not
imply that accepted abstract rules should be violated, and indeed those
rules can play an important role in providing the standards according
to which the heuristic may be judged successful (see section 5). Once
this is granted, we see that we need more axioms–not fewer–so that there
are clear standards to use in evaluating more heuristics of interest. My
proposed hybrid approach thus makes the project of mapping axioms to
contexts much more pressing.
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2.4 Critiques of specific axioms or applications
Our goal is to evaluate AA as a whole (with respect to the goal of fos-
tering improvement), and towards this end critiques of particular ATs or
aspects thereof are not necessarily relevant. Nonetheless, a large enough
collection of serious problems with particular ATs could well cast doubt
on AA’s viability, or at least its short-term utility. One might doubt that
we could develop ATs with sufficient normative pull absent compelling
examples. For this reason, I highlight the best strategies for responding
to some of the stronger objections to particular ATs.
First, there are often objections to the normativity of individual ax-
ioms. This is especially true of EUT (see Mas-Colell et al. [1995, ch. 6]
for the standard modern version), and its independence axiom in partic-
ular (which is implicated in the well-known Allais Paradox [Allais 1953]).
There are many replies to such objections, and collectively they provide
a strong defense. Most basically, to debate the normative status of a par-
ticular axiom (such as independence) is to play the game in a sense, to
accept that there may be abstract rules of rationality and seek the right
ones. AA requires that defensible rules can be found, not that every pro-
posed axiom is in fact normative, or normative with respect to any given
context (recall 2.3). While Allais (1953) objected to the “mathematical” ap-
proach to rationality itself, others have accepted AA and instead sought
ways to weaken or do without problematic axioms. In the case of inde-
pendence, for example, Machina (1982; 1983) shows that expected utility
analysis can proceed with a much weaker requirement (that preferences
be ‘smooth’), and indeed that this change enables a unified representation
of an array of decision “anomalies”.
So-called ‘technical’ axioms (such as EUT’s Archimedean axiom)–which
are included for mathematical reasons, to enable the proof of represen-
tation theorems–can also be controversial. In this case, there is no real
cause to worry that including such axioms will result in misguiding the
agents we wish to advise; it is basically impossible to observe a violation
of the Archimedean axiom (or the non-technical completeness axiom, for
that matter) (Gilboa 2009, ch. 6.3.2). So the general concern that we will
not be able to find axiomatizations of rational choice that are both com-
pelling and powerful enough to place substantial restrictions on rational
behavior has not been borne out. (See also Gilboa [2009, ch. 6.3.3] for a
nice articulation of the argument for the reasonableness of utility maxi-
mization.)
Another important critique applies to the normative interpretation of
work in behavioral economics (hereafter ‘BE’) as part of AA. It is question-
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able whether BE should be taken to be normative at all, as researchers
within the program have typically focused on capturing descriptive facts
(cf., Kahneman 2003; Camerer and Loewenstein 2004) and they have been
criticized for retaining the traditional axiomatic normative standard while
putting forth new descriptive models (Berg and Gigerenzer 2010). If BE is
interpreted normatively, though, there are legitimate worries. BE theo-
ries such as prospect theory are not provided with strong defenses qua
normative theories (as orthodox theories are) and they are much more
complicated than the orthodox theories, with many more adjustable pa-
rameters. This additional complexity makes it difficult even to predict be-
havior for a new sample (see Berg and Gigerenzer [2010] and Brandstätter
et al. [2006] for critiques), let alone to impose substantial restrictions on
rational behavior that would enable mistakes to be identified for individ-
ual agents. For this reason, it is important that the AA proponent need
not (and should not) endorse any AT that, like BE theories, invites a lot of
criticism without offering greater ability to help people improve.5
3Objections to ecological rationality
3.1 Making excuses for inferior reasoning
ER is heavily based in descriptive work, and although proponents en-
dorse descriptive, normative, and ‘engineering’ (i.e., loosely, performance-
increasing) goals, descriptive questions have received the most attention.
The thrust of ER’s descriptive research is that humans (and other animals)
rely on the unconscious application of “fast, frugal, and accurate” heuris-
tics to make decisions and inferences (see, e.g., Gigerenzer and Selten
1999; Gigerenzer et al. 2011). This emphasis gives rise to the complaint
that ER loses all claim to normativity in endorsing psychologically plausi-
ble, yet overly-simplistic heuristic mechanisms. In other words, ER makes
(poor) excuses for humans’ bad reasoning.
According to ER, there is a misconception that they endorse heuristics
because they believe people can (and do) use them, even though people
would be better offusing more traditionally rational methods (Gigerenzer
et al. 2011, intro.). By definition, heuristics ignore or forget some informa-
5This is not to say that BE research is useless from a guidance perspective;
many of their findings are quite informative and the greatly improved understanding
of descriptive choice that has come from their empirical work should surely be incor-
porated into the meliorative project. For instance, Pope and Schweitzer (2011) show
that loss aversion has led to significant financial losses for professional golfers, and
Tversky and Kahneman (1981) show that people may be prone to errors on the basis
of framing (errors which can be detected by EUT). The point, however, is that ortho-
dox ATs provide a better standard by which to evaluate behavior than does prospect
theory, for example.
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tion and make relatively few and simple calculations. It was thus natural
to assume that their outcomes would be inferior to those of more complex
algorithms, even if such losses were worthwhile due to time and energy
savings; ER refers to this phenomenon as the “accuracy-effort trade-off”,
“believed to be one of the few general laws of the mind” (Gigerenzer et al.
2011, xviii).
Yet this critique of ER is faulty for two reasons. First, ER’s most in-
triguing discoveries have to do with the potential for heuristics to out-
perform more complex procedures by uncontroversial standards, mainly
by exploiting environmental regularities and avoiding overfitting (see, e.g.,
Gigerenzer and Goldstein 1996; Berg and Hoffrage 2008). Such findings
are very valuable from a guidance perspective because they prove that suc-
cessful strategies need not be difficult for people to learn or implement.
ER does not forsake performance in emphasizing heuristics, although it
is more explicitly permissive of trading offsome performance for speed
and efficiency (hence the list of three criteria–fast, frugal, accurate–for
heuristics).
Furthermore, this position no more commits ER to requiring simple
mechanisms than AA’s position commits it to requiring complex mecha-
nisms. Gigerenzer et al. (2011, xxi) say as much:
In which environments is a heuristic better than, say, a logistic re-
gression or a Bayesian model, and in which is it not? [. . . ] Once it is
understood that heuristics can be more accurate than more complex
strategies, they are normative in the same sense that optimization
methods [. . . ] can be normative–in one class of environments, but not
in all.
In other words, whether a simple or a complex mechanism is more
rational in a context is contingent on which will produce better results
in that context, a claim that AA proponents–who care about outcomes–
should find agreeable. ER studies the processes that we are interested in
(for the reasons described in 2.2) without thwarting our normative endeav-
ors by holding us to lower standards than the AA; inferior mechanisms
will be recognized as such.
3.2 Substantive standards
How could we answer Gigerenzer’s rhetorical question about when a heuris-
tic is better than a Bayesian calculation? ATs provide clear standards of
rationality via their axioms, and those standards are coherence standards.
It is less clear what standards ER holds people to–in lieu of coherence–and
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whether these standards are substantive and appropriate. What makes a
process a “good match” for an environment, or a better match than an
alternative process? The short answer is captured by the slogan “fast, fru-
gal, and accurate” (see, e.g., Gigerenzer and Selten 1999): it is rational to
apply a process in an environment to the extent that it has these features.
More accurately, it is the expected performance of the process that mat-
ters, since the actual outcome will vary (and as I note in 4.4, this feature
is a virtue).
It is fair to ask if this checklist really amounts to substantive criteria.
Precise definitions of the constituents have yet to be provided, but our
concern is whether the criteria can be spelled out in a way that is meaning-
ful, useful, and compatible with the goals we think rational agents might
have. The meanings of speed and frugality are fairly intuitive, and I would
not expect serious difficulties with defining them precisely and sensibly
(or objections to their value). In contrast, the meaning of ‘accuracy’ is far
from clear and providing an explanation should be a top priority. I explore
a few directions here.
For particular heuristics, ER researchers define the “accurate” outcome
from their own perspective, and their definitions tend to be uncontrover-
sial because there are clear right answers in most of the situations studied
(in the ‘German cities task’, for example, the goal is to choose the city with
the larger population [Gigerenzer et al. 2011, ch. 3]). However, we cannot
expect this to be true in general: especially when considering situations
of risky decision-making or games, as opposed to simple inference tasks,
there may be significant controversy regarding the ‘right’ answer or the
‘good’ outcome; indeed, if this weren’t the case, rational choice would be
a far less interesting subject. But then there would seem to be two al-
ternatives available to ER: either it can set forth and defend a particular
assignment of value to the world, enabling simple and concrete assess-
ments of accuracy, or it can remain agnostic, and define accuracy as most
in accordance with the agent’s own preferences.
The first option is untenable from my perspective: philosophers have
argued for millennia without settling on an account of what has value
and why, or even agreeing that there is anything objective about value in
the first place; so it is quite unlikely that an explication of accuracy that
depended on an exogenously-given assignment of value could be satis-
factorily defended. It is unclear how or why rationality would consist in
obedience to someone else’s standards instead of one’s own.
Now, ER draws inspiration from biology, using the ideas of adaptation
and evolution to explain why humans rely on heuristics and why those
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heuristics work well for us (Gigerenzer and Selten 1999). This suggests
defining accuracy in terms of reproductive fitness, as is done by evolu-
tionary biologists using the tools of game theory, and ER does at times
identify accuracy with ‘success’ (e.g., in Gigerenzer et al. 2011, ch. 2). But
again, this definition would require a convincing argument that rationality
requires one to prioritize the success of one’s genes, and such an argu-
ment is not forthcoming. (See Hands [2014] and Grüne-Yanoff[2010] for
problems with biological arguments for ER.)
The second option avoids these problems by rendering it unneces-
sary, even inappropriate, to put forth a specific conception of value. An
outcome would be accurate insofar as it was in line with the agent’s own
goals or preferences–but this is likely to mean adopting the coherence
standard of AA when it comes to preferential choice. (Similarly, ER would
surely endorse deductive validity as the standard of inference, in the event
that the agent seeks classically valid beliefs.) The argument for this hy-
bridization is explicated in section 5.
As for ER’s other main criteria–speed and frugality–these are defensi-
ble sources of value precisely because they are inescapably connected to
real human preferences; it is obvious that people have a preference for
making their decisions in a timely and efficient fashion (and indeed need
to much of the time). How much these criteria should be weighted relative
to accuracy has not been explained, and there might be room for the worry
that ER will overvalue them; this would re-invite the accusation of making
excuses for humans’ bad reasoning. There is also a worry that–although
ER proponents criticize EUT’s implicit exchange rates between different
sources of value–ER must itself specify some kind of exchange rate be-
tween speed, frugality, and accuracy in order to evaluate the rationality
of agents’ (real and potential) trade-offs between them. Again, these prob-
lems are best addressed by deferring to agents’ own preferences, rather
than exogenously imposing value judgments.
3.3 The generality problem
ER can be viewed as a generalization of reliabilism in epistemology, the
view that the reliability of the processes or methods used is an important
criterion (or even the criterion) for a person’s belief to be knowledge (or
to be justified, etc.) (Goldman and Beddor 2016). Considering objections
to reliabilism is therefore instructive, and one particular objection–the
generality problem (Conee and Feldman 1998; BonJour 2002)–is indeed
quite pertinent.
The problem is this: suppose I look across my friend’s office and form
the belief that there is a copy of Crime and Punishment on her desk. ‘Sim-
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ple reliabilism’ says that this belief is justified iffit is formed by a process
that reliably generates true beliefs, but whether this is the case will de-
pend on the level of generality at which the situation is described; my
visual processes may be only moderately reliable over the full range of
cases they are used, quite reliable for identifying objects around 10 feet
distant, very unreliable for identifying small objects such as books at this
distance, but perfectly reliable with respect to the singleton ‘identifying
a Russian novel exactly 10.5 feet away in bright June morning sunshine’.
Reliability varies according to the description of the process and context,
and there seems to be no non-arbitrary way to single out the ‘correct’ level
of generality at which to describe them.
This problem would seem to affect ER as well, and especially as it is ap-
plied to guide agents towards greater rationality. We can understand the
ecological position as maintaining that rationality claims are conditional
claims, i.e., claims of the form “if the environment is like this, then such
and such process is ecologically rational”. An alternative phrasing would
be “in the class of environments that share such and such features, this
process will generally be more successful than alternatives”. Yet without
a prior reason for studying a particular context or a process that could
be used to derive a context, how should the boundaries of the context
and process be drawn? What is the best level of generalization? (As with
reliabilism, there are problems with both too little and too much general-
ity. See, for example, Lee’s [2007] argument that a heuristic as studied
by ER cannot even be explanatory until both the heuristic and its range of
application have been fully specified; Lee suggests that ER proponents ad-
dress this problem by addressing the methodological questions it raises
for them. Similarly, Kitcher [1992, 66] points out the need to characterize
a process’ target contexts.)
We might try to avoid the problem by acknowledging the validity of
the rationality claims at all levels, and leaving judgment to determine the
appropriate level of generality for any given case in practice. Still, the exis-
tence of multiple, perhaps incompatible evaluations of the same situation
is disconcerting. This is an interesting and highly important issue, and it
will take substantial work to make headway into an answer. Here, suffice
it to say that the problem is bigger than ER, but that the approach should
be able to accommodate a solution since it seems to have no principled
commitments that would prevent this.
This observation also addresses a related concern, that since ER makes
all judgments relative to an environment, there is a danger of losing the
bigger picture. ER may focus on the details of a particular situation to
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such an extent that no general rules emerge that the agent can use to
succeed in a new environment. The ER proponent must acknowledge that
rational agents need to abstract to some extentbecause they cannot use
(or, especially, learn) the unique ideal process for every situation they
encounter (and indeed this “process” would be trivial, simply stipulating
the best-response action for the situation). The question is the extent
to which agents, and theorists, should abstract. ER proponents should
be willing to generalize contexts as far as is sensible, and they have not
said anything to indicate that they would do otherwise. Furthermore, the
hybrid approach suggests a potentially-useful rule for fixing evaluation
contexts: evaluate processes with respect to the context of application of
the relevant axioms. If this context seems too broad, the mapping project
advocated in 2.3 can be used to refine it.
4The costs and benefits of AA and ER
4.1 Chief differences
The foregoing shows that both AA and ER escape fatal flaws that would
render them unserviceable. Notably, both approaches survive scrutiny
because their flexibility allows them to incorporate each other’s insights
into their defensive strategies. Although both approaches aim at the same
end–rationality judgments–the distinct methods their proponents employ
do entail the acceptance of different packages of costs and benefits, and
so their judgments differ in particular ways. The chief difference between
AA and ER (for present purposes) is that ATs judge outcomes, while ER
judges processes. An attendant, less fundamental difference is that ATs’
judgments tend to be all-or-nothing (though AA researchers have sought
ways to render more fine-grained judgments; see, e.g., Schervish et al.
[2000]; Echenique et al. [2011]), while ER judgments are naturally com-
parative (“this process is more ecologically rational than that one in this
context”). The remainder of this section shows how these methodologi-
cal differences cause each approach to perform well with respect to some
desiderata, and less well with respect to others. Again, the purpose with
respect to which the approaches are evaluated is that of producing evalu-
ations that can be used to guide agents towards greater rationality.
4.2 Clear rationality tests
A high-priority desideratum for the meliorative project is clear, relatively
straightforward and objective tests for rationality. A prerequisite to telling
people what to change in order to be more rational is to identify the prob-
lematic aspects of what they are already doing. In order to do this with
proper authority and legitimacy, the criteria according to which the per-
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son is judged should be as clear and objective as possible; compare giving
an agent a short, standardized list of simple requirements that they have
failed to satisfy with giving them a long written argument to the effect that
you think they have made certain mistakes for various subjective reasons.
With respect to this desideratum, ATs are well served by their axioms
and ER pays the cost of judging the rather vague “match between mind
and environment” (Gigerenzer et al. 2011, xix), leaving ‘accuracy’ unspec-
ified, and not defining an exchange rate between speed, frugality and ac-
curacy.6For AA, once an AT is endorsed for a certain domain, the axioms
provide straightforward requirements of rationality and it is fairly simple
to check whether readily-observed behavior conforms to those axioms or
instead violates any axioms or implications thereof. For example, if an
agent makes a series of choices between lotteries, their choices can be
represented on a simplex and there is a very easy geometric test for con-
formity to the EUT axioms (namely that the indifference curves must be
straight, parallel lines, or planes, etc.) (Mas-Colell et al. 1995, ch. 6). Es-
pecially when the number of possible outcomes does not exceed three,
a simple diagram suffices to show whether the choice pattern may be
deemed rational. To use a system of logic to judge argumentative moves
in a multi-agent debate, one might use natural deduction to show that the
claims each agent makes can be derived from agreed-upon premises using
the applicable inference rules; indeed, there are now computer programs
that will quickly check the validity of an argument whose premises and
conclusions are entered in abstract form.
While interpretational problems are not entirely eliminated–we need
to identify the correct objects of choice, the implicit premises, and so on–
axioms thus provide the most straightforward and objective criteria that
could be asked for, given the subject matter. They make the criteria for
rationality explicit, and the theorist need know nothing of an agent’s in-
ner psychology to determine whether those criteria have been met. This
is not an accidental feature of ATs; rather, concepts of interest (e.g., belief
revision, utility maximization) are axiomatized in order to specify and op-
erationalize their meaning. This motivation is manifest in von Neumann
and Morgenstern’s presentation of EUT (1953, ch. 3.5.2); the authors ex-
pound on the need to make economic problems amenable to scientific
treatment by appealing only to observables (for them, choices) and note
the desirability of keeping the set of axioms small and uncomplicated.
6To be clear, performance criteria are specified for particular problems; it is not im-
possible to do so. The issue is rather that a general, theoretical explication is lacking
and, importantly, there are situations of interest for which the right criteria are far
from clear.
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The same motivation pervades economics more generally and can even be
found in the origins of logic (as noted earlier; see Dutilh Novaes [2015]).
4.3 Actionable results
A second desideratum for an approach to rationality with meliorative
goals is that it produce directly actionable judgments, i.e., that the agent
whose rationality is judged be in a position to make real improvements
on the basis of the judgment. AA’s benefit of clear behavioral rationality
tests comes at an actionability cost, while ER’s judgments (if prudently
formulated for the purpose) are directly actionable.
ER evaluates processes, and its evaluations can therefore be read as
recipes for improvement. Processes are ways to complete tasks, and these
can be taught, learned, and implemented, especially when they are sim-
ple (as heuristics are). ER evaluations are also comparative: process A
is more ecologically rational than process B, which is more ecologically
rational than process C (with respect to a particular task and context).
An agent who is told this, and told that they have been using process C,
knows immediately that they can make a rational improvement by switch-
ing to process B, and an even greater improvement by switching to A.
(Of course accounting for the costs–including opportunity costs–of such
switches may be difficult, but the point here is that the recommendations
for improvement follow directly from the evaluations because the focus is
on processes.) One caveat is in order: ER’s judgments may be sensitive to
whether each process is employed unconsciously or deliberately, because
the deliberate application of a process by an agent may take time and
energy that would not be needed if their brain implemented it automati-
cally; it is important not to recommend that an agent switch to a process
that would no longer be judged superior once the costs of deliberately
implementing it were taken into account.
In contrast, there is a gap between AA judgments and implementable
recommendations for improvement. If an agent’s behavior is judged ra-
tional according to the relevant AT, then no action is needed as far as
we can tell. If the behavior is judged irrational, though, the question of
how the agent should respond is left open. Take the Allais Paradox, for
instance: the paradox is that a commonly-displayed pattern of choices
between lotteries violates EUT (Allais 1953). As noted, the AA proponent
is under no obligation to endorse EUT and may well prefer a weakened
theory that permits the Allais choice pattern, but let us suppose that we
endorse EUT and aim to help the agents who made the problematic choice
to avoid the error in the future. It is easy to see that the axioms are vio-
lated, but this does not tell us why the agent made an error, how serious
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the error is (though see Zynda [1996]; Schervish et al. [2000]; Staffel [2015]
for attempts to address this), or how frequently we can expect the agent
to make similar errors (see 4.4 for more on this point). The agent has
no recipe for improvement; perhaps they can (and in the Allais case may
well) avoid making the error if they face exactly the same situation again,
but they cannot hope to avoid similar errors in the future unless it is ex-
plained to them why their original choices are problematic and what to do
differently (i.e., how to choose better). As Kitcher (1992, 68) writes,
The philosophical dichotomies rational / irrational and justified / un-
justified may stand in need of replacement rather than analysis. When
we note that a student falls short of the external ideal (as we conceive
of it), debate about whether the failure to undergo the epistemically
optimal process is excusable or not can profitably be sidestepped in
favor of a psychologically richer explanation of what occurred. Cogni-
tively inferior performances can be based on laziness, methodological
ignorance or misinformation, failure to perceive relevant similarities,
lack of imagination, and numerous other kinds of factors.
I do not suggest that the AA proponent would be unable to generate
sensible recommendations on the basis of axiom violations, but it is im-
portant to recognize that doing so requires going beyond ATs’ basic judg-
ments. The appropriate recommendation is also likely to depend on the
reasons for the error (as Kitcher suggests), i.e., the process that ER but
not AA is explicitly interested in. Furthermore, to the extent that these
recommendations remain informal, subjective supplements to the basic
axiomatic tests, they are unlikely to inherit the full authority of the tests
themselves.
4.4 Generalizable evaluations
A final desideratum is that evaluations of rationality be generalizable; this
is in part an efficiency consideration and in part a corollary of the second
desideratum (in that it is useful to be able to generalize from an agent’s
performance in one case to their expected performance in other cases).
Both ATs and ER produce evaluations that are generalizable, but in differ-
ent respects.
Since ATs evaluate observational records–and features internal to the
agent are not considered–their evaluations apply equally to all agents who
display the same pattern of choices, inferences, and so forth. For exam-
ple, all agents who display the Allais choice pattern choose irrationally ac-
cording to EUT, while all agents who rate the proposition ‘Linda is a bank
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teller and an active feminist’ more probable than ‘Linda is a bank teller’
(Tversky and Kahneman 1983) make an error according to a straightfor-
ward application of probability theory. Axiomatic evaluations generalize
across agents when we hold the problem fixed. They do not generalize,
however, to other problems faced by the same agent: violating axiomatic
requirements in one case does not imply that an agent will violate them in
other cases, nor does conformity in one case imply conformity in general.
A brilliant reasoner may have a bad day and fall prey to a fallacy, while
an agent who makes perfect logical inferences on an exam may (for all the
AT user knows) have flipped a coin on the tougher problems and simply
got lucky.
ER avoids this problem because processes are judged according to
their expected performance in a context; the theorist considers (perhaps
simulates) the track record of results that the process would yield, and
evaluates this bigger picture. The difference between AA and ER in this
respect is analogous to the difference between making a prediction on the
basis of a statistical distribution and doing so on the basis of a single point
sampled from that distribution. While a sample is not uninformative, it
can mislead; knowing the full distribution is far preferable.
ER judgments will also generalize to all cases where the same process
is used in the same context, just as AA judgments generalize to cases with
the same outcomes. But while the possible outcomes are often limited,
the space of processes that agents could use is surely infinite and it may
be difficult or impossible to determine which an agent uses. In practice,
therefore, a particular ER judgment is likely to lack the broad applicability
of an axiomatic judgment of a behavioral pattern.
5Implications
The implication of these distinct packages of costs and benefits is that
neither AA nor ER should be abandoned in favor of the other, especially
once we restrict attention to the meliorative project. The better approach
will be a function of the information available in any given situation: ER
will be advantageous given insight into the processes agents actually use
for a task or given the opportunity to teach agents new strategies, while
AA allows us to evaluate rationality in the (exceedingly common) situation
in which only outcome data is readily available.
Furthermore, the complementarity of the approaches’ costs and bene-
fits suggests a stronger conclusion, namely that we would often be better
served by a strategic combination of AA and ER than by either of them
alone. ER has a significant strength in using process information when
it is available, but the problem of clear rationality tests for those pro-
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cesses looms large (recall 3.2). Berg argues that since the true markers
of well-being for agents are health, wealth, and the like, our normative
projects should assess strategies for achieving those goods (as opposed
to behavioral consistency). Criticizing the use of money-pump arguments
to defend theories of coherent choice, he writes, “[i]f the compelling nor-
mative principle is, for example, wealth, then why not simply study the
correlates of high-wealth-producing decision procedures and rank those
procedures according to the wealth they produce” (Berg 2014a, 382)? Un-
fortunately, such an inquiry will not be entirely sufficient. While Berg
and colleagues are entirely correct to ask whether and to what extent the
traditional rationality (often, coherence) of agents’ choices and beliefs co-
incides with the success those agents achieve according to independent
metrics such as health and wealth (see, e.g., Berg and Lien 2003, 2005;
Berg 2014a; Berg et al. 2016), the claim that coherence metrics are essen-
tially useless (Berg and Gigerenzer 2006; Berg 2014a) is far too strong. I
side instead with Sturm (2012, e.g., 77-78), who suggests that traditional
(often, axiomatic) rationality requirements provide the background stan-
dards against which performance (e.g., the ecological rationality of heuris-
tics) can be evaluated. In spelling out a specific way in which axioms can
provide background standards, I construct a stronger response to Berg’s
challenge than has previously been offered.
Let’s begin by granting the claim (by naturalists, ER proponents, and
others) that in order to make useful normative judgments, we should eval-
uate choice strategies in terms of their expected performance. Perhaps
we want to know which investment strategies to endorse.7First, we must
note that we could not discover the most rational strategies simply by
identifying the wealthiest people and studying the strategies they have
used, because actual wealth is a product of luck and circumstance as well
as one’s own strategy. Instead, we would need to ask which strategies lead
to the most expected wealth.
7Berg (2014b) himself gets at this question indirectly in a paper showing that the best
explanation of entrepreneurs’ business location choices is a simple heuristic model
rather than an optimization model; his discussion is highly suggestive of the idea that
the heuristic, which ignores or fails to gather much of the available information, can
be rationalized by features of the choice environment, which include uncertainty and
frequent change. This paper’s analysis is certainly very useful for understanding the
factors behind which areas see development, the likely consequences of public poli-
cies and taxation strategies, and for providing more evidence that heuristics can lead
to real-world success. Nonetheless–as explained below–I would argue that rigorously
comparing the rationality of the individuals’ available choice processes requires sen-
sitivity to the individuals’ risk preferences, and hence some appeal to coherence stan-
dards. If this is not possible then assessments of heuristics’ success must fall short of
assessments of their rationality.
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Second, we must acknowledge that expected wealth cannot be the cor-
rect rationality criterion for an old, familiar reason: the conception of
rationality as maximizing expected monetary value was replaced with the
conception of maximizing expected subjective utility for the simple reason
that the two differ, and the latter (by definition) expresses the preferences
that we are interested in. Daniel Bernoulli discovered this now-obvious
fact, and the correctness of his reasoning was immediately apparent:
The price of the item is dependent only on the thing itself and is equal
for everyone; the utility, however, is dependent on the particular cir-
cumstances of the person making the estimate. Thus there is no doubt
that a gain of one thousand ducats is more significant to a pauper than
to a rich man though both gain the same amount (Bernoulli 1954, 24).
Bernoulli developed a new theory of expected utility maximization on
the basis of this insight, and famously used it to explain the St. Petersburg
Paradox, which is set up as follows. Suppose a gamble is available with
the payout to be determined by the flipping of a fair coin. Let nbe the
number of the flip on which the coin first lands heads; the gambler then
receives $2n1. In other words, the gambler gets $1 if the coin comes up
heads on the first flip, with the payout doubling each time ‘tails’ appears.
Suppose people have the opportunity to pay in exchange for this gamble.
The puzzle is that the expected value of the gamble is infinite, but most
people would not pay $20 for it, and furthermore this choice is intuitively
reasonable; but if the rational choice is the expected value maximizing
choice, the rational agent would choose the gamble over $20 for certain.
If subjective utility is what matters, however, and the agent values each
additional dollar less than the previous one, then it may be rational to
refuse the gamble even for $10.
The upshot is that the expected monetary value of an option may be
very different from its subjective value, and we are liable to be drasti-
cally misled if we assess rationality on the basis of the former. For exam-
ple, a strategy that often leads to great wealth but occasionally results
in penury may look quite rational from an ‘objective’ perspective that
most real agents would reject. Diminishing marginal utility for money
is likely to be particularly relevant to major choices–such as investment,
insurance, or career choices–which we should be especially concerned to
analyze correctly.
Furthermore, there is no canonical utility function that, once discov-
ered, would solve this problem; individuals may legitimately differ in their
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subjective valuations of money and their implicit risk preferences.8The
third step in our argument is therefore to ask how we could determine
the extent to which a choice strategy results in choices that agree with an
agent’s subjective evaluations. The answer provided by decision theory
is that, since we cannot observe agents’ ‘true’ personal preferences, we
can instead observe their choices and determine whether the agent could
be choosing what is best by their own lights given some preferences that
satisfy simple, compelling properties such as transitivity. While it would
arguably be better to compare choices to verifiably-true preferences, the
decision theorist accepts that this information (if preferences are even
taken to be real) is inaccessible to us and moves on, constructing a the-
ory around available observations. The result, then, is that in attempting
to replace coherence standards with an independent, external standard
of rationality, we find we must fall back on those axiomatic standards if
agents’ subjective preferences are to be respected.
It is critical not to read too much into the subjective preferences that
this argument refers to; adopting the full apparatus of a complete and
stable preference ordering would seem to beg important questions. (Util-
ity likewise should not be read in this section as a modern technical term,
but rather as Bernoulli would have used it.) While it is quite reasonable
to criticize the assumption that people have preferences in the strongest
sense, my argument only requires that people have the sort of preferences
that figure in folk psychology; such preferences are both harder to deny
and a minimum requirement for normative judgments of choice for both
AA and ER. Hence, it will not be easy for the ER-purist to reject my hybrid
approach on the grounds that agents do not have preferences to which it
makes sense to apply axiomatic standards.
In fact, the preferences that EUT must posit are more like folk-psycho-
logical preferences than is often realized. On the strong characterization
of preferences, a person comes equipped with a complete ordering over
all possible outcomes; this ordering is stable over time and reflects their
true, inner self. All of the substantial aspects of this characterization can
be dispensed with, however. First, regarding stability, EUT permits peo-
ple’s preferences to change over time and from situation to situation; as
8Bernoulli (1954, 32) himself defined a unique utility function, the natural logarithm
of the objective value, but this function is not taken to have special normative status; it
is easy to imagine that different people might care differently about different ultimate
levels of wealth as a result of different personal tastes. Even with the Bernoulli loga-
rithmic utility function, it would be necessary to know an agent’s initial wealth level
to determine their expected utility-maximizing choice. For example, the St. Petersburg
gamble would be worth $2 to an agent with no wealth whatsoever, and $6 to an agent
with $1000 of wealth.
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Ross (2014) explains in his defense, it is a mistake to equate the perhaps
short-lived ‘agents’ that EUT refers to with temporally-extended human
beings. If my preferences differ from last week’s, then I am now a dif-
ferent agent. This observation limits our ability to apply EUT over ex-
tended periods of time, but this is exactly as it should be; if my tastes
and goals have changed, it makes no sense to demand coherence between
past and present behavior. Second, assuming that preferences are com-
plete is also fairly innocuous; we need not endorse the metaphysical claim
that an agent’s mind contains a full preference ordering at all times, but
only that the person can form a preference when called upon to choose
(Gilboa 2009, 62). It is no problem for my argument if preferences are
constructed on the fly. Intriguingly, behavioral economics experiments
suggest that agents do this, and that the preferences they construct are
both arbitrary in an important sense (influenced by irrelevant factors such
as priming numbers) and largely coherent (Ariely et al. 2003). Third, these
weak interpretations of the stability and completeness requirements al-
ready suggest that the idea of a ‘true inner self’ is dispensable as well.
Infante et al. (2016) show that this idea is both ill-founded and integral to
the project of “preference purification”, which seeks to align people’s ac-
tual choices with the idealized preferences of their perfectly-rational true
selves. While the authors are right to point out that it is often impossible
to determine which particular choice is mistaken in an incoherent pattern–
and that indeed there may be no fact of the matter–their attendant critique
of behavioral economics’ ‘nudge’ program does not automatically imply a
critique of EUT itself. Importantly, we can deem the incoherent choice
pattern to be irrational simply because it is incoherent, and not because
we think this incoherence indicates a failure of the agent to express their
true self in some particular way. Finally, references to risk preferences
should not be read as implying that individuals have risk aversion or risk
affinity as part of their true natures; as is standard in economics, these la-
bels are merely short-hand for agents who display preferences such that
a set payout is preferred or dispreferred to a risky gamble with the same
expected value. To have risk preferences in this sense is simply to make
choices one way or the other when called upon to do so.
It would be difficult to deny that people have preferences in this weak
sense. Freed of their metaphysical baggage, they are simply an experience
that people have; in von Neumann and Morgenstern’s (1953, 17) words, a
preference is just a “clear intuition” of how two outcomes rank. While the
burden of proof is on those who posit (rather than question) preferences
in the strong sense, the opposite is the case regarding preferences in the
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Patricia Rich / Axiomatic and ecological rationality
weaker sense, as they are a basic part of our folk psychology. One might
then ask whether preferences in the weak sense are too flimsy to support
normative judgments at all; if they might change tomorrow, aiming to
satisfy them today seems less important. But if these preferences cannot
support normative judgments nothing is left to do so, and surely we do
not want to abandon the normative project altogether. Furthermore, as
a matter of fact, we respect people’s rights to their preferences irrespec-
tive of their source or permanence; and we find this natural because our
preferences are usually relatively stable and grounded in other aspects of
our folk psychology. So a reflective agent will be troubled if their current
preferences are shown to be basically inconsistent.
Observe that, while the conclusion of this argument–that coherence
provides our best test of choice rationality–is controversial and rejected
especially by ER proponents, the steps of this chain of reasoning are not
contested as part of such critiques, are not taken to be controversial in
general, and in fact seem quite inescapable. Indeed, in imagining how
we might implement the suggestion to evaluate processes or strategies
rather than coherence in a concrete setting, we are essentially forced to
rehearse the decision-theoretic tradition that culminates in a collection
of axiomatic theories of rational choice. So if an AA opponent wants to
reject this conclusion, it is incumbent on them to explain at which step
the argument goes wrong, and how something better can be provided for
situations in which the standards of success are clearly subjective.
A hybrid approach which evaluates processes as in ER, but uses AA’s
method of checking for conformity to axioms, solves this problem. Ax-
iomatic criteria apply to outcomes, but by simulating the performance of
a process in its intended context, an expected track record of outcomes is
produced. By applying the axiomatic test to this track record instead of
to a single behavior pattern, we also avoid AA’s generalizability problem.
Of course, this hybrid approach can only be applied when processes of
interest can be identified, and it is true that the empirical task of identi-
fying the process an agent actually applies is not easy. “Processes of in-
terest” include many more than those that can be definitively ascribed to
agents, however: a critical component of the meliorative project is teach-
ing agents new strategies for choice and inference, and the theorist can
construct and test candidates without knowing precisely what processes
they might replace.
An example will help to illustrate the hybrid approach and its virtues.
Consider again the Allais Paradox, a sequence of two choices between
pairs of lotteries in which the historic modal choice violates EUT (Allais
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Patricia Rich / Axiomatic and ecological rationality
1953). As discussed above, an AA proponent may apply EUT to determine
that this choice pattern is irrational (or apply another AT to determine
that it is rationally permitted); thus a clear verdict is delivered but ques-
tions about the broader significance of and appropriate response to this
verdict are left unanswered. Proponents of ER provide a causal explana-
tion for the choice pattern: Brandstätter et al.’s (2006) ‘priority heuristic’
is a simple decision procedure for lottery choices–constructed on the ba-
sis of the large body of descriptive findings pertaining to such choices–
that predicts the Allais pattern and a host of other empirical phenomena.
The authors stop short, however, of providing an explicit normative as-
sessment of the priority heuristic, despite the heuristic’s prominence in
the ER literature and the avowed normativity of ER. ER proponents’ em-
phasis on the success humans can achieve by using heuristics suggests
that they view the priority heuristic favorably, but in principle its norma-
tive status should depend on the degree to which it is well-matched to its
context of application. What could this mean in the case of lottery choice?
As already noted, the performance standards to be applied can neither
be biological nor objective. Appeals to biology may be rhetorically useful,
but we simply do not think that rationality requires us to maximize our
expected number of offspring. The only acceptable performance standard
for lottery choice must defer to agents’ subjective preferences, and as the
decision-theoretic tradition shows, the way to determine whether agents
could be choosing in accordance with their subjective preferences is to
apply an axiomatic test to their choices. The hybrid approach provides
a straightforward way to evaluate the rationality of the priority heuristic:
simulate its lottery choices over its purported context of application and
calculate its expected conformity to the chosen AT. This procedure yields
a numerical measure of accuracy, facilitating direct comparison with other
processes. (This is the practical manifestation of the formal compatibility
between AA and ER that I demonstrate in Rich [2014].) ER alone cannot
deliver this.
The particular strategy for combining AA and ER into a hybrid ap-
proach is not just supported by the value of both processes and outcomes,
but also by the related interplay between coherence and correspondence
criteria. These values have long been seen as competing within epistemol-
ogy, leading to different theories of truth, knowledge, and justification
(cf., Goldman 1967; Quine and Ullian 1970). Berg et al. (2016, fn. 3)
credit Hastie and Rasinski (1988) with bringing the distinction between
coherence and correspondence into the psychological literature on ratio-
nal choice and belief. Hammond (1990, 1996, 2007) explores the interplay
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between these values in great detail, taking an interdisciplinary viewpoint
and with an eye towards real-life choice and inference. As he writes in
Beyond rationality (2007, xvi),
[Y]ou don’t turn to logic to prove that the tree you see over there is
larger than the one over here [. . . ] But sometimes there is no “tree”
[. . . ] For example, a story told by someone usually offers no empirical
criterion for its truth. Then, we can evaluate it by referring to the
coherence of the story.
For preferential choice especially, Hammond’s “tree” is conspicuously
absent–hence the development of coherence standards. Discussing ER
specifically, he writes (2007, 98),
There are some judgments–and usually very important ones–that de-
mand justification before the action is taken. However, the justifica-
tion for correspondence judgments (accuracy, speed, and frugality)
can only be determined after the judgment is made. You won’t know
whether the judgment was accurate [. . . ] until later. [. . . ] Since no
empirical criterion for the correctness of such judgments will be avail-
able, the justification will have to be made on the coherence of the
argument for it, and on the argument’s content.
The question often posed to coherentists is what reason we have for
thinking that coherence–for example of an agent’s beliefs–is an indicator
of truth. We can see that this question can just as easily be directed
towards the AA proponent–why think that an agent whose choices merely
avoid manifest incoherence is in fact choosing what is best by their own
lights?–and indeed this concern is an important part of the motivation
for ER, which avoids the concern by getting at the source of the choices,
in a sense. Yet the critical point, as Hammond argues, is that coherence
is often the only criterion we have available; the ultimate goodness of
a choice, inference, or belief revision is simply not accessible to us in
many situations, and especially in situations of preferential choice. For
this reason, even if we endorse naturalism, the meliorative project, and
the core tenets of ER, AA will often be indispensable because it provides
clear, operationalized coherence standards to which there exists no viable
alternative.
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Patricia Rich is a postdoctoral researcher in philosophy, currently at the
University of Bristol and soon to be at the University of Hamburg. Her
main research areas are epistemology and game and decision theory, with
a focus on rationality. In addition to the present topic, she has written on
belief revision in perfect information games and reputation in signaling
games.
Contact e-mail: <pr15102@bristol.ac.uk>
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