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``If . . .'': Satisficing algorithms for mapping
conditional statements onto social domains
Alejandro LoÂpez-Rousseau
Instituto de Empresa, Madrid, Spain
Timothy Ketelaar
New Mexico State University, Las Cruces, USA
People regularly use conditional statements to communicate promises and threats,
advices and warnings, permissions and obligations to other people. Given that all
conditionals are formally equivalentÐ``if P, then Q''Ð the question is: When
confronted with a conditional statement, how do people know whether they are
facing a promise, a threat, or something else? In other words, what is the cognitive
algorithm for mapping a particular conditional statement onto its corresponding
social domain? This paper introduces the pragmatic cues algorithm and the syn-
tactic cue algorithm as partial answers to this question. Two experiments were
carried out to test how well these simple satisficing algorithms approximate the
performance of the actual cognitive algorithm people use to classify conditional
statements into social domains. Conditional statements for promises, threats,
advices, warnings, permissions, and obligations were collected from people, and
given to both other people and the algorithms for their classification. Their cor-
responding performances were then compared. Results revealed that even though
these algorithms utilised a minimum number of cues and drew only a restricted
range of inferences from these cues, they performed well above chance in the task
of classifying conditional statements as promises, threats, advices, warnings,
permissions, and obligations. Moreover, these simple satisficing algorithms
performed comparable to actual people given the same task.
In the beginning was a warning, and the warning was ``If you eat of the tree of
knowledge, you will surely die'' (Genesis 2:17). Since time immemorial people
have used conditional statements like this to warn others of imminent dangers
EUROPEAN JOURNAL OF COGNITIVE PSYCHOLOGY, 2004, 16 (6), 807±823
Correspondence should be addressed to A. LoÂpez-Rousseau, Amor de Dios 4, 28014 Madrid,
Spain. Email: lopezrousseau@yahoo.com
This research was supported by the Max Planck Society (MPG) and the German Research
Council (DFG). Thanks to Gerd Gigerenzer for theoretical inspiration, Alarcos Cieza and Julia
Schmidt for data collection, Gregory Werner for computer assistance, and the Adaptive Behavior and
Cognition (ABC) Research Group for constructive criticism.
#2004 Psychology Press Ltd
http://www.tandf.co.uk/journals/pp/09541446.html DOI:10.1080/09541440340000286
(e.g., ``If you touch the fire, you will get burned''), promise them future rewards
(e.g., ``If you keep my secret, I will give you a gift''), permit them exceptional
undertakings (e.g., ``If you are strong enough, you can ride the horse''), and so
on. Given that all conditional statements are formally equivalentÐ``if condition
Pobtains, then consequence Qensues''Ðthe question remains: When con-
fronted with a conditional statement, how do people know whether they are
facing a warning, a promise, a permission, or something else? Are there cog-
nitive algorithms that map particular conditional statements onto their corre-
sponding social domains? This paper introduces two algorithms as partial
answers to this question.
THE PRAGMATICS OF CONDITIONAL
STATEMENTS
Understanding the social content of conditionals in particular is an interesting
and relevant step towards understanding the interpretation process of language
in general in terms of adaptive reasoning algorithms. The study of how meaning
is attached to verbal statements has been the province of a branch of cognitive
psychology known as pragmatics. According to the pragmatics approach,
arriving at the appropriate meaning of an utteranceÐbe it a warning, a promise,
or anything elseÐrequires that the individual draws appropriate inferences. As
such, the task of discerning the meaning of a statement turns out to be more of a
process of utterance interpretation than utterance decoding (Sperber & Wilson,
1981, 1986). Consider the following utterances:
Woman: I'm leaving you.
Man: Who is he?
Most individuals interpret these utterances in the same way, that is, as statements
occurring in a conversation between romantic lovers, one of whom wishes to end
the relationship, while the other suspects infidelity. Yet, as pragmatics theorists
quickly point out, none of these meanings can be directly recovered by decoding
these utterances (see Sperber & Wilson, 1986). That is, there are no features
(e.g., words) in these two utterances that directly translate into a clear statement
of the nature of the relationship between the two speakers, their intentions, or an
act of infidelity. Such meanings are not decoded from the words in an utterance,
instead they are inferred from a variety of pragmatic (contextual) cues including
the words in an utterance (Sperber & Wilson, 1986).
According to pragmatics theorists, individuals discern the meaning of an
utterance by virtue of drawing certain inferences and not others. The sophisti-
cation of this human ability to draw appropriate inferences from utterances can
be clearly seen in the case of irony (or sarcasm), where the individual correctly
infers the speaker's meaning even though the literal meaning of the speaker's
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ÂPEZ-ROUSSEAU AND KETELAAR
statement is the opposite of their intended meaning (e.g., ``Fred is such an
honest guy, he lies only twice an hour!'').
Given the fact that (1) all conditional statements have the same logical
formÐ``if P, then Q''Ðand (2) the claim from pragmatics that the intended
meaning of a statement is inferred (rather than directly decoded) from pragmatic
cues, how then does an individual actually decide whether a particular condi-
tional statement is, say, a threat or a promise? One intriguing possibility is that
inferences about the appropriate social domain for a conditional statement may
be triggered by the presence of particular cues (e.g., particular words) in the
utterance. Although a simple heuristic process for categorising statements into
social domains (warnings, promises, permissions, etc.) would not necessarily
provide the listener with the full meaning of the utterance, it could allow the
recipient to achieve a quick and dirty approximation of the meaning of the
statement.
DRAWING INFERENCES FROM CONDITIONAL
STATEMENTS
There is a long tradition in psychology of studying the inferences that people
draw about conditional statements beginning with Wason's (1966) classic
research on the selection task (e.g., Schaeken, Schroyens, & Dieussaert, 2001).
In this task, participants are presented with four cards that have letters on one
side and numbers on the other side (e.g., A, B, 1, 2), and then asked to select
only those cards that need to be turned in order to test the conditional rule ``If a
card has a vowel on one side, then it has an even number on the other side.''
This rule is formally equivalent to a logical ``if P, then Q'' rule, where the four
cards correspond to P,not-P,not-Q, and Q,respectively. The typical finding in
this task is that most participants fail to select the necessary not-Q card (i.e., the
1-card). This failure has been interpreted as a difficulty in reasoning according
to the logic of modus tollensÐ``if P, then Q''; ``not-Q''; ``therefore not-P''Ð
and people have been thus depicted as bad logical reasoners.
Further studies have shown that when the original task is provided with social
content, people do better (e.g., Griggs & Cox, 1982). For example, participants
are presented with four cards representing people at a bar that have their drinks
on one side and their ages on the other side (e.g., beer, cola, 16, 20), and then
asked to select only those cards that need to be turned in order to test the
conditional rule ``If a person is drinking beer, then she must be over 18 years
old.'' This rule is also formally equivalent to a logical ``if P, then Q'' rule, but
the typical finding now is that most participants do select the necessary not-Q
card (i.e., the 16-card), apparently reasoning according to modus tollens. People
have been thus depicted as good social reasoners.
Different theoretical explanations have been offered for this social content
effect on the Wason selection task. For example, Cheng and Holyoak (1985;
SATISFICING ALGORITHMS 809
Cheng, Holyoak, Nisbett, & Oliver, 1986) suggest that people do not reason
according to formal logic but to pragmatic reasoning schemas such as per-
missions and obligations. In a permission schema, when a given precondition is
not satisfied (e.g., being over 18 years old), a given action must not be taken
(e.g., drinking beer). Testing whether this holds amounts to selecting the not-Q
card in any Wason selection task that maps onto a permission schema (e.g., the
bar scenario).
Alternatively, Cosmides and Tooby (1992; Cosmides, 1989) suggest that
people reason according to evolved Darwinian algorithms such as social con-
tracts and threats. In a social contract, you must pay a given cost (e.g., being
over 18 years old) to take a given benefit (e.g., drinking beer). Testing whether
this holds amounts to detecting cheaters, and to now selecting the not-Q card in
any Wason selection task that maps onto a social contract (e.g., the bar sce-
nario).
Moreover, Gigerenzer and Hug (1992) suggest that cheating on a social
contract depends on the pragmatic perspective of their participants. For exam-
ple, whereas not working paid hours is cheating from the perspective of an
employer, not paying worked hours is cheating from the perspective of an
employee. Thus, this would lead to employers and employees selecting different
cards to test the conditional rule ``If an employee works some hours, then the
employer must pay those hours.'' In particular, employees would select the P
and not-Q cards, and employers would select the Qand not-P cards. In sum,
whereas their explanations differ, all authors above agree that proper reasoning
about conditionals is not done according to a general logical formalism but to
specific psychological mechanisms.
However, although both the pragmatic schema and the evolved algorithm
explanations account for reasoning about conditional statements, these expla-
nations still beg a fundamental question: When confronted with a conditional
statement, how do people know whether they are facing a permission and not an
obligation, or a social contract and not a threat, or neither of these but something
else? In other words, if discerning the appropriate meaning of a conditional
statement entails employing the right schema or algorithm, what is the
mechanism for mapping a particular conditional statement onto its corre-
sponding schema or algorithm? This paper is an attempt to provide an ecolo-
gically valid answer to this question by studying conditional statements as used
in natural language.
CONDITIONALS STATEMENTS AND DOMAIN
SPECIFICITY
Linguists such as Fillenbaum (1975, 1976, 1977) have shown that everyday
reasoning about conditional statements is domain specific. That is, reasoning
about threats is not the same as reasoning about promises or other social
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ÂPEZ-ROUSSEAU AND KETELAAR
domains. For example, whereas conditional threats (e.g., ``If you hurt me, I'll
beat you up'') can be paraphrased as disjunctives (e.g., ``Don't hurt me or I'll
beat you up''), conditional promises (e.g., ``If you help me, I'll take you out'')
cannot be paraphrased as disjunctives (e.g., ``Don't help me or I'll take you
out''). Moreover, domain-specific reasoning about conditionals is not necessa-
rily logical. For example, conditionals (e.g., ``If you order food, you must pay
for it'') invite for some inferences (e.g., ``If I don't order food, I mustn't pay for
it'') that are logically invalid (i.e., ``if not-P, then not-Q'') but make perfect
social sense nonetheless. Finally, domain-specific reasoning about conditional
statements is not triggered by their general formÐ``if P, then Q''Ðbut by their
specific content and context. For example, although a conditional promise (e.g.,
``If you help me, I'll take you out'') and a conditional threat (e.g., ``If you hurt
me, I'll beat you up'') are formally equivalent, one is regarded as a promise and
the other as a threat by virtue of their distinct consequences, namely, a benefit
and a cost for the listener, respectively.
THE PRAGMATIC CUES APPROACH
Given the constraints of time and cognitive resources that typically confront
individuals in the world, the cognitive algorithm for classifying conditional
statements into social domains is assumed to be a satisficing algorithm: A simple
serial procedure sufficing for satisfactory classifications in most cases (Giger-
enzer, Todd, & ABC Research Group, 1999; Simon, 1982). Take as an example
a situation in which someone tells you ``If you move, I'll kill you.'' You better
know with accuracy and speed that this conditional is a threat to react appro-
priately. But exactly how do you know that this particular statement is a threat?
Certainly the content and context of the conditional statement, as conveyed by
linguistic cues (e.g., the word ``kill'' instead of the word ``kiss'') and non-
linguistic cues (e.g., a mean look instead of a nice smile), provide some gui-
dance. Although the actual cognitive algorithm that individuals employ when
classifying conditional statements into social domains probably includes both
kinds of cues, the first satisficing algorithm introduced here includes only lin-
guistic cues for simplification. Moreover, although the actual cognitive algo-
rithm probably includes syntactic, semantic, and pragmatic linguistic cues, this
algorithm includes only pragmatic cues for the simple reason that social domains
are essentially pragmatic. Finally, although the cognitive algorithm probably
includes all social domains, this algorithm only includes six domains given their
natural relevance and historical precedence in the literature (e.g., Cheng &
Holyoak, 1985; Cosmides & Tooby, 1992; Fillenbaum, 1975). The domains are
the following: promises (e.g., ``If you help me, I'll take you out''), threats (e.g.,
``If you hurt me, I'll beat you up''), advice (e.g., ``If you exercise, you'll be
fit''), warnings (e.g., ``If you smoke, you'll get sick''), permissions (e.g., ``If
you work now, you can rest later''), and obligations (e.g., ``If you order food,
SATISFICING ALGORITHMS 811
you must pay for it''). In sum, a satisficing algorithm for classifying conditionals
by pragmatic cues was analytically derived, and consequently called the prag-
matic cues algorithm.
The pragmatic cues algorithm
The pragmatic cues algorithm is a binary decision tree based on three pragmatic
cues that sequentially prune the tree until one of six social domains is left (see
Figure 1). The cues are the following:
1. Is the conditional statement's consequent Qmeant as a benefit for the
listener? If it is meant as a benefit for the listener, the conditional statement
represents a promise, an advice, or a permission. If it does not, the conditional
statement represents a threat, a warning, or an obligation.
2. Does the conditional statement's consequent Qinvolve an act of the
speaker? If it does involve an act of the speaker, the conditional statement
represents a promise or a threat, depending on the first cue value. If it does
not, the conditional statement represents an advice, a permission, a warning,
or an obligation, depending on the first cue value.
3. Does the conditional statement's consequent Qmake an act of the listener
possible or necessary? If it does make an act of the listener possible, then the
conditional statement represents a permission or an obligation, depending on
the first two cue values. If it does not, the conditional statement represents an
advice or a warning, depending on the first two cue values.
Take again as example the conditional statement ``If you move, I'll kill you.''
The pragmatic cues algorithm would process this conditional statement by
yesyes
yes
no
no
no
no
yes
yes
no
THREAT
WARNING
OBLIGATION
Q
makes
act of listener
necessary?
Q
involves
act of speaker?
PERMISSION
ADVICE
Q
makes
act of listener
possible?
PROMISE
Q
involves
act of speaker?
Q
meant as
benefit for listener?
Figure 1. The pragmatic cues algorithm.
812 LO
ÂPEZ-ROUSSEAU AND KETELAAR
applying its first cue, and asking whether the conditional statement's consequent
Qis meant as a benefit for the listener. Because being killed is not a benefit for
the listener, the algorithm would follow its ``no'' branch to the second cue, and
ask whether the conditional statement's consequent Qinvolves an act of the
speaker. Because the killing is done by the speaker, the algorithm would follow
its ``yes'' branch to the threat domain, and stop there. Thus, according to this
algorithm, the conditional statement ``If you move, I'll kill you'' is a threat.
Different conditional statements are mapped onto different domains as can be
verified by applying the algorithm to the following three examples: ``If you
smoke, you'll get sick'', ``If you work now, you can rest later'', and ``If you
exercise, you'll be fit'' (see Figure 1).
The pragmatic cues algorithm is meant to be simple by including the mini-
mum possible of three cues to classify six domains. The algorithm is also meant
to be serial by adopting the sequential form of a decision tree, which further
simplifies the classification process by discarding already three domains from
consideration after the first cue, and possibly two more domains after the second
cue. And the algorithm is meant to be satisficing by producing correct classi-
fications in most but not all cases. In this regard, the pragmatic cues algorithm
could misclassify any conditional statement belonging to other (social) domains
and/or depending on other (pragmatic) cues. For example, the algorithm would
misclassify the conditional fact ``If water boils, it evaporates'', the conditional
request ``If you leave the room, please close the door'', and the conditional
promise ``If I get a raise, I'll quit smoking'' (see Figure 1). Still, the pragmatic
cues algorithm would correctly classify most conditional promises, threats,
advices, warnings, permissions, and obligations.
Overview of Experiment 1
Given that a vast number of complex and/or parallel and/or optimising alter-
native algorithms could be used for this categorisation task, an experiment was
designed to empirically test how well the more parsimonious pragmatic cues
algorithm approximates the performance of the actual cognitive algorithm that
people use to classify conditionals statements into social domains. Briefly,
conditional statements for promises, threats, advices, warnings, permissions, and
obligations were collected from people, and given to both other people and the
pragmatic cues algorithm for their classification. Their corresponding perfor-
mances were then compared.
Evidently, it was expected that people would correctly classify all of other
people's conditional statements except for obvious generation and/or inter-
pretation errors. It was also expected that the pragmatic cues algorithm would
correctly classify most conditional statements. And both people and the prag-
matic cues algorithm were expected to perform far above chance. However, it
was also expected that the pragmatic cues algorithm would perform somewhat
SATISFICING ALGORITHMS 813
worse than the actual cognitive algorithm that people use to classify conditionals
statements into social domains. This is the case because the pragmatic cues
algorithm was designed as a simple satisficing algorithm that draws only a
restricted range of inferences from a minimum number of cues, whereas people
might have access to a larger number of cues and inferences.
In sum, the pragmatic cues algorithm would have to perform both as bad as
chance and far worse than people in order for it to be rejected as an approx-
imation of the actual cognitive algorithm people use to classify conditionals
statements into social domains. Here rests the power of this empirical test to
discriminate between the proposed analytical-cues algorithm and any other
random-cues algorithm.
EXPERIMENT 1
Method
Participants and materials. Sixty-two properly informed and protected
students at the University of Munich volunteered for this experiment, originally
in German. Typewritten booklets contained the instructions for the participants.
Design and procedure. This experiment had three conditions: the genera-
tion, evaluation, and algorithm conditions. In the generation condition, 50 par-
ticipants separately provided each a written conditional promise, advice,
permission, threat, warning, and obligation, for a total of 300 conditionals. The
instructions were the following:
We are interested in how you use if±then statements to communicate a promise,
advice, permission, threat, warning, or obligation to someone else. Please write an
example of each.
Promise If _______________________________________________________,
then _____________________________________________________.
For instance, one participant wrote the statement ``If you don't study, then you'll
fail the exam'' as an example of a warning. Thus, this conditional was one of the
50 warnings provided in the generation condition.
In the evaluation condition, three judges separately classified each of the 300
randomly ordered, nonlabelled conditionals as a promise, advice, permission,
threat, warning, or obligation. The instructions were the following:
This booklet contains 300 if±then statements. For each statement, please state if the
speaker meant it as a promise (P), an advice (A), a permission (E), a threat (T), a
warning (W), or an obligation (O) for the listener.
1. If you don't study,
then you'll fail the exam. _____
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ÂPEZ-ROUSSEAU AND KETELAAR
Each conditional was then classified into the domain agreed upon by two out of
the three judges. For example, the three judges wrote that the speaker meant the
statement ``If you don't study, then you'll fail the exam'' as a warning (W) for
the listener. Thus, this conditional was classified as a warning in the evaluation
condition.
In the algorithm condition, nine judges separately provided the pragmatic cue
values for each of the 300 randomly ordered, nonlabelled conditionals. There
were three judges per cue. The instructions for the first cue were the following:
This booklet contains 300 if±then statements. For each statement, please state if its
then-part is meant as a benefit for the listener (Y), or not (N).
1. If you don't study,
then you'll fail the exam. _____
The instructions for the second cue were: ``This booklet contains 300 if±then
statements. For each statement, please state if its then-part involves an act of
the speaker (Y), or not (N).'' Finally, the instructions for the third cue were:
``This booklet contains 300 if±then statements. For each statement, please state
if its then-part makes an act of the listener possible or necessary (Y), or not
(N).''
Each conditional was then assigned the cue values agreed upon by two out of
three judges per cue, and classified into the domain obtained following the
pragmatic cues algorithm. For example, the three judges wrote that the then-part
of the statement ``If you don't study, then you'll fail the exam'' is not meant as a
benefit for the listener (N), does not involve an act of the speaker (N), and does
not make an act of the listener possible or necessary (N).
1
Thus, following the
pragmatic cues algorithm, this conditional was classified as a warning in the
algorithm condition.
Participants were tested individually in all conditions.
Results and discussion
Figure 2 shows the percentage of conditional promises, advices, permissions,
threats, warnings, and obligations provided in the generation condition that were
correctly classified as such in the evaluation and algorithm conditions.
Results show that people classified most conditional statements correctly
across domains (average: 94%; range: 88% to 100%), and that the pragmatic
cues algorithm did almost as well as people (average: 85%; range: 68% to 94%).
Both the algorithm's and people's classifications were far better than chance
1
The last cue value was agreed upon by two out of the three judges.
SATISFICING ALGORITHMS 815
(17%), and their misclassifications were randomly distributed across domains.
2
These findings indicate that the pragmatic cues algorithm approximates well the
performance of the cognitive algorithm for mapping conditional statements onto
social domains. The small difference is probably due to the additional cues the
cognitive algorithm depends on. These findings thus suggest that the parsimo-
niously simple, serial, and satisficing pragmatic cues algorithm might be an
integral part of the cognitive algorithm for classifying conditionals.
But what other cues and domains might also be integral parts of the cognitive
algorithm? Besides pragmatic cues, the cognitive algorithm probably includes
semantic, syntactic, and nonlinguistic cues. Moreover, the cognitive algorithm
probably includes orders, requests, and other social domains. The second
satisficing algorithm introduced here explores the role of syntactic cues in the
cognitive algorithm for classifying conditional statements.
THE SYNTACTIC CUES APPROACH
The inclusion of syntactic cues in the cognitive algorithm can be exemplified by
means of conditional requests (e.g., ``If you call, please send my regards''),
2
Except for the algorithms' misclassifications of advices mostly as permissions (11 out of 16).
For example, the advice ``If you talk more, then you can solve your problems'' was also mis-
classified as a permission. This is due to the algorithm's third cue (i.e., Does the conditional's
consequent Qmake an act of the listener possible or necessary?), where ``possible'' can broadly
mean ``plausible'' or narrowly mean ``permissible''. A cue's rephrasing might better convey the
intended narrow meaning (e.g., Does the conditional's consequent Qinvolve an authority making an
act of the listener possible or necessary?).
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
1
0
0
T
h
r
e
a
t W
a
r
n
i
n
g O
b
l
i
g
a
t
i
o
n P
e
r
m
i
s
s
i
o
n A
d
v i
c
e P
r
o
m
i
s
e
Generation
%
C
o
r
r
e
c
t
E
v
a
l
u
a
t
i
o
n
A
l
g
o
r
i
t
h
m
chance
Figure 2. The percentage of correctly classified conditionals by condition.
816 LO
ÂPEZ-ROUSSEAU AND KETELAAR
which usually initiate their consequents with the word ``please''. This syntactic
cue signals a following request. Whether a request actually follows is then
determined by additional pragmatic cues. Thus, the cognitive algorithm is here
assumed to include syntactic cues as early detectors of social domains, which are
later (dis)confirmed by pragmatic cues.
Take conditional threats as a less obvious example. Threats are typically used
to induce people in doing something they are not doing (e.g., ``If you don't pay,
I'll break your arm''). Thus, conditional threats usually include the word ``not''
in their antecedents. This syntactic cue detects an imminent threat, which is then
(dis)confirmed by the pragmatic cues proposed above (see pragmatic cues
algorithm). In sum, to explore the role of syntactic cues in the cognitive algo-
rithm for classifying conditional statements, a satisficing algorithm for detecting
threats by syntactic cues was designed, and consequently called the syntactic cue
algorithm.
The syntactic cue algorithm
The syntactic cue algorithm is a binary decision tree based on just a single
syntactic cue that prunes the tree into threats and nonthreats (see Figure 3). The
cue is the following:
1. Does the conditional statement's antecedent Pcontain the word ``not''? If it
does contain the word ``not'', the conditional statement represents a threat. If it
does not, the conditional statement represents no threat.
Take again as example the conditional statement ``If you don't pay, I'll break
your arm.'' The syntactic cue algorithm would process this conditional statement
by applying its only cue, and asking whether the conditional statement's ante-
cedent Pcontains the word ``not''. Because it does, the algorithm would follow its
``yes'' branch to the threat domain, and stop there. Thus, according to the
algorithm, the conditional statement ``If you don't pay, I'll break your arm'' is a
threat. Evidently, the syntactic cue algorithm would not detect any conditional
threat excluding ``not'' from its antecedent (e.g., ``If you testify, I'll cut out your
no
yes
NO THREAT
P
contains
word "not"?
THREAT
Figure 3. The syntactic cue algorithm.
SATISFICING ALGORITHMS 817
tongue''), and would wrongly detect any conditional nonthreat including ``not''
in its antecedent (e.g., ``If you don't mind, I'll invite you to dinner''). Still, the
algorithm is expected to correctly detect most conditional threats.
Overview of Experiment 2
Given that the actual cognitive algorithm for classifying conditional statements
no doubt depends on additional pragmatic cues, a second experiment was
designed to empirically test how well the minimalistic syntactic cue algorithm
approximates the performance of the actual cognitive algorithm people use in
detecting conditional threats. Briefly, conditional statements in the form con-
ditional threats and nonthreats were collected from people, and given to both
other people and the syntactic cue algorithm for their classification. Their cor-
responding performances were then compared.
Again, it was expected that people would correctly classify all of other
people's conditional threats except for obvious generation and/or interpretation
errors. It was also expected that the pragmatic cues algorithm would correctly
classify most conditional threats. Although both people and the pragmatic cues
algorithm were expected to perform far above chance, it was expected that the
actual cognitive algorithm that people employ to classify conditionals statements
into social domains would perform somewhat better than the syntactic cue
algorithm. This is because the syntactic cue algorithm was designed as a simple
satisficing algorithm that relies on just a single syntactic cue to discriminate
threats from nonthreats, whereas people might have access to a larger number of
cues and inferences.
Also again, the syntactic cue algorithm would have to perform both as bad as
chance and far worse than people in order for it to be rejected as an approx-
imation of the actual cognitive algorithm people use to classify conditional
threats. Here rests the power of this empirical test to discriminate between the
proposed analytical-cue algorithm and any other random-cue algorithm.
EXPERIMENT 2
Method
Participants and materials. Thirty-seven properly informed and protected
students at the University of Munich volunteered for this experiment, originally
in German. Typewritten booklets contained the instructions for the participants.
Design and procedure. This experiment had three conditions: the genera-
tion, evaluation, and algorithm conditions. In the generation condition, 33
participants separately provided each six written conditional threats (three)
818 LO
ÂPEZ-ROUSSEAU AND KETELAAR
and nonthreats (three), for a total of 200 conditionals.
3
The instructions were the
following:
We are interested in how you use if±then statements to communicate a threat to
someone else. Please write three examples of threats and three examples of non-
threats.
Threat If ________________________________________________________,
then ______________________________________________________.
For instance, one participant wrote the statement ``If you're not quiet, then I'll
bawl you out'' as an example of a threat. Thus, this conditional statement was
one of the 100 threats provided in the generation condition.
In the evaluation condition, three judges separately classified each of the 200
randomly ordered, nonlabelled conditional statements as a threat or nonthreat.
The instructions were the following:
This booklet contains 200 if±then statements. For each statement, please write if
the speaker meant it as a threat (T) or a nonthreat (N) for the listener.
1. If you're not quiet,
then I'll bawl you out. _____
Each conditional statement was then classified as a threat or nonthreat as agreed
upon by two out of the three judges. For example, the three judges wrote that the
speaker meant the statement ``If you're not quiet, then I'll bawl you out'' as a
threat (T) for the listener. Thus, this conditional was classified as a threat in the
evaluation condition.
In the algorithm condition, one judge provided the syntactic cue value for
each of the 200 randomly ordered, nonlabelled conditional statements. The
instructions for the one cue were the following:
This booklet contains 200 if±then statements. For each statement, please write if its
if-part contains the word ``not'' (Y), or not (N).
1. If you're not quiet,
then I'll bawl you out. _____
Each conditional statement was then assigned the cue value given by the judge,
and classified into the domain obtained following the syntactic cue algorithm.
For example, the judge wrote that the if-part of the statement ``If you're not
quiet, then I'll bawl you out'' contains the word ``not'' (Y). Thus, following the
syntactic cue algorithm, this conditional statement was classified as a threat in
the algorithm condition.
Participants were tested individually in all conditions.
3
One participant was asked to provide four threats and four nonthreats.
SATISFICING ALGORITHMS 819
Results and discussion
Figure 4 shows the percentage of hits (i.e., threats classified as threats), misses
(i.e., threats classified as nonthreats), and false alarms (i.e., nonthreats classified
as threats) for conditional threats in the evaluation and algorithm conditions.
Results show that people correctly detected most conditional threats (88%
hits and 12% misses), and that the syntactic cue algorithm did just 20% worse
than people (67% hits and 33% misses). Both the algorithm's and people's hit
rates were better than chance (50%), and their false alarm rates were low (2%
and 17%, respectively). These findings indicate that the syntactic cue algorithm
tends to approximate the performance of the cognitive algorithm in detecting
conditional threats. The observed difference is certainly due to the additional
pragmatic cues the cognitive algorithm depends on. These findings thus suggest
that the minimalistic syntactic cue algorithm might be another integral part of
the cognitive algorithm for mapping conditional statements onto social domains.
More generally, these findings suggest that the cognitive algorithm might
include syntactic cues as early detectors of social domains, which might be later
(dis)confirmed by pragmatic cues.
A follow-up study was designed to further test whether the syntactic cue
algorithm is an integral part of the cognitive algorithm for classifying condi-
tional statements. In this study, 100 properly informed and protected students at
the University of Munich volunteered for separately answering the following
typewritten question, originally in German:
4
4
Options (a) and (b) were counterbalanced.
0
10
20
30
40
50
60
70
80
90
100
Hits Misses False Alarms
Threats
P
e
r
c
e
n
t
a
g
e
Evaluation
Algorithm
chance
Figure 4. The percentage of hits, misses, and false alarms for threats by condition.
820 LO
ÂPEZ-ROUSSEAU AND KETELAAR
Suppose a speaker says the following to a listener:
If you don't do that, then . . .
What do you think the speaker means by it: (a) or (b)?
(a) A threat for the listener.
(b) No threat for the listener.
Notice that the conditional statement ``If you don't do that, then . . .'' has a
content- and context-free antecedent, and no consequent. Thus, only the syn-
tactic cue algorithm could be possibly used to classify this conditional statement
as a threat. In fact, results show that most participants (88%) thought that the
speaker means a threat for the listener by the conditional statement. This finding
indicates that the syntactic cue algorithm was possibly used to classify the
conditional as a threat. This finding suggests again that the syntactic cue
algorithm might be an integral part of the cognitive algorithm for mapping
conditional statements onto social domains. Moreover, this finding suggests that
the cognitive algorithm might depend on syntactic cues alone to detect social
domains, when additional pragmatic cues are not available.
A second follow-up study was designed to control for a possible task-demand
effect on the results of Experiment 2 and the first follow-up study. Specifically,
these results may be affected by contrasting threats with no threats instead of
specific social domains like promises. Thus, the syntactic cue algorithm may well
discriminate between threats and no threats, but may not discriminate between
threats and other specific social domains. To test this possibility, the 300 con-
ditionals generated in Experiment 1 were classified following the syntactic cue
algorithm (for details, see algorithm condition of Experiment 2). Figure 5 shows
0
10
20
30
40
50
60
70
80
90
100
Threat Warning Obligation Permission Advice Promise
As Threat
P
e
r
c
e
n
t
a
g
e
Algorithm
chance
Figure 5. The percentage of each domain classified as a threat by the algorithm.
SATISFICING ALGORITHMS 821
the percentage of conditional threats classified as threats (hits), and conditional
warnings, obligations, permissions, advices, and promises classified as threats
(false alarms) by the algorithm.
Results show that the syntactic cue algorithm correctly detected most con-
ditional threats (64%). This hit rate was far better than chance (17%), and
similar to the hit rate in Experiment 2 (67%). Except for warnings (58%), the
false alarm rate was uniformly low (obligations 4%, permissions 4%, advices
8%, and promises 2%, respectively). On average (15%), this false alarm rate was
also similar to the false alarm rate in Experiment 2 (17%). These findings
indicate that the syntactic cue algorithm does not discriminate between threats
and warnings, but does indeed discriminate between threats and four specific
social domains (plus nonthreats). Certainly, the syntactic cue algorithm has to be
revised to include warnings (see Figure 6), which are only pragmatically dis-
criminated from threats by their consequents (see pragmatic cues algorithm).
These findings thus suggest that the results of Experiment 2 and the first follow-
up study were not a task-demand effect. Again, these findings suggest that the
syntactic cue algorithm might be an integral part of the cognitive algorithm for
mapping conditional statements onto social domains. Generally, these findings
suggest that the cognitive algorithm might include syntactic cues as early
detectors of social domains, which might be later (dis)confirmed by pragmatic
cues.
CONCLUSIONS
Are there cognitive algorithms that map particular conditional statements onto
their corresponding social domains? Actual people no doubt have access to a
vast number of cues and inferences that they can use to map conditional
statements onto their social domains. The challenge in the current study was to
determine whether relatively simple algorithms could perform as well as actual
people. This was done by introducing two simple satisficing algorithms for
classifying conditional statements into their appropriate social domains: the
pragmatic cues and syntactic cue algorithms. Results revealed that even though
these algorithms utilised a minimum number of cues and drew only a restricted
no
yes
OTHER
P
contains
word "not"?
THREAT
or
WARNING
Figure 6. The revised syntactic cue algorithm.
822 LO
ÂPEZ-ROUSSEAU AND KETELAAR
range of inferences from these cues, they performed well above chance in the
task of classifying conditional statements as promises, threats, advices, warn-
ings, permissions, and obligations. Moreover, these simple satisficing algorithms
performed comparable to actual people given the same task.
Gigerenzer (1995) has proposed that the psychological and linguistic
approaches to studying reasoning about conditional statements could be inte-
grated into a two-step research programme. According to Gigerenzer, the first
step would be to model the cognitive algorithm that maps conditional statements
onto social domains. The second step would be to model the cognitive module
that reasons and acts accordingly in each domain. This paper is an attempt to
specify the first step of the proposed programme by demonstrating how simple
satisficing algorithms can approximate the performance of people.
Manuscript received October 2001
Revised manuscript received January 2003
PrEview proof published online October 2003
REFERENCES
Cheng, P. W., & Holyoak, K. J. (1985). Pragmatic reasoning schemas. Cognitive Psychology,17,
391±416.
Cheng, P. W., Holyoak, K. J., Nisbett, R. E., & Oliver, L. M. (1986). Pragmatic versus syntactic
approaches to training deductive reasoning. Cognitive Psychology,18, 293±328.
Cosmides, L. (1989). The logic of social exchange: Has natural selection shaped how humans
reason? Studies with the Wason selection task. Cognition,31, 187±276.
Cosmides, L., & Tooby, J. (1992). Cognitive adaptations for social exchange. In J. H. Barkow, L.
Cosmides, & J. Tooby (Eds.), The adapted mind: Evolutionary psychology and the generation of
culture. Oxford, UK: Oxford University Press.
Fillenbaum, S. (1975). If: Some uses. Psychological Research,37, 245±260.
Fillenbaum, S. (1976). Inducements: On the phrasing and logic of conditional promises, threats, and
warnings. Psychological Research,38, 231±250.
Fillenbaum, S. (1977). A condition on plausible inducements. Language and Speech,20, 136±141.
Gigerenzer, G. (1995). The taming of content: Some thoughts about domains and modules. Thinking
and Reasoning,1, 289±400.
Gigerenzer, G., & Hug, K. (1992). Domain specific reasoning: Social contracts, cheating, and per-
spective change. Cognition,43, 127±171.
Gigerenzer, G., Todd, P., & ABC Research Group (1999). Simple heuristics that make us smart. New
York: Oxford University Press.
Griggs, R. A., & Cox, J. R. (1982). The elusive thematic-materials effect in Wason's selection task.
British Journal of Psychology,73, 407±420.
Schaeken, W., Schroyens, W., & Dieussaert, K. (2001). Conditional assertions, tense, and explicit
negatives. European Journal of Cognitive Psychology,4, 433±450.
Simon, H. A. (1982). Models of bounded rationality. Cambridge, MA: MIT Press.
Sperber, D., & Wilson, D. (1981). Pragmatics. Cognition,10, 281±286.
Sperber, D., & Wilson, D. (1986). Relevance: Communication and cognition. Cambridge, MA:
Harvard University Press.
Wason, P. (1966). Reasoning. In B. M. Foss (Ed.), New horizons in psychology. Harmondsworth,
UK: Penguin.
SATISFICING ALGORITHMS 823
