[Paleopsych] BBS: Individual Differences in Reasoning

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Individual Differences in Reasoning
http://www.bbsonline.org/documents/a/00/00/04/77/bbs00000477-00/bbs.stanovich.html
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Below is the unedited draft of:

Keith E. Stanovich & Richard F. West (2000) Individual Differences in
Reasoning: Implications for the Rationality Debate?
Behavioral and Brain Sciences 22 (5): XXX-XXX.

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   _________________________________________________________________

Individual Differences in Reasoning:
Implications for the Rationality Debate?

Keith E. Stanovich
Department of Human Development and Applied Psychology
University of Toronto
252 Bloor Street West
Toronto, ON
Canada M5S 1V6
[4]kstanovich at oise.utoronto.ca

Richard F. West
School of Psychology
MSC 7401
James Madison University
Harrisonburg, VA 22807
USA
[5]westrf at jmu.edu
   _________________________________________________________________




[stanovich.stanovich.jpg] Keith E. Stanovich is Professor of Human
Development and Applied Psychology at the University of Toronto. He is
the author of over 125 scientific articles in the areas of literacy
and reasoning, including Who Is Rational? Studies of Individual
Differences in Reasoning (Erlbaum, 1999). He is a Fellow of APA and
APS and has received the Sylvia Scribner Award from the American
Educational Research Association for contributions to research.
[stanovich.west.jpg] Richard F. West is a Professor in the School of
Psychology at James Madison University, where he has been named a
Madison Scholar. He received his Ph.D. in Psychology from the
University of Michigan. The author of over 50 publications, his main
scientific interests are the study of rational thought, reasoning,
decision making, the cognitive consequences of literacy, and cognitive
processes of reading.

   _________________________________________________________________

Abstract

Much research in the last two decades has demonstrated that human
responses deviate from the performance deemed normative according to
various models of decision making and rational judgment (e.g., the
basic axioms of utility theory). This gap between the normative and
the descriptive can be interpreted as indicating systematic
irrationalities in human cognition. However, four alternative
interpretations preserve the assumption that human behavior and
cognition is largely rational. These explanations posit that the gap
is due to (1) performance errors, (2) computational limitations, (3)
the wrong norm being applied by the experimenter and (4) a different
construal of the task by the subject. In the debates about the
viability of these alternative explanations, attention has been
focused too narrowly on the modal response. In a series of experiments
involving most of the classic tasks in the heuristics and biases
literature, we have examined the implications of individual
differences in performance for each of the four explanations of the
normative and descriptive gap. Performance errors are a minor factor
in the gap, computational limitations underlie non-normative
responding on several tasks, particularly those that involve some type
of cognitive decontextualization. Unexpected patterns of covariance
can suggest when the wrong norm is being applied to a task or when an
alternative construal of the task is called for.

Keywords:
rationality, normative models, descriptive models, heuristics, biases,
reasoning, individual differences

______________________________________________________________________

Individual Differences in Reasoning:
Implications for the Rationality Debate?

1. Introduction

A substantial research literature--one comprising literally hundreds
of empirical studies conducted over nearly three decades--has firmly
established that people's responses often deviate from the performance
considered normative on many reasoning tasks. For example, people
assess probabilities incorrectly, they display confirmation bias, they
test hypotheses inefficiently, they violate the axioms of utility
theory, they do not properly calibrate degrees of belief, they
overproject their own opinions onto others, they allow prior knowledge
to become implicated in deductive reasoning, and they display numerous
other information processing biases (for summaries of the large
literature, see Baron, 1994, 1998; Evans, 1989; Evans & Over, 1996;
Kahneman, Slovic, & Tversky, 1982; Newstead & Evans, 1995; Nickerson,
1998; Osherson, 1995; Piattelli-Palmarini, 1994; Plous, 1993; Reyna,
Lloyd, & Brainerd, in press; Shafir, 1994; Shafir & Tversky, 1995).
Indeed, demonstrating that descriptive accounts of human behavior
diverged from normative models was a main theme of the so-called
heuristics and biases literature of the 1970s and early 1980s (see
Arkes & Hammond, 1986; Kahneman, Slovic, & Tversky, 1982).

The interpretation of the gap between descriptive models and normative
models in the human reasoning and decision making literature has been
the subject of contentious debate for almost two decades now (a
substantial portion of that debate appearing in this journal; for
summaries, see Baron, 1994; Cohen, 1981, 1983; Evans & Over, 1996;
Gigerenzer, 1996a; Kahneman, 1981; Kahneman & Tversky, 1983, 1996;
Koehler, 1996; Stein, 1996). The debate has arisen because some
investigators wished to interpret the gap between the descriptive and
the normative as indicating that human cognition was characterized by
systematic irrationalities. Due to the emphasis that these theorists
place on reforming human cognition, they were labelled the Meliorists
by Stanovich (1999). Disputing this contention were numerous
investigators (termed the Panglossians, see Stanovich, 1999) who
argued that there were other reasons why reasoning might not accord
with normative theory (see Cohen, 1981 and Stein, 1996 for extensive
discussions of the various possibilities)--reasons that prevent the
ascription of irrationality to subjects. First, instances of reasoning
might depart from normative standards due to performance
errors--temporary lapses of attention, memory deactivation, and other
sporadic information processing mishaps. Second, there may be stable
and inherent computational limitations that prevent the normative
response (Cherniak, 1986; Goldman, 1978; Harman, 1995; Oaksford &
Chater, 1993, 1995, 1998; Stich, 1990). Third, in interpreting
performance, we might be applying the wrong normative model to the
task (Koehler, 1996). Alternatively, we may be applying the correct
normative model to the problem as set, but the subject might have
construed the problem differently and be providing the normatively
appropriate answer to a different problem (Adler, 1984, 1991; Berkeley
& Humphreys, 1982; Broome, 1990; Hilton, 1995; Schwarz, 1996).

However, in referring to the various alternative explanations (other
than systematic irrationality) for the normative/descriptive gap, Rips
(1994) warns that "a determined skeptic can usually explain away any
instance of what seems at first to be a logical mistake" (p. 393). In
an earlier criticism of Henle's (1978) Panglossian position,
Johnson-Laird (1983) made the same point: "There are no criteria
independent of controversy by which to make a fair assessment of
whether an error violates logic. It is not clear what would count as
crucial evidence, since it is always possible to provide an
alternative explanation for an error." (p. 26). The most humorous
version of this argument was made by Kahneman (1981) in his dig at the
Panglossians who seem to have only two categories of errors,
"pardonable errors by subjects and unpardonable ones by psychologists"
(p. 340). Referring to the four classes of alternative explanation
discussed above--performance errors, computational limitations,
alternative problem construal, and incorrect norm
application--Kahneman notes that Panglossians have "a handy kit of
defenses that may be used if [subjects are] accused of errors:
temporary insanity, a difficult childhood, entrapment, or judicial
mistakes--one of them will surely work, and will restore the
presumption of rationality" (p. 340).

These comments by Rips (1994), Johnson-Laird (1983), and Kahneman
(1981) highlight the need for principled constraints on the
alternative explanations of normative/descriptive discrepancies. In
this target article we describe a research logic aimed at inferring
such constraints from patterns of individual differences that are
revealed across a wide range of tasks in the heuristics and biases
literature. We argue here--using selected examples of empirical
results (Stanovich, 1999; Stanovich & West, 1998a, 1998b, 1998c,
1998d, 1999)--that these individual differences and their patterns of
covariance have implications for explanations of why human behavior
often departs from normative models^1.

2. Performance Errors

Panglossian theorists who argue that discrepancies between actual
responses and those dictated by normative models are not indicative of
human irrationality (e.g., Cohen, 1981) sometimes attribute the
discrepancies to performance errors. Borrowing the idea of a
competence/performance distinction from linguists (see Stein, 1996,
pp. 8-9), these theorists view performance errors as the failure to
apply a rule, strategy, or algorithm that is part of a person's
competence because of a momentary and fairly random lapse in ancillary
processes necessary to execute the strategy (lack of attention,
temporary memory deactivation, distraction, etc.). Stein (1996)
explains the idea of a performance error by referring to a "mere
mistake"--a more colloquial notion that involves "a momentary lapse, a
divergence from some typical behavior. This is in contrast to
attributing a divergence from norm to reasoning in accordance with
principles that diverge from the normative principles of reasoning.
Behavior due to irrationality connotes a systematic divergence from
the norm" (p. 8). Similarly, in the heuristics and biases literature,
the term bias is reserved for systematic deviations from normative
reasoning and does not refer to transitory processing errors ("a bias
is a source of error which is systematic rather than random," Evans,
1984, p. 462).

Another way to think of the performance error explanation is to
conceive of it within the true score/measurement error framework of
classical test theory. Mean or modal performance might be viewed as
centered on the normative response--the response all people are trying
to approximate. However, scores will vary around this central tendency
due to random performance factors (error variance).

It should be noted that Cohen (1981) and Stein (1996) sometimes
encompass computational limitations within their notion of a
performance error. In the present target article, the two are
distinguished even though both are identified with the algorithmic
level of analysis (see Anderson, 1990; Marr, 1982; and the discussion
below on levels of analysis in cognitive theory) because they have
different implications for covariance relationships across tasks.
Here, performance errors represent algorithmic-level problems that are
transitory in nature. Nontransitory problems at the algorithmic level
that would be expected to recur on a readministration of the task are
termed computational limitations.

This notion of a performance error as a momentary attention, memory,
or processing lapse that causes responses to appear nonnormative even
when competence is fully normative has implications for patterns of
individual differences across reasoning tasks. For example, the
strongest possible form of this view is that all discrepancies from
normative responses are due to performance errors. This strong form of
the hypothesis has the implication that there should be virtually no
correlations among nonnormative processing biases across tasks. If
each departure from normative responding represents a momentary
processing lapse due to distraction, carelessness, or temporary
confusion, then there is no reason to expect covariance among biases
across tasks (or covariance among items within tasks, for that matter)
because error variances should be uncorrelated.

In contrast, positive manifold (uniformly positive bivariate
associations in a correlation matrix) among disparate tasks in the
heuristics and biases literature--and among items within tasks--would
call into question the notion that all variability in responding can
be attributable to performance errors. This was essentially Rips and
Conrad's (1983) argument when they examined individual differences in
deductive reasoning: "Subjects' absolute scores on the propositional
tests correlated with their performance on certain other reasoning
tests....If the differences in propositional reasoning were merely due
to interference from other performance factors, it would be difficult
to explain why they correlate with these tests" (p. 282-283). In fact,
a parallel argument has been made in economics where, as in reasoning,
models of perfect market rationality are protected from refutation by
positing the existence of local market mistakes of a transitory nature
(temporary information deficiency, insufficient attention due to small
stakes, distractions leading to missed arbitrage opportunities, etc.).

Advocates of perfect market rationality in economics admit that people
make errors but defend their model of idealized competence by claiming
that the errors are essentially random. The following defense of the
rationality assumption in economics is typical in the way it defines
performance errors as unsystematic: "In mainstream economics, to say
that people are rational is not to assume that they never make
mistakes, as critics usually suppose. It is merely to say that they do
not make systematic mistakes--i.e., that they do not keep making the
same mistake over and over again" (The Economist, December 12, 1998,
p. 80). Not surprisingly, others have attempted to refute the view
that the only mistakes in economic behavior are unpredictable
performance errors by pointing to the systematic nature of some of the
mistakes: "The problem is not just that we make random computational
mistakes; rather it is that our judgmental errors are often
systematic" (Frank, 1990, p. 54). Likewise, Thaler (1992) argues that
"a defense in the same spirit as Friedman's is to admit that of course
people make mistakes, but the mistakes are not a problem in explaining
aggregate behavior as long as they tend to cancel out. Unfortunately,
this line of defense is also weak because many of the departures from
rational choice that have been observed are systematic" (pp. 4-5).
Thus, in parallel to our application of an individual differences
methodology to the tasks in the heuristics and biases literature,
Thaler argues that variance and covariance patterns can potentially
falsify some applications of the performance error argument in the
field of economics.

Thus, as in economics, we distinguish systematic from unsystematic
deviations from normative models. The latter we label performance
errors and view them as inoculating against attributions of
irrationality. Just as random, unsystematic errors of economic
behavior do not impeach the model of perfect market rationality,
transitory and random errors in thinking on a heuristics and biases
problem do not impeach the Panglossian assumption of ideal rational
competence. Systematic and repeatable failures in algorithmic-level
functioning likewise do not impeach intentional-level rationality, but
they are classified as computational limitations in our taxonomy and
are discussed in Section [6]3. Systematic mistakes not due to
algorithmic-level failure do call into question whether the
intentional-level description of behavior is consistent with the
Panglossian assumption of perfect rationality--provided the normative
model being applied is not inappropriate (see Section [7]4) or that
the subject has not arrived at a different, intellectually-defensible
interpretation of the task (see Section [8]5).

In several studies, we have found very little evidence for the strong
version of the performance error view. With virtually all of the tasks
from the heuristics and biases literature that we have examined, there
is considerable internal consistency. Further, at least for certain
classes of task, there are significant cross-task correlations. For
example, in two different studies (Stanovich & West, 1998c) we found
correlations in the range of .25 to .40 (considerably higher when
corrected for attenuation) among the following measures:

1. Nondeontic versions of Wason's (1966) selection task: The subject
is shown four cards lying on a table showing two letters and two
numbers (A, D, 3, 7). They are told that each card has a number on one
side and a letter on the other and that the experimenter has the
following rule (of the if P, then Q type) in mind with respect to the
four cards: "If there is an A on one side then there is a 3 on the
other". The subject is then told that he/she must turn over whichever
cards are necessary to determine whether the experimenter's rule is
true or false. Only a small number of subjects make the correct
selections of the A card (P) and 7 card (not-Q) and, as a result, the
task has generated a substantial literature (Evans, Newstead, & Byrne,
1993; Johnson-Laird, 1999; Newstead & Byrne, 1995).

2. A syllogistic reasoning task in which logical validity conflicted
with the believability of the conclusion (see Evans, Barston, &
Pollard, 1983). An example item is: All mammals walk. Whales are
mammals. Conclusion: Whales walk

3. Statistical reasoning problems of the type studied by the Nisbett
group (e.g., Fong, Krantz, & Nisbett, 1986) and inspired by the
finding that human judgment is overly influenced by vivid but
unrepresentative personal and case evidence and under-influenced by
more representative and diagnostic, but pallid, statistical evidence.
The quintessential problem involves choosing between contradictory car
purchase recommendations--one from a large-sample survey of car buyers
and the other the heartfelt and emotional testimony of a single
friend.

4. A covariation detection task modeled on the work of Wasserman,
Dorner, and Kao (1990). Subjects evaluated data derived from a 2 x 2
contingency matrix.

5. A hypothesis testing task modeled on Tschirgi (1980) in which the
score on the task was the number of times subjects attempted to test a
hypothesis in a manner that did not unconfound variables.

6. A measure of outcome bias modelled on the work of Baron and Hershey
(1988). This bias is demonstrated when subjects rate a decision with a
positive outcome as superior to a decision with a negative outcome
even when the information available to the decision maker was the same
in both cases.

7. A measure of if/only thinking bias (Epstein, Lipson, Holstein, &
Huh, 1992; Miller, Turnbull, & McFarland, 1990). If/only bias refers
to the tendency for people to have differential responses to outcomes
based on the differences in counterfactual alternative outcomes that
might have occurred. The bias is demonstrated when subjects rate a
decision leading to a negative outcome as worse than a control
condition when the former makes it easier to imagine a positive
outcome occurring.

8. An argument evaluation task (Stanovich & West, 1997) that tapped
reasoning skills of the type studied in the informal reasoning
literature (Baron, 1995; Klaczynski, Gordon, & Fauth, 1997; Perkins,
Farady, & Bushey, 1991). Importantly, it was designed so that to do
well on it one had to adhere to a stricture not to implicate prior
belief in the evaluation of the argument.

3. Computational Limitations

Patterns of individual differences have implications that extend
beyond testing the view that discrepancies between descriptive models
and normative models arise entirely from performance errors. For
example, patterns of individual differences also have implications for
prescriptive models of rationality. Prescriptive models specify how
reasoning should proceed given the limitations of the human cognitive
apparatus and the situational constraints (e.g., time pressure) under
which the decision maker operates (Baron, 1985). Thus, normative
models might not always be prescriptive for a given individual and
situation. Judgments about the rationality of actions and beliefs must
take into account the resource-limited nature of the human cognitive
apparatus (Cherniak, 1986; Goldman, 1978; Harman, 1995; Oaksford &
Chater, 1993, 1995, 1998; Stich, 1990). More colloquially, Stich
(1990) has argued that "it seems simply perverse to judge that
subjects are doing a bad job of reasoning because they are not using a
strategy that requires a brain the size of a blimp" (p. 27).

Following Dennett (1987) and the taxonomy of Anderson (1990; see also,
Marr, 1982; Newell, 1982), we distinguish the algorithmic/design level
from the rational/intentional level of analysis in cognitive science
(the first term in each pair is that preferred by Anderson, the second
that preferred by Dennett). The latter provides a specification of the
goals of the system's computations (what the system is attempting to
compute and why). At this level, we are concerned with the goals of
the system, beliefs relevant to those goals, and the choice of action
that is rational given the system's goals and beliefs (Anderson, 1990;
Bratman, Israel, & Pollack, 1991; Dennett, 1987; Newell, 1982, 1990;
Pollock, 1995). However, even if all humans were optimally rational at
the intentional level of analysis, there may still be computational
limitations at the algorithmic level (e.g., Cherniak, 1986; Goldman,
1978; Oaksford & Chater, 1993, 1995). We would therefore still expect
individual differences in actual performance (despite equal
rational-level competence) due to differences at the algorithmic
level.

Using such a framework, we view the magnitude of the correlation
between performance on a reasoning task and cognitive capacity as an
empirical clue about the importance of algorithmic limitations in
creating discrepancies between descriptive and normative models. A
strong correlation suggests important algorithmic-level limitations
that might make the normative response not prescriptive for those of
lower cognitive capacity (Panglossian theorists drawn to this
alternative explanation of normative/descriptive gaps were termed
Apologists by Stanovich, 1999). In contrast, the absence of a
correlation between the normative response and cognitive capacity
suggests no computational limitation and thus no reason why the
normative response should not be considered prescriptive (see Baron,
1985).

In our studies, we have operationalized cognitive capacity in terms of
well-known cognitive ability (intelligence) and academic aptitude
tasks^2 but have most often used the total score on the Scholastic
Aptitude Test^3,4. All are known to load highly on psychometric g
(Carpenter, Just, & Shell, 1990; Carroll, 1993; Matarazzo, 1972), and
such measures have been linked to neurophysiological and information
processing indicators of efficient cognitive computation (Caryl, 1994;
Deary, 1995; Deary & Stough, 1996; Detterman, 1994; Fry & Hale, 1996;
Hunt, 1987; Stankov & Dunn, 1993; Vernon, 1991, 1993). Furthermore,
measures of general intelligence have been shown to be linked to
virtually all of the candidate subprocesses of mentality that have
been posited as determinants of cognitive capacity (Carroll, 1993).
For example, working memory is the quintessential component of
cognitive capacity (in theories of computability, computational power
often depends on memory for the results of intermediate computations).
Consistent with this interpretation, Bara, Bucciarelli, and
Johnson-Laird, (1995) have found that "as working memory improves--for
whatever reason--it enables deductive reasoning to improve too" (p.
185). But it has been shown that, from a psychometric perspective,
variation in working memory is almost entirely captured by measures of
general intelligence (Kyllonen, 1996; Kyllonen & Christal, 1990).

Measures of general cognitive ability such as those utilized in our
research are direct marker variables for Spearman's (1904, 1927)
positive manifold--that performance on all reasoning tasks tends to be
correlated. Below, we will illustrate how we use this positive
manifold to illuminate reasons for the normative/descriptive gap.

[9]Table 1 indicates the magnitude of the correlation between one such
measure--Scholastic Aptitude Test total scores--and the eight
different reasoning tasks studied by Stanovich and West (1998c,
Experiments 1 and 2) and mentioned in the previous section. In
Experiment 1, syllogistic reasoning in the face of interfering content
displayed the highest correlation (.470) and the other three
correlations were roughly equal in magnitude (.347 to .394). All were
statistically significant (p < .001). The remaining correlations in
the table are the results from a replication and extension experiment.
Three of the four tasks from the previous experiment were carried over
(all but the selection task) and displayed correlations similar in
magnitude to those obtained in the first experiment. The correlations
involving the four new tasks introduced in Experiment 2 were also all
statistically significant. The sign on the hypothesis testing, outcome
bias, and if/only thinking tasks was negative because high scores on
these tasks reflect susceptibility to non-normative cognitive biases.
The correlations on the four new tasks were generally lower (range
.172 to .239) than the correlations involving the other tasks (.371 to
.410). The scores on all of the tasks in Experiment 2 were
standardized and summed to yield a composite score. The composite's
correlation with SAT scores was .547. It thus appears that to a
moderate extent, discrepancies between actual performance and
normative models can be accounted for by variation in computational
limitations at the algorithmic level--at least with respect to the
tasks investigated in these particular experiments.

Table 1
Correlations Between the Reasoning Tasks and Scholastic Aptitude Test
Total Scores in the Stanovich and West (1998c) Studies
Experiment 1
Syllogisms .470**
Selection task .394**
Statistical reasoning .347**
Argument evaluation task .358**
Experiment 2
Syllogisms .410**
Statistical reasoning .376**
Argument evaluation task .371**
Covariation detection .239**
Hypothesis testing bias -.223**
Outcome bias -.172**
If/Only thinking -.208**
Composite score .547**
** = p < .001, all two-tailed
Ns = 178 to 184 in Experiment 1 and 527 to 529 in Experiment 2

However, there are some tasks in the heuristics and biases literature
which lack any association at all with cognitive ability. The
so-called false consensus effect in the opinion prediction paradigm
(Krueger & Clement, 1994; Krueger & Zeiger, 1993) displays complete
dissociation with cognitive ability (Stanovich, 1999; Stanovich &
West, 1998c). Likewise, the overconfidence effect in the knowledge
calibration paradigm (e.g., Lichtenstein, Fischhoff, & Phillips, 1982)
displays a negligible correlation with cognitive ability (Stanovich,
1999; Stanovich & West, 1998c).

Collectively, these results indicate that computational limitations
seem far from absolute. That is, although computational limitations
appear implicated to some extent in many of the tasks, the normative[
]responses for all of them were computed by some university students
who had modest cognitive abilities (e.g., below the mean in a
university sample). Such results help to situate the relationship
between prescriptive and normative models for the tasks in question
because the boundaries of prescriptive recommendations for particular
individuals might be explored by examining the distribution of the
cognitive capacities of individuals who gave the normative response on
a particular task. For most of these tasks, only a small number of the
students with the very lowest cognitive ability in this sample would
have prescriptive models for any of these tasks that deviated
substantially from the normative model for computational reasons. Such
findings also might be taken to suggest that perhaps other factors
might account for variation--a prediction that will be confirmed when
work on styles of epistemic regulation is examined in section [10]7.
Of course, the deviation between the normative and prescriptive model
due to computational limitations will certainly be larger in
unselected or nonuniversity populations. This point also serves to
reinforce the caveat that the correlations observed in [11]Table 1
were undoubtedly attenuated due to restriction of range in the sample.
Nevertheless, if the normative/prescriptive gap is indeed modest, then
there may well be true individual differences at the intentional
level--that is, true individual differences in rational thought.

All of the camps in the dispute about human rationality recognize that
positing computational limitations as an explanation for differences
between normative and descriptive models is a legitimate strategy.
Meliorists agree on the importance of assessing such limitations.
Likewise, Panglossians will, when it is absolutely necessary, turn
themselves into Apologists to rescue subjects from the charge of
irrationality. Thus, they too acknowledge the importance of assessing
computational limitations. In the next section, however, we examine an
alternative explanation of the normative/descriptive gap that is much
more controversial--the notion that incorrect normative models have
been applied to certain tasks in the heuristics and biases literature.

4. Applying the Wrong Normative Model

The possibility of incorrect norm application arises because
psychologists must appeal to the normative models of other disciplines
(statistics, logic, etc.) in order to interpret the responses on
various tasks, and these models must be applied to a particular
problem or situation. Matching a problem to a normative model is
rarely an automatic or clear cut procedure. The complexities involved
in matching problems to norms make possible the argument that the gap
between the descriptive and normative occurs because psychologists are
applying the wrong normative model to the situation. It is a potent
strategy for the Panglossian theorist to use against the advocate of
Meliorism and such claims have become quite common in critiques of the
heuristics and biases literature:

   "many critics have insisted that in fact it is Kahneman & Tversky,
   not their subjects, who have failed to grasp the logic of the
   problem" (Margolis, 1987, p. 158).

   "if a 'fallacy' is involved, it is probably more attributable to
   the researchers than to the subjects" (Messer & Griggs, 1993, p.
   195).

   "When ordinary people reject the answers given by normative
   theories, they may do so out of ignorance and lack of expertise, or
   they may be signaling the fact that the normative theory is
   inadequate" (Lopes, 1981, p. 344).

   "in the examples of alleged base rate fallacy considered by
   Kahneman and Tversky, they, and not their experimental subjects,
   commit the fallacies" (Levi, 1983, p. 502).

   "what Wason and his successors judged to be the wrong response is
   in fact correct" (Wetherick, 1993, p. 107).

   "Perhaps the only people who suffer any illusion in relation to
   cognitive illusions are cognitive psychologists" (Ayton & Hardman,
   1997, p. 45).

These quotations reflect the numerous ongoing critiques of the
heuristics and biases literature in which it is argued that the wrong
normative standards have been applied to performance. For example,
Lopes (1982) has argued that the literature on the inability of human
subjects to generate random sequences (e.g., Wagenaar, 1972) has
adopted a narrow concept of randomness that does not acknowledge
broader conceptions that are debated in the philosophy and mathematics
literature. Birnbaum (1983) has demonstrated that conceptualizing the
well-known taxicab base-rate problem (see Bar-Hillel, 1980; Tversky &
Kahneman, 1982) within a signal-detection framework can lead to
different estimates than those assumed to be normatively correct under
the less flexible Bayesian model that is usually applied. Gigerenzer
(1991a, 1991b, 1993; Gigerenzer et al., 1991) has argued that the
overconfidence effect in knowledge calibration experiments
(Lichtenstein, Fischhoff, & Phillips, 1982) and the conjunction effect
in probability judgment (Tversky & Kahneman, 1983) have been
mistakenly classified as a cognitive biases because of the application
of an inappropriate normative model of probability assessment (i.e.,
requests for single-event subjective judgments when under some
conceptions of probability such judgments are not subject to the rules
of a probability calculus). Dawes (1989, 1990) and Hoch (1987) have
argued that social psychologists have too hastily applied an overly
simplified normative model in labeling performance in opinion
prediction experiments as displaying a so-called false consensus (see
also Krueger & Clement, 1994; Krueger & Zeiger, 1993).


4.1 From the Descriptive to the Normative in Reasoning and Decision
Making

The cases just mentioned provide examples of how the existence of
deviations between normative models and actual human reasoning have
been called into question by casting doubt on the appropriateness of
the normative models used to evaluate performance. Stein (1996, p.
239) terms this the "reject-the-norm" strategy. It is noteworthy that
this strategy is used exclusively by the Panglossian camp in the
rationality debate, although this connection is not a necessary one.
Specifically, the reject-the-norm-application strategy is exclusively
used to eliminate gaps between descriptive models of performance and
normative models. When this type of critique is employed, the
normative model that is suggested as a substitute for the one
traditionally used in the heuristics and biases literature is one that
coincides perfectly with the descriptive model of the subjects'
performance--thus preserving a view of human rationality as ideal. It
is rarely noted that the strategy could be used in just the opposite
way--to create gaps between the normative and descriptive. Situations
where the modal response coincides with the standard normative model
could be critiqued, and alternative models could be suggested that
would result in a new normative/descriptive gap. But this is never
done. The Panglossian camp, often highly critical of empirical
psychologists ("Kahneman and Tversky...and not their experimental
subjects, commit the fallacies" Levi, 1983, p. 502), is never critical
of psychologists who design reasoning tasks in instances where the
modal subject gives the response the experimenters deem correct.
Ironically, in these cases, according to the Panglossians, the same
psychologists seem never to err in their task designs and
interpretations.

The fact that the use of the reject-the-norm-application strategy is
entirely contingent on the existence or nonexistence of a
normative/descriptive gap suggests that the strategy is empirically,
not conceptually, triggered (normative applications are never rejected
for purely conceptual reasons when they coincide with the modal human
response). What this means is that in an important sense the norms
being endorsed by the Panglossian camp are conditioned (if not indexed
entirely) by descriptive facts about human behavior. The debate itself
is, reflexively, evidence that the descriptive models of actual
behavior condition expert notions of the normative. That is, there
would have been no debate (or at least much less of one) had people
behaved in accord with the then-accepted norms.

Gigerenzer (1991b) is clear about his adherence to an
empirically-driven reject-the-norm-application strategy: "Since its
origins in the mid-seventeenth century....When there was a striking
discrepancy between the judgment of reasonable men and what
probability theory dictated--as with the famous St. Petersburg
paradox--then the mathematicians went back to the blackboard and
changed the equations (Daston, 1980). Those good old days have
gone....If, in studies on social cognition, researchers find a
discrepancy between human judgment and what probability theory seems
to dictate, the blame is now put on the human mind, not the
statistical model" (p. 109).

One way of framing the current debate between the Panglossians and
Meliorists is to observe that the Panglossians wish for a return of
the "good old days" where the normative was derived from the
intuitions of the untutored layperson ("an appeal to people's
intuitions is indispensable," Cohen, 1981, p. 318); whereas the
Meliorists (with their greater emphasis on the culturally constructed
nature of norms) view the mode of operation during the "good old days"
as a contingent fact of history--the product of a period when few
aspects of epistemic and pragmatic rationality had been codified and
preserved for general diffusion through education.

Thus, the Panglossian reject-the-norm-application view can in essence
be seen as a conscious application of the naturalistic fallacy
(deriving ought from is). For example, Cohen (1981), like Gigerenzer,
feels that the normative is indexed to the descriptive in the sense
that a competence model of actual behavior can simply be interpreted
as the normative model. Stein (1996) notes that proponents of this
position believe that the normative can simply be "read off" from a
model of competence because "whatever human reasoning competence turns
out to be, the principles embodied in it are the normative principles
of reasoning" (p. 231). Although both endorse this linking of the
normative to the descriptive, Gigerenzer (1991b) and Cohen (1981) do
so for somewhat different reasons. For Cohen (1981), it follows from
his endorsement of narrow reflective equilibrium as the sine qua non
of normative justification. Gigerenzer's (1991b) endorsement is
related to his position in the "cognitive ecologist" camp (to use
Piattelli-Palmarini's, 1994, p. 183 term) with its emphasis on the
ability of evolutionary mechanisms to achieve an optimal Brunswikian
tuning of the organism to the local environment (Brase, Cosmides, &
Tooby, 1998; Cosmides & Tooby, 1994, 1996; Oaksford & Chater, 1994,
1998; Pinker, 1997).

That Gigerenzer and Cohen concur here--even though they have somewhat
different positions on normative justification--simply shows how
widespread is the acceptance of the principle that descriptive facts
about human behavior condition our notions about the appropriateness
of the normative models used to evaluate behavior. In fact, stated in
such broad form, this principle is not restricted to the Panglossian
position. For example, in decision science, there is a long tradition
of acknowledging descriptive influences when deciding which normative
model to apply to a particular situation. Slovic (1995) refers to this
"deep interplay between descriptive phenomena and normative
principles" (p. 370). Larrick, Nisbett, and Morgan (1993) have
reminded us that "there is also a tradition of justifying, and
amending, normative models in response to empirical considerations"
(p. 332). March (1988) refers to this tradition when he discusses how
actual human behavior has conditioned models of efficient problem
solving in artificial intelligence and in the area of organizational
decision making. The assumptions underlying the naturalistic project
in epistemology (e.g., Kornblith, 1985, 1993) have the same
implication--that findings about how humans form and alter beliefs
should have a bearing on which normative theories are correctly
applied when evaluating the adequacy of belief acquisition. This
position is in fact quite widespread:

   "if people's (or animals') judgments do not match those predicted
   by a normative model, this may say more about the need for revising
   the theory to more closely describe subjects' cognitive processes
   than it says about the adequacy of those processes" (Alloy &
   Tabachnik, 1984, p. 140).

   "We must look to what people do in order to gather materials for
   epistemic reconstruction and self-improvement" (Kyburg, 1991, p.
   139).

   "When ordinary people reject the answers given by normative
   theories, they may do so out of ignorance and lack of expertise, or
   they may be signaling the fact that the normative theory is
   inadequate" (Lopes, 1981, p. 344).

Of course, in this discussion we have conjoined disparate views that
are actually arrayed on a continuum. The reject-the-norm advocates
represent the extreme form of this view--they simply want to read off
the normative from the descriptive: "the argument under consideration
here rejects the standard picture of rationality and takes the
reasoning experiments as giving insight not just into human reasoning
competence but also into the normative principles of reasoning"
(Stein, 1996, p. 233). In contrast, other theorists (e.g., March,
1988) simply want to subtly fine-tune and adjust normative
applications based on descriptive facts about reasoning performance.

One thing that all of the various camps in the rationality dispute
have in common is that each conditions their beliefs about the
appropriate norm to apply based on the centraltendency of the
responses to a problem. They all seem to see that single aspect of
performance as the only descriptive fact that is relevant to
conditioning their views about the appropriate normative model to
apply. For example, advocates of the reject-the-norm-application
strategy for dealing with normative/descriptive discrepancies view the
mean, or modal, response as a direct pointer to the appropriate
normative model. One goal of the present research program is to expand
the scope of the descriptive information used to condition our views
about appropriate norms.

4.2 Putting Descriptive Facts to Work: The Understanding/Acceptance
Assumption

How should we interpret situations where the majority of individuals
respond in ways that depart from the normative model applied to the
problem by reasoning experts? Thagard (1982) calls the two different
interpretations the populist strategy and the elitist strategy: "The
populist strategy, favored by Cohen (1981), is to emphasize the
reflective equilibrium of the average person....The elitist strategy,
favored by Stich and Nisbett (1980), is to emphasize the reflective
equilibrium of experts" (p. 39). Thus, Thagard (1982) identifies the
populist strategy with the Panglossian position and the elitist
strategy with the Meliorist position.

But there are few controversial tasks in the heuristics and biases
literature where all untutored laypersons disagree with the experts.
There are always some who agree. Thus, the issue is not the untutored
average person versus experts (as suggested by Thagard's formulation),
but experts plus some laypersons versus other untutored individuals.
Might the cognitive characteristics of those departing from expert
opinion have implications for which normative model we deem
appropriate? Larrick, Nisbett, and Morgan (1993) made just such an
argument in their analysis of what justified the cost-benefit
reasoning of microeconomics: "Intelligent people would be more likely
to use cost-benefit reasoning. Because intelligence is generally
regarded as being the set of psychological properties that makes for
effectiveness across environments...intelligent people should be more
likely to use the most effective reasoning strategies than should less
intelligent people" (p. 333). Larrick et al. (1993) are alluding to
the fact that we may want to condition our inferences about
appropriate norms based not only on what response the majority of
people make but also on what response the most cognitively competent
subjects make.

Slovic and Tversky (1974) made essentially this argument years ago,
although it was couched in very different terms in their paper and
thus was hard to discern. Slovic and Tversky (1974) argued that
descriptive facts about argument endorsement should condition the
inductive inferences of experts regarding appropriate normative
principles. In response to the argument that there is "no valid way to
distinguish between outright rejection of the axiom and failure to
understand it" (p. 372), Slovic and Tversky observed that "the deeper
the understanding of the axiom, the greater the readiness to accept
it" (pp. 372-373). Slovic and Tversky (1974) argued that this
understanding/acceptance congruence suggested that the gap between the
descriptive and normative was due to an initial failure to fully
process and/or understand the task.

We might call Slovic and Tversky's argument the
understanding/acceptance assumption--that more reflective and engaged
reasoners are more likely to affirm the appropriate normative model
for a particular situation. From their understanding/acceptance
principle, it follows that if greater understanding resulted in more
acceptance of the axiom, then the initial gap between the normative
and descriptive would be attributed to factors that prevented problem
understanding (for example lack of ability or reflectiveness on the
part of the subject). Such a finding would increase confidence in the
normative appropriateness of the axioms and/or in their application to
a particular problem. In contrast, if better understanding failed to
result in greater acceptance of the axiom, then its normative status
for that particular problem might be considered to be undermined.

Using their understanding/acceptance principle, Slovic and Tversky
(1974) examined the Allais (1953) problem and found little support for
the applicability of the independence axiom of utility theory (the
axiom stating that if the outcome in some state of the world is the
same across options, then that state of the world should be ignored;
Baron, 1993; Savage, 1954). When presented with arguments to explicate
both the Allais (1953) and Savage (1954) positions, subjects found the
Allais argument against independence at least as compelling and did
not tend to change their task behavior in the normative direction (see
MacCrimmon, 1968 and MacCrimmon & Larsson, 1979 for more mixed results
on the independence axiom using related paradigms). Although Slovic
and Tversky (1974) failed to find support for this particular
normative application, they presented a principle that may be of
general usefulness in theoretical debates about why human performance
deviates from normative models. The central idea behind Slovic and
Tversky's (1974) development of the understanding/acceptance
assumption is that increased understanding should drive performance in
the direction of the truly normative principle for the particular
situation--so that the direction that performance moves in response to
increased understanding provides an empirical clue as to what is the
proper normative model to be applied.

One might conceive of two generic strategies for applying the
understanding/acceptance principle based on the fact that variation in
understanding can be created or it can be studied by examining
naturally occurring individual differences. Slovic and Tversky
employed the former strategy by providing subjects with explicated
arguments supporting the Allais or Savage normative interpretation
(see also Doherty, Schiavo, Tweney, & Mynatt, 1981; Stanovich & West,
1999). Other methods of manipulating understanding have provided
consistent evidence in favor of the normative principle of descriptive
invariance (see Kahneman & Tversky, 1984). For example, it has been
found that being forced to take more time or to provide a rationale
for selections increases adherence to descriptive invariance (Larrick,
Smith, & Yates, 1992; Miller & Fagley, 1991; Sieck & Yates, 1997;
Takemura, 1992, 1993, 1994). Moshman and Geil (1998) found that group
discussion facilitated performance on Wason's selection task.

As an alternative to manipulating understanding, the
understanding/acceptance principle can be transformed into an
individual differences prediction. For example, the principle might be
interpreted as indicating that more reflective, engaged, and
intelligent reasoners are more likely to respond in accord with
normative principles. Thus, it might be expected that those
individuals with cognitive/personality characteristics more conducive
to deeper understanding would be more accepting of the appropriate
normative principles for a particular problem. This was the emphasis
of Larrick et al. (1993) when they argued that more intelligent people
should be more likely to use cost-benefit principles. Similarly, need
for cognition--a dispositional variable reflecting the tendency toward
thoughtful analysis and reflective thinking--has been associated with
aspects of epistemic and practical rationality (Cacioppo, Petty,
Feinstein, & Jarvis, 1996; Kardash & Scholes, 1996; Klaczynski et al.,
1997; Smith & Levin, 1996; Verplanken, 1993). This particular
application of the understanding/acceptance principle derives from the
assumption that a normative/descriptive gap that is disproportionately
created by subjects with a superficial understanding of the problem
provides no warrant for amending the application of standard normative
models.

4.3 Tacit Acceptance of the Understanding/Acceptance Principle as a
Mechanism for Adjudicating Disputes About the Appropriate Normative
Models to Apply

It is important to point out that many theorists on all sides of the
rationality debate have acknowledged the force of the
understanding/acceptance argument (without always labeling the
argument as such or citing Slovic & Tversky, 1974). For example,
Gigerenzer and Goldstein (1996) lament the fact that Apologist
theorists who emphasize Simon's (1956, 1957, 1983) concept of bounded
rationality seemingly accept the normative models applied by the
heuristics and biases theorists by their assumption that, if
computational limitations were removed, individuals' responses would
indeed be closer to the behavior those models prescribe.

Lopes and Oden (1991) also wish to deny this tacit assumption in the
literature on computational limitations: "discrepancies between data
and model are typically attributed to people's limited capacity to
process information....There is, however, no support for the view that
people would choose in accord with normative prescriptions if they
were provided with increased capacity" (pp. 208-209). In stressing the
importance of the lack of evidence for the notion that people would
"choose in accord with normative prescriptions if they were provided
with increased capacity" (p. 209), Lopes and Oden (1991) acknowledge
the force of the individual differences version of the
understanding/acceptance principle--because examining variation in
cognitive ability is just that: looking at what subjects who have
"increased capacity" actually do with that increased capacity.

In fact, critics of the heuristics and biases literature have
repeatedly drawn on an individual differences version of the
understanding/acceptance principle to bolster their critiques. For
example, Cohen (1982) critiques the older "bookbag and poker chip"
literature on Bayesian conservatism (Phillips & Edwards, 1966; Slovic,
Fischhoff, Lichtenstein, 1977) by noting that "if so-called
'conservatism' resulted from some inherent inadequacy in people's
information-processing systems one might expect that, when individual
differences in information-processing are measured on independently
attested scales, some of them would correlate with degrees of
'conservatism.' In fact, no such correlation was found by Alker and
Hermann (1971). And this is just what one would expect if
'conservatism' is not a defect, but a rather deeply rooted virtue of
the system" (pp. 259-260). This is precisely how Alker and Hermann
(1971) themselves argued in their paper: "Phillips et al. (1966) have
proposed that conservatism is the result of intellectual deficiencies.
If this is the case, variables such as rationality, verbal
intelligence, and integrative complexity should have related to
deviation from optimality--more rational, intelligent, and complex
individuals should have shown less conservatism" (p. 40).

Wetherick (1971, 1995) has been a critic of the standard
interpretation of the four-card selection task (Wason, 1966) for over
25 years. As a Panglossian theorist, he has been at pains to defend
the modal response chosen by roughly 50% of the subjects (the P and Q
cards). As did Cohen (1982) and Lopes and Oden (1991), Wetherick
(1971) points to the lack of associations with individual differences
to bolster his critique of the standard interpretation of the task:
"in Wason's experimental situation subjects do not choose the not-Q
card nor do they stand and give three cheers for the Queen, neither
fact is interesting in the absence of a plausible theory predicting
that they should....If it could be shown that subjects who choose
not-Q are more intelligent or obtain better degrees than those who do
not this would make the problem worth investigation, but I have seen
no evidence that this is the case" (Wetherick, 1971, p. 213).

Funder (1987), like Cohen (1982) and Wetherick (1971), uses a finding
about individual differences to argue that a particular attribution
bias is not necessarily produced by a process operating suboptimally.
Block and Funder (1986) analyzed the role effect observed by Ross,
Amabile, and Steinmetz (1977): that people rated questioners more
knowledgeable than contestants in a quiz game. Although the role
effect is usually viewed as an attributional error--people allegedly
failed to consider the individual's role when estimating the knowledge
displayed--Block and Funder (1986) demonstrated that subjects most
susceptible to this attributional "error" were more socially
competent, more well adjusted, and more intelligent. Funder (1987)
argued that "manifestation of this 'error,' far from being a symptom
of social maladjustment, actually seems associated with a degree of
competence" (p. 82) and that the so-called error is thus probably
produced by a judgmental process that is generally efficacious. In
short, the argument is that the signs of the correlations with the
individual difference variables point in the direction of the response
that is produced by processes that are ordinarily useful.

Thus, Funder (1987), Lopes and Oden (1991), Wetherick (1971), and
Cohen (1982) all make recourse to patterns of individual differences
(or the lack of such patterns) to pump our intuitions (Dennett, 1980)
in the direction of undermining the standard interpretations of the
tasks under consideration. In other cases, however, examining
individual differences may actually reinforce confidence in the
appropriateness of the normative models applied to problems in the
heuristics and biases literature.

4.4 The Understanding/Acceptance Principle and Spearman's Positive
Manifold

With these arguments in mind, it is thus interesting to note that the
direction of all of the correlations displayed in Table 1 is
consistent with the standard normative models used by psychologists
working in the heuristics and biases tradition. The directionality of
the systematic correlations with intelligence are embarrassing for
those reject-the-norm-application theorists who argue that norms are
being incorrectly applied if we interpret the correlations in terms of
the understanding/acceptance principle (a principle which, as seen in
section [12]4.3, is endorsed in various forms by a host of Panglossian
critics of the heuristics and biases literature). Surely we would want
to avoid the conclusion that individuals with more computational power
are systematically computing the nonnormative response. Such an
outcome would be an absolute first in a psychometric field that is one
hundred years and thousands of studies old (Brody, 1997; Carroll,
1993, 1997; Lubinski & Humphreys, 1997; Neisser et al., 1996;
Sternberg & Kaufman, 1998). It would mean that Spearman's (1904, 1927)
positive manifold for cognitive tasks--virtually unchallenged for one
hundred years--had finally broken down. Obviously, parsimony dictates
that positive manifold remains a fact of life for cognitive tasks and
that the response originally thought to be normative actually is.

In fact, it is probably helpful to articulate the
understanding/acceptance principle somewhat more formally in terms of
positive manifold--the fact that different measures of cognitive
ability almost always correlate with each other (see Carroll, 1993,
1997). The individual differences version of the
understanding/acceptance principle puts positive manifold to use in
areas of cognitive psychology where the nature of the appropriate
normative model to apply is in dispute. The point is that scoring a
vocabulary item on a cognitive ability test and scoring a
probabilistic reasoning response on a task from the heuristics and
biases literature are not the same. The correct response in the former
task has a canonical interpretation agreed upon by all investigators;
whereas the normative appropriateness of responses on tasks from the
latter domain has been the subject of extremely contentious dispute
(Cohen, 1981, 1982, 1986; Cosmides & Tooby, 1996; Einhorn & Hogarth,
1981; Gigerenzer, 1991a, 1993, 1996a; Kahneman & Tversky, 1996;
Koehler, 1996; Stein, 1996). Positive manifold between the two classes
of task would only be expected if the normative model being used for
directional scoring of the tasks in the latter domain is correct^5.
Likewise, given that positive manifold is the norm among cognitive
tasks, the negative correlation (or, to a lesser extent, the lack of a
correlation) between a probabilistic reasoning task and more standard
cognitive ability measures might be taken as a signal that the wrong
normative model is being applied to the former task or that there are
alternative models that are equally appropriate. The latter point is
relevant because the pattern of results in our studies has not always
mirrored the positive manifold displayed in Table 1. We have
previously mentioned the false-consensus effect and overconfidence
effect as such examples, and further instances are discussed in the
next section.

4.5 Noncausal Base Rates

The statistical reasoning problems utilized in the experiments
discussed so far (those derived from Fong, et al. 1986) involved
causal aggregate information, analogous to the causal base rates
discussed by Ajzen (1977) and Bar-Hillel (1980, 1990)--that is, base
rates that had a causal relationship to the criterion behavior.
Noncausal base-rate problems--those involving base rates with no
obvious causal relationship to the criterion behavior--have had a much
more controversial history in the research literature. They have been
the subject of over a decade's worth of contentious dispute
(Bar-Hillel, 1990; Birnbaum, 1983; Cohen, 1979, 1982, 1986; Cosmides &
Tooby, 1996; Gigerenzer, 1991b, 1993, 1996a; Gigerenzer & Hoffrage,
1995; Kahneman & Tversky, 1996; Koehler, 1996; Kyburg, 1983; Levi,
1983; Macchi, 1995)--important components of which have been
articulated in this journal (e.g., Cohen, 1981, 1983; Koehler, 1996;
Krantz, 1981; Kyburg, 1983; Levi, 1983).

In several experiments, we have examined some of the noncausal
base-rate problems that are notorious for provoking philosophical
dispute. One was an AIDS testing problem modeled on Casscells,
Schoenberger, and Grayboys (1978):

   "Imagine that AIDS occurs in one in every 1000 people. Imagine also
   there is a test to diagnose the disease that always gives a
   positive result when a person has AIDS. Finally, imagine that the
   test has a false positive rate of 5 percent. This means that the
   test wrongly indicates that AIDS is present in 5 percent of the
   cases where the person does not have AIDS. Imagine that we choose a
   person randomly, administer the test, and that it yields a positive
   result (indicates that the person has AIDS). What is the
   probability that the individual actually has AIDS, assuming that we
   know nothing else about the individual's personal or medical
   history?"

The Bayesian posterior probability for this problem is slightly less
than .02. In several analyses and replications (see Stanovich, 1999;
Stanovich & West, 1998c) in which we have classified responses of less
than 10% as Bayesian, responses of over 90% as indicating strong
reliance on indicant information, and responses between 10% and 90% as
intermediate, we have found that subjects giving the indicant response
were higher in cognitive ability than those giving the Bayesian
response^6. Additionally, when tested on causal base-rate problems
(e.g., Fong et al., 1986), the greatest base-rate usage was displayed
by the group highly reliant on the indicant information in the AIDS
problem. The subjects giving the Bayesian answer on the AIDS problem
were least reliant on the aggregate information in the causal
statistical reasoning problems.

A similar violation of the expectation of positive manifold was
observed on the notorious cab problem (see Bar-Hillel, 1980; Lyon &
Slovic, 1976; Tversky & Kahneman, 1982)--also the subject of almost
two decades-worth of dispute: "A cab was involved in a hit-and-run
accident at night. Two cab companies, the Green and the Blue, operate
in the city in which the accident occurred. You are given the
following facts: 85 percent of the cabs in the city are Green and 15
percent are Blue. A witness identified the cab as Blue. The court
tested the reliability of the witness under the same circumstances
that existed on the night of the accident and concluded that the
witness correctly identified each of the two colors 80 percent of the
time. What is the probability that the cab involved in the accident
was Blue?"

Bayes' rule yields .41 as the posterior probability of the cab being
blue. Thus, responses over 70% were classified as reliant on indicant
information, responses between 30% and 70% as Bayesian, and response
less than 30% as reliant on indicant information. Again, it was found
that subjects giving the indicant response were higher in cognitive
ability and need for cognition than those giving the Bayesian or
base-rate response (Stanovich & West, 1998c, 1999). Finally, both the
cabs problem and the AIDS problem were subjected to the second of
Slovic and Tversky's (1974) methods of operationalizing the
understanding/acceptance principle--presenting the subjects with
arguments explicating the traditional normative interpretation
(Stanovich & West, 1999). On neither problem was there a strong
tendency for responses to move in the Bayesian direction subsequent to
explication.

The results from both of these problems indicate that the noncausal
base-rate problems display patterns of individual differences quite
unlike those shown on the causal aggregate problems. On the latter,
subjects giving the statistical response (choosing the aggregate
rather than the case or indicant information) scored consistently
higher on measures of cognitive ability. This pattern did not hold for
the AIDS and cab problem where the significant differences were in the
opposite direction--subjects strongly reliant on the indicant
information scored higher on measures of cognitive ability and were
more likely to give the Bayesian response on causal base-rate
problems.

We examined the processing of noncausal base rates in another task
with very different task requirements (see Stanovich, 1999; Stanovich
& West, 1998d)--a selection task in which individuals were not forced
to compute a Bayesian posterior, but instead simply had to indicate
whether or not they thought the base rate was relevant to their
decision. The task was taken from the work of Doherty and Mynatt
(1990). Subjects were given the following instructions: "Imagine you
are a doctor. A patient comes to you with a red rash on his fingers.
What information would you want in order to diagnose whether the
patient has the disease Digirosa? Below are four pieces of information
that may or may not be relevant to the diagnosis. Please indicate all
of the pieces of information that are necessary to make the diagnosis,
but only those pieces of information that are necessary to do so."
Subjects then chose from the alternatives listed in the order: % of
people without Digirosa who have a red rash, % of people with
Digirosa, % of people without Digirosa, and % of people with Digirosa
who have a red rash. These alternatives represented the choices of
P(D/~H), P(H), P(~H), and P(D/H), respectively.

The normatively correct choice of P(H), P(D/H), and P(D/~H) was made
by 13.4% of our sample. The most popular choice (made by 35.5% of the
sample) was the two components of the likelihood ratio, (P(D/H) and
P(D/~H); 21.9% of the sample chose P(D/H) only; and 22.7% chose the
base rate, P(H), and the numerator of the likelihood ratio,
P(D/H)--ignoring the denominator of the likelihood ratio, P(D/~H).
Collapsed across these combinations, almost all subjects (96.0%)
viewed P(D/H) as relevant and very few (2.8%) viewed P(~H) as
relevant. Overall, 54.3% of the subjects deemed that P(D/~H) was
necessary information and 41.5% of the sample thought it was necessary
to know the base rate, P(H).

We examined the cognitive characteristics of the subjects who thought
the baserate was relevant and found that the did not display higher
SAT than those who did not choose the baserate. The pattern of
individual differences was quite different for the denominator of the
likelihood ratio, P(D/~H)--a component which is normatively
uncontroversial. Subjects seeing this information as relevant had
significantly higher SAT scores.

Interestingly, in light of these patterns of individual differences
showing lack of positive manifold when the tasks are scored in terms
of the standard Bayesian approach, noncausal base-rate problems like
the AIDS and cab problem have been the focus of intense debate in the
literature (Cohen, 1979, 1981, 1982, 1986; Koehler, 1996; Kyburg,
1983; Levi, 1983). Several authors have argued that a rote application
of the Bayesian formula to these problems is unwarranted because
noncausal base rates of the AIDS-problem type lack relevance and
reference-class specificity. Finally, our results might also suggest
that the Bayesian subjects on the AIDS problem might not actually be
arriving at their response through anything resembling Bayesian
processing (whether or not they were operating in a frequentist mode;
Gigerenzer & Hoffrage, 1995), because on causal aggregate statistical
reasoning problems these subjects were less likely to rely on the
aggregate information.

5. Alternative Task Construals

Theorists who resist interpreting the gap between normative and
descriptive models as indicating human irrationality have one more
strategy available in addition to those previously described. In the
context of empirical cognitive psychology, it is a commonplace
argument, but it is one that continues to create enormous controversy
and to bedevil efforts to compare human performance to normative
standards. It is the argument that although the experimenter may well
be applying the correct normative model to the problem as set, the
subject might be construing the problem differently and be providing
the normatively appropriate answer to a different problem--in short,
that subjects have a different interpretation of the task (see, for
example, Adler, 1984, 1991; Broome, 1990; Henle, 1962; Hilton, 1995;
Levinson, 1995; Margolis, 1987; Schick, 1987, 1997; Schwarz, 1996).

Such an argument is somewhat different from any of the critiques
examined thus far. It is not the equivalent of positing that a
performance error has been made, because performance errors (attention
lapses, etc.)--being transitory and random--would not be expected to
recur in exactly the same way in a readministration of the same task.
Whereas, if the subject has truly misunderstood the task, they would
be expected to do so again on an identical re-administration of the
task.

Correspondingly, this criticism is different from the argument that
the task exceeds the computational capacity of the subject. The latter
explanation locates the cause of the suboptimal performance within the
subject. In contrast, the alternative task construal argument places
the blame at least somewhat on the shoulders of the experimenter for
failing to realize that there were task features that might lead
subjects to frame the problem in a manner different from that
intended^7.

As with incorrect norm application, the alternative construal argument
locates the problem with the experimenter. However, it is different in
that in the wrong norm explanation it is assumed that the subject is
interpreting the task as the experimenter intended--but the
experimenter is not using the right criteria to evaluate performance.
In contrast, the alternative task construal argument allows that the
experimenter may be applying the correct normative model to the
problem the experimenter intends the subject to solve--but posits that
the subject has construed the problem in some other way and is
providing a normatively appropriate answer to a different problem.

It seems that in order to comprehensively evaluate the rationality of
human cognition it will be necessary to evaluate the appropriateness
of various task construals. This is because--contrary to thin theories
of means/ends rationality that avoid evaluating the subject's task
construal (Elster, 1983; Nathanson, 1994)--it will be argued here that
if we are going to have any normative standards at all, then we must
also have standards for what are appropriate and inappropriate task
construals. In the remainder of this section, we will sketch the
arguments of philosophers and decision scientists who have made just
this point. Then it will be argued that: 1) in order to tackle the
difficult problem of evaluating task construals, criteria of wide
reflective equilibrium come into play; 2) it will be necessary to use
all descriptive information about human performance that could
potentially affect expert wide reflective equilibrium; 3) included in
the relevant descriptive facts are individual differences in task
construal and their patterns of covariance. This argument will again
make use of the understanding/acceptance principle of Slovic and
Tversky (1974) discussed in Section [13]4.2.

5.1 The Necessity of Principles of Rational Construal

It is now widely recognized that the evaluation of the normative
appropriateness of a response to a particular task is always relative
to a particular interpretation of the task. For example, Schick (1987)
argues that "how rationality directs us to choose depends on which
understandings are ours....[and that] the understandings people have
bear on the question of what would be rational for them" (pp. 53, 58).
Likewise, Tversky (1975) argued that "the question of whether utility
theory is compatible with the data or not, therefore, depends
critically on the interpretation of the consequences" (p. 171).

However, others have pointed to the danger inherent in too
permissively explaining away nonnormative responses by positing
different construals of the problem. Normative theories will be
drained of all of their evaluative force if we adopt an attitude that
is too charitable toward alternative construals. Broome (1990)
illustrates the problem by discussing the preference reversal
phenomenon (Lichtenstein & Slovic, 1971; Slovic, 1995). In a choice
between two gambles, A and B, a person chooses A over B. However, when
pricing the gambles, the person puts a higher price on B. This
violation of procedural invariance leads to what appears to be
intransitivity. Presumably there is an amount of money, M, that would
be preferred to A but given a choice of M and B the person would
choose B. Thus, we appear to have B > M, M > A, A > B. Broome (1990)
points out that when choosing A over B the subject is choosing A and
is simultaneously rejecting B. Evaluating A in the M versus A
comparison is not the same. Here, when choosing A, the subject is not
rejecting B. The A alternative here might be considered to be a
different prospect (call it A'), and if it is so considered there is
no intransitivity (B > M, M > A', A > B). Broome (1990) argues that
whenever the basic axioms such as transitivity, independence, or
descriptive or procedural invariance are breached, the same
inoculating strategy could be invoked--that of individuating outcomes
so finely that the violation disappears.

Broome's (1990) point is that the thinner the categories we use to
individuate outcomes, the harder it will be to attribute irrationality
to a set of preferences if we evaluate rationality only in
instrumental terms. He argues that we need, in addition to the formal
principles of rationality, those that deal with content so as to
enable us to evaluate the reasonableness of a particular individuation
of outcomes. Broome (1990) acknowledges that "this procedure puts
principles of rationality to work at a very early stage of decision
theory. They are needed in fixing the set of alternative prospects
that preferences can then be defined upon. The principles in question
might be called "'rational principles of indifference'" (p. 140).
Broome (1990) admits that "many people think there can be no
principles of rationality apart from the formal ones. This goes along
with the common view that rationality can only be
instrumental....[however] if you acknowledge only formal principles of
rationality, and deny that there are any principles of indifference,
you will find yourself without any principles of rationality at all"
(pp. 140-141).

Broome cites Tversky (1975) as concurring in this view: "I believe
that an adequate analysis of rational choice cannot accept the
evaluation of the consequences as given, and examine only the
consistency of preferences. There is probably as much irrationality in
our feelings, as expressed in the way we evaluate consequences, as
there is in our choice of actions. An adequate normative analysis must
deal with problems such as the legitimacy of regret in Allais'
problem....I do not see how the normative appeal of the axioms could
be discussed without a reference to a specific interpretation"
(Tversky, 1975, p. 172).

Others agree with the Broome/Tversky analysis (see Baron, 1993, 1994;
Frisch, 1994; Schick, 1997). But while there is some support for
Broome's generic argument, the contentious disputes about rational
principles of indifference and rational construals of the tasks in the
heuristics and biases literature (Adler, 1984, 1991; Berkeley &
Humphreys, 1982; Cohen, 1981, 1986; Gigerenzer, 1993, 1996a; Hilton,
1995; Jepson, Krantz, & Nisbett, 1983; Kahneman & Tversky, 1983, 1996;
Lopes, 1991; Nisbett, 1981; Schwarz, 1996) highlight the difficulties
to be faced when attempting to evaluate specific problem construals.
For example, Margolis (1987) agrees with Henle (1962) that the
subjects' nonnormative responses will almost always be logical
responses to some other problem representation. But unlike Henle
(1962), Margolis (1987) argues that many of these alternative task
construals are so bizarre--so far from what the very words in the
instructions said--that they represent serious cognitive errors that
deserve attention: "But in contrast to Henle and Cohen, the detailed
conclusions I draw strengthen rather than invalidate the basic claim
of the experimenters. For although subjects can be--in fact, I try to
show, ordinarily are--giving reasonable responses to a different
question, the different question can be wildly irrelevant to anything
that plausibly could be construed as the meaning of the question
asked. The locus of the illusion is shifted, but the force of the
illusion is confirmed not invalidated or explained away" (p. 141)

5.2 Evaluating Principles of Rational Construal: The
Understanding/Acceptance Assumption Revisited

Given current arguments that principles of rational construal are
necessary for a full normative theory of human rationality (Broome,
1990; Einhorn & Hogarth, 1981; Jungermann, 1986; Schick, 1987, 1997;
Shweder, 1987; Tversky, 1975), how are such principles to be derived?
When searching for principles of rational task construal the same
mechanisms of justification used to assess principles of instrumental
rationality will be available. Perhaps in some cases--instances where
the problem structure maps the world in an unusually close and
canonical way--problem construals could be directly evaluated by how
well they serve the decision maker in achieving their goals (Baron,
1993, 1994). In such cases, it might be possible to prove the
superiority or inferiority of certain construals by appeals to Dutch
Book or money pump arguments (de Finetti, 1970/1990; Maher, 1993;
Skyrms, 1986; Osherson, 1995; Resnik, 1987).

Also available will be the expert wide reflective equilibrium view
discussed by Stich and Nisbett (1980; see Stanovich, 1999; Stein,
1996). In contrast, Baron (1993, 1994) and Thagard (1982) argue that
rather than any sort of reflective equilibrium, what is needed here
are "arguments that an inferential system is optimal with respect to
the criteria discussed" (Thagard, 1982, p. 40). But in the area of
task construal, finding optimization of criteria may be
unlikely--there will be few money pumps or Dutch Books to point the
way. If in the area of task construal there will be few money pumps or
Dutch Books to prove that a particular task interpretation has
disastrous consequences, then the field will be again thrust back upon
the debate that Thagard (1982) calls the argument between the
populists and the elitists. But as argued before, this is really a
misnomer. There are few controversial tasks in the heuristics and
biases literature where all untutored laypersons interpret tasks
differently from those of the experts who designed them. The issue is
not the untutored average person versus experts, but experts plus some
laypersons versus other untutored individuals. The cognitive
characteristics of those departing from the expert construal
might--for reasons parallel to those argued in section [14]4--have
implications for how we evaluate particular task interpretations. It
is argued here that Slovic and Tversky's (1974) assumption ("the
deeper the understanding of the axiom, the greater the readiness to
accept it" pp. 372-373) can again be used as a tool to condition the
expert reflective equilibrium regarding principles of rational task
construal.

Framing effects are ideal vehicles for demonstrating how the
understanding/acceptance principle might be utilized. First, it has
already been shown that there are consistent individual differences
across a variety of framing problems (Frisch, 1993). Second, framing
problems have engendered much dispute regarding issues of appropriate
task construal. The Disease Problem of Tversky and Kahneman (1981) has
been the subject of much contention:

   Problem 1. Imagine that the U.S. is preparing for the outbreak of
   an unusual disease, which is expected to kill 600 people. Two
   alternative programs to combat the disease have been proposed.
   Assume that the exact scientific estimates of the consequences of
   the programs are as follows: If Program A is adopted, 200 people
   will be saved. If Program B is adopted, there is a one-third
   probability that 600 people will be saved and a two-thirds
   probability that no people will be saved. Which of the two programs
   would you favor, Program A or Program B?

   Problem 2. Imagine that the U.S. is preparing for the outbreak of
   an unusual disease, which is expected to kill 600 people. Two
   alternative programs to combat the disease have been proposed.
   Assume that the exact scientific estimates of the consequences of
   the programs are as follows: If Program C is adopted, 400 people
   will die. If Program D is adopted, there is a one-third probability
   that nobody will die and a two-thirds probability that 600 people
   will die. Which of the two programs would you favor, Program C or
   Program D?

Many subjects select alternatives A and D in these two problems
despite the fact that the two problems are redescriptions of each
other and that Program A maps to Program C rather than D. This
response pattern violates the assumption of descriptive invariance of
utility theory. However, Berkeley and Humphreys (1982) argue that the
Programs A and C might not be descriptively invariant in subjects'
interpretations. They argue that the wording of the outcome of Program
A ("will be saved") combined with the fact that its outcome is
seemingly not described in the exhaustive way as the consequences for
Program B suggests the possibility of human agency in the future which
might enable the saving of more lives (see also, Kuhberger, 1995). The
wording of the outcome of Program C ("will die") does not suggest the
possibility of future human agency working to possibly save more lives
(indeed, the possibility of losing a few more might be inferred by
some people). Under such a construal of the problem, it is no longer
non-normative to choose Programs A and D. Likewise, Macdonald (1986)
argues that, regarding the "200 people will be saved" phrasing, "it is
unnatural to predict an exact number of cases" (p. 24) and that
"ordinary language reads 'or more' into the interpretation of the
statement" (p. 24; see also Jou, Shanteau, & Harris, 1996).

However, consistent with the finding that being forced to provide a
rationale or take more time reduces framing effects (e.g., Larrick et
al., 1992; Sieck & Yates, 1997; Takemura, 1994) and that people higher
in need for cognition displayed reduced framing effects (Smith &
Levin, 1996), in our within-subjects study of framing effects on the
Disease Problem (Stanovich & West, 1998b), we found that subjects
giving a consistent response to both descriptions of the problem--who
were actually the majority in our within-subjects experiment--were
significantly higher in cognitive ability than those subjects
displaying a framing effect. Thus, the results of studies
investigating the effects of giving a rationale, taking more time,
associations with cognitive engagement, and associations with
cognitive ability are all consistent in suggesting that the response
dictated by the construal of the problem originally favored by Tversky
and Kahneman (1981) should be considered the correct response because
it is endorsed even by untutored subjects as long as they are
cognitively engaged with the problem, had enough time to process the
information, and had the cognitive ability to fully process the
information^8.

Perhaps no finding in the heuristics and biases literature has been
the subject of as much criticism as Tversky and Kahneman's (1983)
claim to have demonstrated a conjunction fallacy in probabilistic
reasoning. Most of the criticisms have focused on the issue of
differential task construal, and several critics have argued that
there are alternative construals of the tasks that are, if anything,
more rational than that which Tversky and Kahneman (1983) regard as
normative for examples such as the well-known Linda problem:

   Linda is 31 years old, single, outspoken, and very bright. She
   majored in philosophy. As a student, she was deeply concerned with
   issues of discrimination and social justice, and also participated
   in anti-nuclear demonstrations. Please rank the following
   statements by their probability, using 1 for the most probable and
   8 for the least probable.

   a. Linda is a teacher in an elementary school
   b. Linda works in a bookstore and takes Yoga classes
   c. Linda is active in the feminist movement
   d. Linda is a psychiatric social worker
   e. Linda is a member of the League of Women Voters
   f. Linda is a bank teller
   g. Linda is an insurance salesperson
   h. Linda is a bank teller and is active in the feminist movement

Because alternative h is the conjunction of alternatives c and f, the
probability of h cannot be higher than that of either c or f, yet 85%
of the subjects in Tversky and Kahneman's (1983) study rated
alternative h as more probable than f. What concerns us here is the
argument that there are subtle linguistic and pragmatic features of
the problem that lead subjects to evaluate alternatives different than
those listed. For example, Hilton (1995) argues that under the
assumption that the detailed information given about the target means
that the experimenter knows a considerable amount about Linda, then it
is reasonable to think that the phrase "Linda is a bank teller" does
not contain the phrase "and is not active in the feminist movement"
because the experimenter already knows this to be the case. If "Linda
is a bank teller" is interpreted in this way, then rating h as more
probable than f no longer represents a conjunction fallacy.

Similarly, Morier and Borgida (1984) point out that the presence of
the unusual conjunction "Linda is a bank teller and is active in the
feminist movement" itself might prompt an interpretation of "Linda is
a bank teller" as "Linda is a bank teller and is not active in the
feminist movement". Actually, Tversky and Kahneman (1983) themselves
had concerns about such an interpretation of the "Linda is a bank
teller" alternative and ran a condition in which this alternative was
rephrased as "Linda is a bank teller whether or not she is active in
the feminist movement". They found that conjunction fallacy was
reduced from 85% of their sample to 57% when this alternative was
used. Several other investigators have suggested that pragmatic
inferences lead to seeming violations of the logic of probability
theory in the Linda Problem^9 (see Adler, 1991; Dulany & Hilton, 1991;
Levinson, 1995; Macdonald & Gilhooly, 1990; Politzer & Noveck, 1991;
Slugoski & Wilson, 1998). These criticisms all share the implication
that actually committing the conjunction fallacy is a rational
response to an alternative construal of the different statements about
Linda.

Assuming that those committing the so-called conjunction fallacy are
making the pragmatic interpretation and that those avoiding the
fallacy are making the interpretation that the investigators intended,
we examined whether the subjects making the pragmatic interpretation
were subjects who were disproportionately the subjects of higher
cognitive ability. Because this group is in fact the majority in most
studies--and because the use of such pragmatic cues and background
knowledge is often interpreted as reflecting adaptive information
processing (e.g., Hilton, 1995)--it might be expected that these
individuals would be the subjects of higher cognitive ability.

In our study (Stanovich & West, 1998b), we examined the performance of
150 subjects on the Linda Problem presented above. Consistent with the
results of previous experiments on this problem (Tversky & Kahneman,
1983), 80.7% of our sample committed the conjunction effect--they
rated the feminist bank teller alternative as more probable than the
bank teller alternative. The mean SAT score of the 121 subjects who
committed the conjunction fallacy was 82 points lower than the mean
score of the 29 who avoided the fallacy. This difference was highly
significant and it translated into an effect size of .746, which
Rosenthal and Rosnow (1991, p. 446) classify as "large."

Tversky and Kahneman (1983) and Reeves and Lockhart (1993) have
demonstrated that the incidence of the conjunction fallacy can be
decreased if the problem describes the event categories in some finite
population or if the problem is presented in a frequentist manner (see
also Fiedler, 1988; Gigerenzer, 1991b, 1993). We have replicated this
well-known finding, but we have also found that frequentist
representations of these problems markedly reduce--if not
eliminate--cognitive ability differences (Stanovich & West, 1998b).

Another problem that has spawned many arguments about alternative
construals is Wason's (1966) selection task. Performance on abstract
versions of the selection task is extremely low (see Evans, Newstead,
& Byrne, 1993). Typically, less than 10% of subjects make the correct
selections of the A card (P) and 7 card (not-Q). The most common
incorrect choices made by subjects are the A card and the 3 card (P
and Q) or the selection of the A card only (P). The preponderance of P
and Q responses has most often been attributed to a so-called matching
bias that is automatically triggered by surface-level relevance cues
(Evans, 1996; Evans & Lynch, 1973), but some investigators have
championed an explanation based on an alternative task construal. For
example, Oaksford and Chater (1994, 1996; see also Nickerson, 1996)
argue that rather than interpreting the task as one of deductive
reasoning (as the experimenter intends), many subjects interpret it as
an inductive problem of probabilistic hypothesis testing. They show
that the P and Q response is expected under a formal Bayesian analysis
which assumes such an interpretation in addition to optimal data
selection.

We have examined individual differences in responding on a variety of
abstract and deontic selection task problems (Stanovich & West, 1998a,
1998c). Typical results are displayed in [15]Table 2. The table
presents the mean SAT scores of subjects responding correctly (as
traditionally interpreted--with the responses P and not-Q) on various
versions of selection task problems. One was a commonly used
nondeontic problem with content, the so-called Destination Problem
(e.g., Manktelow & Evans, 1979). Replicating previous research, few
subjects responded correctly on this problem. However, those that did
had significantly higher SAT scores than those that did not and the
difference was quite large in magnitude (effect size of .815). Also
presented in the table are two well-known problems (Dominowski, 1995;
Griggs, 1983; Griggs & Cox, 1982, 1983; Newstead & Evans, 1995) with
deontic rules (reasoning about rules used to guide human
behavior--about what "ought to" or "must" be done, see Manktelow &
Over, 1991)--the Drinking-Age Problem (If a person is drinking beer
then the person must be over 21 years of age) and the Sears Problem
(Any sale over $30 must be approved by the section manager, Mr.
Jones). Both are known to facilitate performance and this effect is
clearly replicated in the data presented in [16]Table 2. However, it
is also clear that the differences in cognitive ability are much less
in these two problems. The effect size is reduced from .815 to .347 in
the case of the Drinking-Age Problem and it fails to even reach
statistical significance in the case of the Sears Problem (effect size
of .088). The bottom half of the table indicates that exactly the same
pattern was apparent when the P and not-Q responders were compared
only with the P and Q responders on the Destination Problem--the
latter being the response that is most consistent with an inductive
construal of the problem (see Nickerson, 1996; Oaksford & Chater,
1994, 1996).

Table 2
Mean SAT Total Scores of Subjects Who Gave the Correct and Incorrect
Responses to Three Different Selection Task Problems
(Numbers in Parentheses are the Number of Subjects)

Incorrect

P & not-Q
(Correct)

  t value

  Effect Size^a

Nondeontic Problem:
Destination Problem

1187 (197)

1270 (17)

  3.21***

.815

Deontic Problems:
Drinking-Age Problem

1170 (72)

1206 (143)

   2.39**

.347

Sears Problem

1189 (87)

1198 (127)

0.63

.088

Nondeontic Problem:

   P & Q

P & not-Q

  t value

  Effect Size^a

Destination Problem

1195 (97)

1270 (17)

  3.06***

.812

Note: df = 212 for the Destination and Sears Problems and 213 for the
Drinking-Age Problem; df = 112 for the P&Q comparison on the
Destination Problem
* = p < .05, ** = p < .025, *** = p < .01, all two-tailed
^a Cohen's d

Thus, on the selection task, it appears that cognitive ability
differences are strong in cases where there is a dispute about the
proper construal of the task (in nondeontic tasks). In cases where
there is little controversy about alternative construals--the deontic
rules of the Drinking-Age and Sears problems--cognitive ability
differences are markedly attenuated. This pattern--cognitive ability
differences large on problems where there is contentious dispute
regarding the appropriate construal and cognitive ability differences
small when there is no dispute about task construal--is mirrored in
our results on the conjunction effect and framing effect (Stanovich &
West, 1998b).


6. Dual Process Theories and Alternative Task Construals

The sampling of results just presented (for other examples, see
Stanovich, 1999) has demonstrated that the responses associated with
alternative construals of a well-known framing problem (the Disease
Problem), for the Linda Problem, and for the nondeontic selection task
were consistently associated with lower cognitive ability. How might
we interpret this consistent pattern displayed on three tasks from the
heuristics and biases literature where alternative task construals
have been championed?

One possible interpretation of this pattern is in terms of two-process
theories of reasoning (Epstein, 1994; Evans, 1984, 1996; Evans & Over,
1996; Sloman, 1996). A summary of the generic properties distinguished
by several two-process views are presented in [17]Table 3. Although
the details and technical properties of these dual-process theories do
not always match exactly, nevertheless there are clear family
resemblances (for discussions, see Evans & Over, 1996; Gigerenzer &
Regier, 1996; Sloman, 1996). In order to emphasize the prototypical
view that is adopted here, the two systems have simply been
generically labeled System 1 and System 2.

Table 3
The Terms for the Two Systems Used by a Variety of Theorists and the
Properties of Dual-Process Theories of Reasoning

  System 1

  System 2

Dual-Process Theories:
Sloman (1996) associative system rule-based system
Evans (1984, 1989) heuristic processing analytic processing
Evans & Over (1996) tacit thought processes explicit thought processes
Reber (1993) implicit cognition explicit learning
Levinson (1995) interactional intelligence analytic intelligence
Epstein (1994) experiential system rational system
Pollock (1991) quick & inflexible modules intellection
Hammond (1996) intuitive cognition analytical cognition
Klein (1998) recognition-primed decisions rational choice strategy
Johnson-Laird (1983) implicit inferences explicit inferences
Properties: associative rule-based
holistic analytic
automatic controlled
relatively undemanding of cognitive capacity demanding of cognitive
capacity
relatively fast relatively slow
acquisition by biology, exposure, and personal experience acquisition
by cultural and formal tuition
Task Construal: highly contextualized decontextualized
personalized  depersonalized
conversational and social  asocial
Type of Intelligence Indexed: interactional
(conversational implicature)  analytic
(psychometric IQ)

The key differences in the properties of the two systems are listed
next. System 1 is characterized as automatic, largely unconscious, and
relatively undemanding of computational capacity. Thus, it conjoins
properties of automaticity and heuristic processing as these
constructs have been variously discussed in the literature. These
properties characterize what Levinson (1995) has termed interactional
intelligence--a system composed of the mechanisms that support a
Gricean theory of communication that relies on intention-attribution.
This system has as its goal the ability to model other minds in order
to read intention and to make rapid interactional moves based on those
modeled intentions. System 2 conjoins the various characteristics that
have been viewed as typifying controlled processing. System 2
encompasses the processes of analytic intelligence that have
traditionally been studied by information processing theorists trying
to uncover the computational components underlying intelligence.

For the purposes of the present discussion, the most important
difference between the two systems is that they tend to lead to
different types of task construals. Construals triggered by System 1
are highly contextualized, personalized, and socialized. They are
driven by considerations of relevance and are aimed at inferring
intentionality by the use of conversational implicature even in
situations that are devoid of conversational features (see Margolis,
1987). The primacy of these mechanisms leads to what has been termed
the fundamental computational bias in human cognition (Stanovich,
1999)--the tendency toward automatic contextualization of problems. In
contrast, System 2's more controlled processes serve to
decontextualize and depersonalize problems. This system is more adept
at representing in terms of rules and underlying principles. It can
deal with problems without social content and is not dominated by the
goal of attributing intentionality or by the search for conversational
relevance.

Using the distinction between System 1 and System 2 processing, it is
conjectured here that in order to observe large cognitive ability
differences in a problem situation, the two systems must strongly cue
different responses^10. It is not enough simply that both systems are
engaged. If both cue the same response (as in deontic selection task
problems), then this could have the effect of severely diluting any
differences in cognitive ability. One reason that this outcome is
predicted is that it is assumed that individual differences in System
1 processes (interactional intelligence) bear little relation to
individual differences in System 2 processes (analytic intelligence).
This is a conjecture for which there is a modest amount of evidence.
Reber (1993) has shown preconscious processes to have low variability
and to show little relation to analytic intelligence (see Jones & Day,
1997; McGeorge, Crawford, & Kelly, 1997; Reber, Walkenfeld, &
Hernstadt, 1991).

In contrast, if the two systems cue opposite responses, rule-based
System 2 will tend to differentially cue those of high analytic
intelligence and this tendency will not be diluted by System 1 (the
associative system) nondifferentially drawing subjects to the same
response. For example, the Linda Problem maximizes the tendency for
the two systems to prime different responses and this problem produced
a large difference in cognitive ability. Similarly, in nondeontic
selection tasks there is ample opportunity for the two systems to cue
different responses. A deductive interpretation conjoined with an
exhaustive search for falsifying instances yields the response P and
not-Q. This interpretation and processing style is likely associated
with the rule-based System 2--individual differences in which underlie
the psychometric concept of analytic intelligence. In contrast, within
the heuristic-analytic framework of Evans (1984, 1989, 1996), the
matching response of P and Q reflects the heuristic processing of
System 1 (in Evans' theory, a linguistically-cued relevance response).

In deontic problems, both deontic and rule-based logics are cuing
construals of the problem that dictate the same response (P and
not-Q). Whatever is one's theory of responding in deontic
tasks--preconscious relevance judgments, pragmatic schemas, or
Darwinian algorithms (e.g., Cheng & Holyoak, 1989; Cosmides, 1989;
Cummins, 1996; Evans, 1996)--the mechanisms triggering the correct
response resemble heuristic or modular structures that fall within the
domain of System 1. These structures are unlikely to be strongly
associated with analytic intelligence (Cummins, 1996; Levinson, 1995;
McGeorge, Crawford, & Kelly, 1997; Reber, 1993; Reber, Walkenfeld, &
Hernstadt, 1991), and hence they operate to draw subjects of both high
and low analytic intelligence to the same response dictated by the
rule-based system--thus serving to dilute cognitive ability
differences between correct and incorrect responders (see Stanovich &
West, 1998a for a data simulation).

6.1 Alternative Construals: Evolutionary Optimization Versus Normative
Rationality

The sampling of experimental results reviewed here (see Stanovich,
1999 for further examples) has demonstrated that the response dictated
by the construal of the inventors of the Linda Problem (Tversky &
Kahneman, 1983), Disease Problem (Tversky & Kahneman, 1981), and
selection task (Wason, 1966) is the response favored by subjects of
high analytic intelligence. The alternative responses dictated by the
construals favored by the critics of the heuristics and biases
literature were the choices of the subjects of lower analytic
intelligence. In this section we will explore the possibility that
these alternative construals may have been triggered by heuristics
that make evolutionary sense, but that subjects higher in a more
flexible type of analytic intelligence (and those more cognitively
engaged, see Smith & Levin, 1996) are more prone to follow normative
rules that maximize personal utility. In a very restricted sense, such
a pattern might be said to have relevance for the concept of rational
task construal.

The argument depends on the distinction between evolutionary
adaptation and instrumental rationality (utility maximization given
goals and beliefs). The key point is that for the latter (variously
termed practical, pragmatic, or means/ends rationality), maximization
is at the level of the individual person. Adaptive optimization in the
former case is at the level of the genes. In Dawkins' (1976, 1982)
terms, evolutionary adaptation concerns optimization processes
relevant to the so-called replicators (the genes), whereas
instrumental rationality concerns utility maximization for the
so-called vehicle (or interactor, to use Hull's, 1982, term), which
houses the genes. Anderson (1990, 1991) emphasizes this distinction in
his treatment of adaptionist models in psychology. In his advocacy of
such models, Anderson (1990, 1991) eschews Dennett's (1987) assumption
of perfect rationality in the instrumental sense (hereafter termed
normative rationality) for the somewhat different assumption of
evolutionary optimization (i.e., evolution as a local fitness
maximizer). Anderson (1990) accepts Stich's (1990; see also Cooper,
1989; Skyrms, 1996) argument that evolutionary adaptation (hereafter
termed evolutionary rationality)^11 does not guarantee perfect human
rationality in the normative sense: "Rationality in the adaptive
sense, which is used here, is not rationality in the normative sense
that is used in studies of decision making and social judgment....It
is possible that humans are rational in the adaptive sense in the
domains of cognition studied here but not in decision making and
social judgment" (p. 31). Thus, Anderson (1991) acknowledges that
there may be arguments for "optimizing money, the happiness of oneself
and others, or any other goal. It is just that these goals do not
produce optimization of the species" (pp. 510-511). As a result, a
descriptive model of processing that is adaptively optimal could well
deviate substantially from a normative model. This is because
Anderson's (1990, 1991) adaptation assumption is that cognition is
optimally adapted in an evolutionary sense--and this is not the same
as positing that human cognitive activity will result in normatively
appropriate responses.

Such a view can encompass both the impressive record of descriptive
accuracy enjoyed by a variety of adaptionist models (Anderson, 1990,
1991; Oaksford & Chater, 1994, 1996, 1998) as well as the fact that
cognitive ability sometimes dissociates from the response deemed
optimal on an adaptionist analysis (Stanovich & West, 1998a). As
discussed above, Oaksford and Chater (1994) have had considerable
success in modeling the nondeontic selection task as an inductive
problem in which optimal data selection is assumed (see also,
Oaksford, Chater, Grainger, & Larkin, 1997). Their model predicts the
modal response of P and Q and the corresponding dearth of P and not-Q
choosers. Similarly, Anderson (1990, p. 157-160) models the 2 x 2
contingency assessment experiment using a model of optimally adapted
information processing and shows how it can predict the
much-replicated finding that the D cell (cause absent and effect
absent) is vastly underweighted (see also Friedrich, 1993; Klayman &
Ha, 1987). Finally, a host of investigators (Adler, 1984, 1991; Dulany
& Hilton, 1991; Hilton, 1995; Levinson, 1995) have stressed how a
model of rational conversational implicature predicts that violating
the conjunction rule in the Linda Problem reflects the adaptive
properties of interactional intelligence.

Yet in all three of these cases--despite the fact that the adaptionist
models predict the modal response quite well--individual differences
analyses demonstrate associations that also must be accounted for.
Correct responders on the nondeontic selection task (P and not-Q
choosers--not those choosing P and Q) are higher in cognitive ability.
In the 2 x 2 covariation detection experiment, it is those subjects
weighting cell D more equally (not those underweighting the cell in
the way that the adaptionist model dictates) who are higher in
cognitive ability and who tend to respond normatively on other tasks
(Stanovich & West, 1998d). Finally, despite conversational
implicatures indicating the opposite, individuals of higher cognitive
ability disproportionately tend to adhere to the conjunction rule.
These patterns make sense if it is assumed that the two systems of
processing are optimized for different situations and different goals
and that these data patterns reflect the greater probability that the
analytic intelligence of System 2 will override the interactional
intelligence of System 1 in individuals of higher cognitive ability.

In summary, the biases introduced by System 1 heuristic processing may
well be universal--because the computational biases inherent in this
system are ubiquitous and shared by all humans. However, it does not
necessarily follow that errors on tasks from the heuristics and biases
literature will be universal (we have known for some time that they
are not). This is because, for some individuals, System 2 processes
operating in parallel (see Evans & Over, 1996) will have the requisite
computational power (or a low enough threshold) to override the
response primed by System 1.

It is hypothesized that the features of System 1 are designed to very
closely track increases in the reproduction probability of genes.
System 2, while also clearly an evolutionary product, is also
primarily a control system focused on the interests of the whole
person. It is the primary maximizer of an individual's personal
utility^12. Maximizing the latter will occasionally result in
sacrificing genetic fitness (Barkow, 1989; Cooper, 1989; Skyrms,
1996). Because System 2 is more attuned to normative rationality than
is System 1, System 2 will seek to fulfill the individual's goals in
the minority of cases where those goals conflict with the responses
triggered by System 1.

It is proposed that just such conflicts are occurring in three of the
tasks discussed previous previously (the Disease Problem, the Linda
Problem, and the selection task). This conjecture is supported by the
fact that evolutionary rationality has been conjoined with Gricean
principles of conversational implicature by several theorists
(Gigerenzer, 1996b; Hilton, 1995, Levinson, 1995) who emphasize the
principle of "conversationally rational interpretation" (Hilton, 1995,
pp. 265). According to this view, the pragmatic heuristics are not
simply inferior substitutes for computationally costly logical
mechanisms which would work better. Instead, the heuristics are
optimally designed to solve an evolutionary problem in another
domain--attributing intentions to conspecifics and coordinating mutual
intersubjectivity so as to optimally negotiate cooperative behavior
(Cummins, 1996; Levinson, 1995; Skyrms, 1996).

It must be stressed though that in the vast majority of mundane
situations, the evolutionary rationality embodied in System 1
processes will also serve the goals of normative rationality. Our
automatic, System 1 processes for accurately navigating around objects
in the natural world were adaptive in an evolutionary sense, and they
likewise serve our personal goals as we carry out our lives in the
modern world (that is, navigational abilities are an evolutionary
adaptation that serve the instrumental goals of the vehicle as well).

One way to view the difference between what we have termed here
evolutionary and normative rationality is to note that they are not
really two different types of rationality (see Oaksford & Chater,
1998, pp. 291-297) but are instead terms for characterizing
optimization procedures operating at the subpersonal and personal
levels, respectively. That there are two optimization procedures in
operation here that could come into conflict is a consequence of the
insight that the genes--as subpersonal replicators--can increase their
fecundity and longevity in ways that do not necessarily serve the
instrumental goals of the vehicles built by the genome (Cooper, 1989;
Skyrms, 1996).

Skyrms (1996) devotes an entire book on evolutionary game theory to
showing that the idea that "natural selection will weed out
irrationality" (p. x) is false because optimization at the subpersonal
replicator level is not coextensive with the optimization of the
instrumental goals of the vehicle (i.e., normative rationality).
Gigerenzer (1996b) provides an example by pointing out that neither
rats nor humans maximize utility in probabilistic contingency
experiments. Instead of responding by choosing the most probable
alternative on every trial, subjects alternate in a manner that
matches the probabilities of the stimulus alternatives. This behavior
violates normative strictures on utility maximization, but Gigerenzer
(1996b) demonstrates how probability matching could actually be an
evolutionarily stable strategy (see Cooper, 1989, and Skyrms, 1996 for
many such examples).

Examples such as this led Skyrms (1996) to note that "when I contrast
the results of the evolutionary account with those of rational
decision theory, I am not criticizing the normative force of the
latter. I am just emphasizing the fact that the different questions
asked by the two traditions may have different answers" (p. xi).
Skyrms' (1996) book articulates the environmental and population
parameters under which "rational choice theory completely parts ways
with evolutionary theory" (p. 106; see also Cooper, 1989). Cognitive
mechanisms that were fitness enhancing might well thwart our goals as
personal agents in an industrial society (see Baron, 1998) because the
assumption that our cognitive mechanisms are adapted in the
evolutionary sense (Pinker, 1997) does not entail normative
rationality. Thus, situations where evolutionary and normative
rationality dissociate might well put the two processing Systems in
partial conflict with each other. These conflicts may be rare, but the
few occasions on which they occur might be important ones. This is
because knowledge-based, technological societies often put a premium
on abstraction and decontextualization, and they sometimes require
that the fundamental computational bias of human cognition be
overridden by System 2 processes.

6.2 The Fundamental Computational Bias and Task Interpretation

The fundamental computational bias, that "specific features of problem
content, and their semantic associations, constitute the dominant
influence on thought" (Evans et al., 1983, p. 295; Stanovich, 1999),
is no doubt rational in the evolutionary sense. Selection pressure was
probably in the direction of radical contextualization. An organism
that could bring more relevant information to bear (not forgetting the
frame problem) on the puzzles of life probably dealt with the world
better than competitors and thus reproduced with greater frequency and
contributed more of its genes to future generations.

Evans and Over (1996) argue that an overemphasis on normative
rationality has led us to overlook the adaptiveness of
contextualization and the nonoptimality of always decoupling prior
beliefs from problem situations ("beliefs that have served us well are
not lightly to be abandoned," p. 114). Their argument here parallels
the reasons that philosophy of science has moved beyond naive
falsificationism (see Howson & Urbach, 1993). Scientists do not
abandon a richly confirmed and well integrated theory at the first
little bit of falsifying evidence, because abandoning the theory might
actually decrease explanatory coherence (Thagard, 1992). Similarly,
Evans and Over (1996) argue that beliefs that have served us well in
the past should be hard to dislodge, and projecting them on to new
information--because of their past efficacy--might actually help in
assimilating the new information.

Evans and Over (1996) note the mundane but telling fact that when
scanning a room for a particular shape, our visual systems register
color as well. They argue that we do not impute irrationality to our
visual systems because they fail to screen out the information that is
not focal. Our systems of recruiting prior knowledge and contextual
information to solve problems with formal solutions are probably
likewise adaptive in the evolutionary sense. However, Evans and Over
(1996) do note that there is an important disanalogy here as well,
because studies of belief bias in syllogistic reasoning have shown
that "subjects can to some extent ignore belief and reason from a
limited number of assumptions when instructed to do so" (p. 117). That
is, in the case of reasoning--as opposed to the visual domain--some
people do have the cognitive flexibility to decouple unneeded systems
of knowledge and some do not.

The studies reviewed here indicate that those who do have the
requisite flexibility are somewhat higher in cognitive ability and in
actively open-minded thinking (see Stanovich & West, 1997). These
styles and skills are largely System 2, not System 1, processes. Thus,
the heuristics triggering alternative task construals in the various
problems considered here may well be the adaptive evolutionary
products embodied in System 1 as Levinson (1995) and others argue.
Nevertheless, many of our personal goals may have become detached from
their evolutionary context (see Barkow, 1989). As Morton (1997) aptly
puts it: "We can and do find ways to benefit from the pleasures that
our genes have arranged for us without doing anything to help the
genes themselves. Contraception is probably the most obvious example,
but there are many others. Our genes want us to be able to reason, but
they have no interest in our enjoying chess" (p. 106).

Thus, we seek "not evolution's end of reproductive success but
evolution's means, love-making. The point of this example is that some
human psychological traits may, at least in our current environment,
be fitness-reducing" (see Barkow, 1989, p. 296). And if the latter are
pleasurable, analytic intelligence achieves normative rationality by
pursuing them--not the adaptive goals of our genes. This is what
Larrick et al. (1993) argue when they speak of analytic intelligence
as "the set of psychological properties that enables a person to
achieve his or her goals effectively. On this view, intelligent people
will be more likely to use rules of choice that are effective in
reaching their goals than will less intelligent people" (p. 345).

Thus, high analytic intelligence may lead to task construals that
track normative rationality; whereas the alternative construals of
subjects low in analytic intelligence (and hence more dominated by
System 1 processing) might be more likely to track evolutionary
rationality in situations that put the two types of rationality in
conflict--as is conjectured to be the case with the problems discussed
previously. If construals consistent with normative rationality are
more likely to satisfy our current individual goals (Baron, 1993,
1994) than are construals determined by evolutionary rationality
(which are construals determined by our genes' metaphorical
goal--reproductive success), then it is in this very restricted sense
that individual difference relationships such as those illustrated
here tell us which construals are "best".

6.3 The Fundamental Computational Bias and the Ecology of the Modern
World

A conflict between the decontextualizing requirements of normative
rationality and the fundamental computational bias may perhaps be one
of the main reasons that normative and evolutionary rationality
dissociate. The fundamental computational bias is meant to be a global
term that captures the pervasive bias toward the contextualization of
all informational encounters. It conjoins the following processing
tendencies: (a) the tendency to adhere to Gricean conversational
principles even in situations that lack many conversational features
(Adler, 1984; Hilton, 1995); (b) the tendency to contextualize a
problem with as much prior knowledge as is easily accessible, even
when the problem is formal and the only solution is a content-free
rule (Evans, 1982, 1989; Evans, Barston, & Pollard, 1983); (c) the
tendency to see design and pattern in situations that are either
undesigned, unpatterned, or random (Levinson, 1995); (d) the tendency
to reason enthymematically--to make assumptions not stated in a
problem and then reason from those assumptions (Henle, 1962; Rescher,
1988); (e) the tendency toward a narrative mode of thought (Bruner,
1986, 1990). All of these properties conjoined together represent a
cognitive tendency toward radical contextualization. The bias is
termed fundamental because it is thought to stem largely from System 1
and that system is assumed to be primary in that it permeates
virtually all of our thinking (e.g., Evans & Over, 1996). If the
properties of this system are not to be the dominant factors in our
thinking, then they must be overridden by System 2 processes so that
the latter can carry out one of their important functions of
abstracting complex situations into canonical representations that are
stripped of context. Thus, it is likely that one computational task of
System 2 is to decouple (see Navon, 1989a, 1989b) contextual features
automatically supplied by System 1 when they are potentially
interfering.

In short, one of the functions of System 2 is to serve as an override
system (see Pollock, 1991) for some of the automatic and obligatory
computational results provided by System 1 . This override function
might only be needed in a tiny minority of information processing
situations (in most cases, the two Systems will interact in concert),
but they may be unusually important ones. For example, numerous
theorists have warned about a possible mismatch between the
fundamental computational bias and the processing requirements of many
tasks in a technological society containing many symbolic artifacts
and often requiring skills of abstraction (Adler, 1984, 1991;
Donaldson, 1978, 1993). Hilton (1995) warns that the default
assumption that Gricean conversational principles are operative may be
wrong for many technical settings because "many reasoning heuristics
may have evolved because they are adaptive in contexts of social
interaction. For example, the expectation that errors of
interpretation will be quickly repaired may be correct when we are
interacting with a human being but incorrect when managing a complex
system such as an aircraft, a nuclear power plant, or an economy. The
evolutionary adaptiveness of such an expectation to a conversational
setting may explain why people are so bad at dealing with lagged
feedback in other settings" (p. 267).

Concerns about the real-world implications of the failure to engage in
necessary cognitive abstraction (see Adler, 1984) were what led Luria
(1976) to warn against minimizing the importance of decontextualizing
thinking styles. In discussing the syllogism, he notes that "a
considerable proportion of our intellectual operations involve such
verbal and logical systems; they comprise the basic network of codes
along which the connections in discursive human thought are channeled"
(p. 101). Likewise, regarding the subtle distinctions on many
decontextualized language tasks, Olson (1986) has argued that "the
distinctions on which such questions are based are extremely important
to many forms of intellectual activity in a literate society. It is
easy to show that sensitivity to the subtleties of language are
crucial to some undertakings. A person who does not clearly see the
difference between an expression of intention and a promise or between
a mistake and an accident, or between a falsehood and a lie, should
avoid a legal career or, for that matter, a theological one" (p. 341).
Objective measures of the requirements for cognitive abstraction have
been increasing across most job categories in technological societies
throughout the past several decades (Gottfredson, 1997). This is why
measures of the ability to deal with abstraction remains the best
employment predictor and the best earnings predictor in postindustrial
societies (Brody, 1997; Gottfredson, 1997; Hunt, 1995).

Einhorn and Hogarth (1981) highlighted the importance of
decontextualized environments in their discussion of the optimistic
(Panglossian/Apologist) and pessimistic (Meliorist) views of the
cognitive biases revealed in laboratory experimentation. They noted
that "the most optimistic asserts that biases are limited to
laboratory situations which are unrepresentative of the natural
ecology" (p. 82), but they go on to caution that "in a rapidly
changing world it is unclear what the relevant natural ecology will
be. Thus, although the laboratory may be an unfamiliar environment,
lack of ability to perform well in unfamiliar situations takes on
added importance" (p. 82). There is a caution in this comment for
critics of the abstract content of most laboratory tasks and
standardized tests. The issue is that, ironically, the argument that
the laboratory tasks and tests are not like "real life" is becoming
less and less true. "Life," in fact, is becoming more like the tests!

The cognitive ecologists have, nevertheless, contributed greatly in
the area of remediation methods for our cognitive deficiencies (Brase
et al., 1998; Cosmides & Tooby, 1996; Fiedler, 1988; Gigerenzer &
Hoffrage, 1995; Sedlmeier, 1997). Their approach is, however, somewhat
different from that of the Meliorists. The ecologists concentrate on
shaping the environment (changing the stimuli presented to subjects)
so that the same evolutionarily adapted mechanisms that fail the
standard of normative rationality under one framing of the problem
give the normative response under an alternative (e.g., frequentistic)
version. Their emphasis on environmental alteration provides a
much-needed counterpoint to the Meliorist emphasis on cognitive
change. The latter, with their emphasis on reforming human thinking,
no doubt miss opportunities to shape the environment so that it fits
the representations that our brains are best evolved to deal with.
Investigators framing cognition within a Meliorist perspective are
often blind to the fact that there may be remarkably efficient
mechanisms available in the brain--if only it was provided with the
right type of representation.

On the other hand, it is not always the case that the world will let
us deal with representations that are optimally suited to our
evolutionarily designed cognitive mechanisms. For example, in a series
of elegant experiments, Gigerenzer, Hoffrage, and Kleinbolting (1991)
have shown how at least part of the overconfidence effect in knowledge
calibration studies is due to the unrepresentative stimuli used in
such experiments--stimuli that do not match the subjects' stored cue
validities which are optimally tuned to the environment. But there are
many instances in real-life when we are suddenly placed in
environments where the cue validities have changed. Metacognitive
awareness of such situations (a System 2 activity) and strategies for
suppressing incorrect confidence judgments generated by the responses
to cues automatically generated by System 1 will be crucial here.
Every high school musician who aspires to a career in music has to
recalibrate when they arrive at university and encounter large numbers
of talented musicians for the first time. If they persist in their old
confidence judgments they may not change majors when they should. Many
real-life situations where accomplishment yields a new environment
with even more stringent performance requirements share this logic.
Each time we "ratchet up" in the competitive environment of a
capitalist economy we are in a situation just like the overconfidence
knowledge calibration experiments with their unrepresentative
materials (Frank & Cook, 1995). It is important to have learned System
2 strategies that will temper one's overconfidence in such situations
(Koriat, Lichtenstein, & Fischhoff, 1980).


7. Individual Differences and the Normative/Descriptive Gap

In our research program, we have attempted to demonstrate that a
consideration of individual differences in the heuristics and biases
literature may have implications for debates about the cause of the
gap between normative models and descriptive models of actual
performance. Patterns of individual differences have implications for
arguments that all such gaps reflect merely performance errors.
Individual differences are also directly relevant to theories that
algorithmic-level limitations prevent the computation of the normative
response in a system that would otherwise compute it. The wrong norm
and alternative construal explanations of the gap involve many
additional complications but, at the very least, patterns of
individual differences might serve as "intuition pumps" (Dennett,
1980) and alter our reflective equilibrium regarding the plausibility
of such explanations (Stanovich, 1999).

Different outcomes occurred across the wide range of tasks we have
examined in our research program. Of course, all the tasks had some
unreliable variance and thus some responses that deviated from the
response considered normative could easily be considered as
performance errors. But not all deviations could be so explained.
Several tasks (e.g., syllogistic reasoning with interfering content,
four-card selection task) were characterized by heavy computational
loads that made the normative response not prescriptive for some
subjects--but these were usually few in number^13. Finally, a few
tasks yielded patterns of covariance that served to raise doubts about
the normative models applied to them and/or the task construals
assumed by the problem inventors (e.g., several noncausal baserate
items, false consensus effect).

Although many normative/descriptive gaps could be reduced by these
mechanisms, not all of the discrepancies could be explained by factors
that do not bring human rationality into question. Algorithmic-level
limitations were far from absolute. The magnitude of the associations
with cognitive ability left much room for the possibility that the
remaining reliable variance might indicate that there are systematic
irrationalities in intentional-level psychology. A heretofore
unmentioned component of our research program produced data consistent
with this possibility. Specifically, it was not the case that once
capacity limitations had been controlled, that the remaining
variations from normative responding were unpredictable (which would
have indicated that the residual variance consisted largely of
performance errors). In several studies, we have shown that there was
significant covariance among the scores from a variety of tasks in the
heuristics and biases literature after they had been residualized on
measures of cognitive ability (Stanovich, 1999). The residual variance
(after partialling cognitive ability) was also systematically
associated with questionnaire responses that were conceptualized as
intentional-level styles relating to epistemic regulation (Sá, West, &
Stanovich, 1999; Stanovich & West, 1997, 1998c). Both of these
findings are indications that the residual variance is systematic.
They falsify models that attempt to explain the normative/descriptive
gap entirely in terms of computational limitations and random
performance errors. Instead, the findings support the notion that the
normative/descriptive discrepancies that remain after computational
limitations have been accounted for reflect a systematically
suboptimal intentional-level psychology.

One of the purposes of the present research program is to reverse the
figure and ground in the rationality debate, which has tended to be
dominated by the particular way that philosophers frame the
competence/performance distinction. For example, Cohen (1982) argues
that there really are only two factors affecting performance on
rational thinking tasks: "normatively correct mechanisms on the one
side, and adventitious causes of error on the other" (p. 252). Not
surprisingly given such a conceptualization, the processes
contributing to error ("adventitious causes") are of little interest
to Cohen (1981, 1982). But from a psychological standpoint, there may
be important implications in precisely the aspects of performance that
have been backgrounded in this controversy ("adventitious causes").
For example, Johnson-Laird and Byrne (1993) articulate a view of
rational thought that parses the competence/performance distinction
much differently from that of Cohen (1981, 1982, 1986) and that
simultaneously leaves room for systematically varying cognitive styles
to play a more important role in theories of rational thought. At the
heart of the rational competence that Johnson-Laird and Byrne (1993)
attribute to humans is not perfect rationality but instead just one
meta-principle: People are programmed to accept inferences as valid
provided that they have constructed no mental model of the premises
that contradict the inference. Inferences are categorized as false
when a mental model is discovered that is contradictory. However, the
search for contradictory models is "not governed by any systematic or
comprehensive principles" (p. 178).

The key point in Johnson-Laird and Byrne's (1993; see Johnson-Laird,
1999; Johnson-Laird & Byrne, 1991) account^14 is that once an
individual constructs a mental model from the premises, once the
individual draws a new conclusion from the model, and once the
individual begins the search for an alternative model of the premises
which contradicts the conclusion, the individual "lacks any systematic
method to make this search for counter-examples" (p. 205; see
Bucciarelli & Johnson-Laird, in press). Here is where Johnson-Laird
and Byrne's (1993) model could be modified to allow for the influence
of thinking styles in ways that the impeccable competence view of
Cohen (1981, 1982) does not. In this passage, Johnson-Laird and Byrne
seem to be arguing that there are no systematic control features of
the search process. But styles of epistemic regulation (Sá et al.,
1999; Stanovich & West, 1997) may in fact be reflecting just such
control features. Individual differences in the extensiveness of the
search for contradictory models could arise from a variety of
cognitive factors that, although they may not be completely
systematic, may be far from "adventitious" (see Johnson-Laird &
Oatley, 1992; Oatley, 1992; Overton, 1985, 1990)--factors such as
dispositions toward premature closure, cognitive confidence,
reflectivity, dispositions toward confirmation bias, ideational
generativity, etc.

Dennett (1988) argues that we use the intentional stance for humans
and dogs but not for lecterns because for the latter "there is no
predictive leverage gained by adopting the intentional stance" (p.
496). In the experiments just mentioned (Sá et al., 1999; Stanovich &
West, 1997, 1998c), it has been shown that there is additional
predictive leverage to be gained by relaxing the idealized rationality
assumption of Dennett's (1987, 1988) intentional stance and by
positing measurable and systematic variation in intentional-level
psychologies. Knowledge about such individual differences in people's
intentional-level psychologies can be used to predict variance in the
normative/descriptive gap displayed on many reasoning tasks.
Consistent with the Meliorist conclusion that there can be individual
differences in human rationality, our results show that there is
variability in reasoning that cannot be accommodated within a model of
perfect rational competence operating in the presence of performance
errors and computational limitations.


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   _________________________________________________________________

Footnotes

^1 Individual differences on tasks in the heuristics and biases
literature have been examined previously by investigators such as Hoch
and Tschirgi (1985), Jepson, Krantz, and Nisbett, (1983), Rips and
Conrad (1983), Slugoski and Wilson (1998), and Yates, Lee, and
Shinotsuka (1996). Our focus here is the examination of individual
differences through a particular metatheoretical lens--as providing
principled constraints on alternative explanations for the
normative/descriptive gap.

^2 All of the work cited here was conducted within Western cultures
which matched the context of the tests. Of course, we recognize the
inapplicability of such measures as indicators of cognitive ability in
cultures other than those within which the tests were derived (Ceci,
1996; Greenfield, 1997; Scribner & Cole, 1981). Nevertheless, it is
conceded by even those supporting more contextualist views of
intelligence (e.g., Sternberg, 1985; Sternberg & Gardner, 1982) that
measures of general intelligence do identify individuals with superior
reasoning ability--reasoning ability that is then applied to problems
that may have a good degree of cultural specificity (see Sternberg,
1997; Sternberg & Kaufman, 1998).

^3 The Scholastic Aptitude Test is a three-hour paper-and-pencil exam
used for university admissions testing. The verbal section of the SAT
test contains four types of items: antonyms, reading comprehension,
verbal analogies, and sentence completion items in which the examinee
chooses words or phrases to fill in a blank or blanks in a sentence.
The mathematical section contains "varied items chiefly requiring
quantitative reasoning and inductive ability" (Carroll, 1993, p. 705).

^4 We note that the practice of analyzing a single score from such
ability measures does not imply the denial of the existence of
second-order factors in a hierarchical model of intelligence. However,
theorists from a variety of persuasions (Carroll, 1993, 1997; Hunt,
1997; Snyderman & Rothman, 1990; Sternberg & Gardner, 1982; Sternberg
& Kaufman, 1998) acknowledge that the second order factors are
correlated. Thus, such second-order factors are not properly
interpreted as separate faculties (despite the popularity of such
colloquial interpretations of so-called "multiple intelligences"). In
the most comprehensive survey of intelligence researchers, Snyderman
and Rothman (1990) found that by a margin of 58% to 13%, the surveyed
experts endorsed a model of "a general intelligence factor with
subsidiary group factors" over a "separate faculties" model.
Throughout this target article we utilize a single score which loads
highly on the general factor, but analyses which separated out group
factors (Stratum II in Carroll's widely accepted model based on his
analysis of 460 data sets, see Carroll, 1993) would reveal convergent
trends.

^5 Positive correlations with developmental maturity (e.g., Byrnes &
Overton, 1986; Jacobs & Potenza, 1991; Klahr, Fay, & Dunbar, 1993;
Markovits & Vachon, 1989; Moshman & Franks, 1986) would seem to have
the same implication.

^6 However, we have found (Stanovich & West, 1999) that the patterns
of individual differences reversed somewhat when the potentially
confusing term "false positive rate" was removed from the problem (see
Cosmides & Tooby, 1996 for work on the effect of this factor). It is
thus possible that this term was contributing to an incorrect
construal of the problem (see Section [18]5).

^7 However, sometimes alternative construals might be computational
escape hatches (Stanovich, 1999). That is, an alternative construal
might be hiding an inability to compute the normative model. Thus, for
example, in the selection task, perhaps some people represent the task
as an inductive problem of optimal data sampling in the manner that
Oaksford and Chater (1994, 1996) have outlined because of the
difficulty of solving the problem if interpreted deductively. As
O'Brien (1995) demonstrates, the abstract selection task is a very
hard problem for a mental logic without direct access to the truth
table for the material conditional. Likewise, Johnson-Laird and Byrne
(1991) have shown that tasks requiring the generation of
counter-examples are difficult unless the subject is primed to do so.

^8 The results with respect to the framing problems studied by Frisch
(1993) do not always go in this direction. See Stanovich and West
(1998b) for examples of framing problems where the more cognitively
able subjects are not less likely to display framing effects.

^9 Kahneman and Tversky (1982) themselves (pp. 132-135) were among the
first to discuss the issue of conversational implicatures in the tasks
employed in the heuristics and biases research program.

^10 Of course, another way that cognitive ability differences might be
observed is if the task engages only System 2. For the present
discussion, this is an uninteresting case.

^11 It should be noted that the distinction between normative and
evolutionary rationality used here is different from the distinction
between rationality[1] and rationality[2 ]utilized by Evans and Over
(1996). They define rationality[1] as reasoning and acting "in a way
that is generally reliable and efficient for achieving one's goals"
(p. 8). Rationality[2] concerns reasoning and acting "when one has a
reason for what one does sanctioned by a normative theory" (p. 8).
Because normative theories concern goals at the personal level, not
the genetic level, both of the rationalities defined by Evans and Over
(1996) fall within what has been termed here normative rationality.
Both concern goals at the personal level. Evans and Over (1996) wish
to distinguish the explicit (i.e., conscious) following of a normative
rule (rationality[2]) from the largely unconscious processes "that do
much to help them achieve their ordinary goals" (p. 9). Their
distinction is between two sets of algorithmic mechanisms that can
both serve normative rationality. The distinction we draw is in terms
of levels of optimization (at the level of the replicator itself--the
gene--or the level of the vehicle); whereas theirs is in terms of the
mechanism used to pursue personal goals (mechanisms of conscious,
reason-based rule following versus tacit heuristics).

It should also be noted that, for the purposes of our discussion here,
the term evolutionary rationality has less confusing connotations than
the term 'adaptive rationality' discussed by Oaksford and Chater
(1998). The latter could potentially blur precisely the distinction
stressed here--that between behavior resulting from adaptations in
service of the genes and behavior serving the organism's current
goals.

^12 Evidence for this assumption comes from voluminous data indicating
that analytic intelligence is related to the very type of outcomes
that normative rationality would be expected to maximize. For example,
the System 2 processes that collectively comprise the construct of
cognitive ability are moderately and reliably correlated with job
success and with the avoidance of harmful behaviors (Brody, 1997;
Lubinski & Humphreys, 1997; Gottfredson, 1997).

^13 Even on tasks with clear computational limitations, some subjects
from the lowest strata of cognitive ability solved the problem.
Conversely, on virtually all the problems, some university subjects of
the highest cognitive ability failed to give the normative response.
Fully 55.6% of the university subjects who were at the 75%ile or above
in our sample in cognitive ability committed the conjunction fallacy
on the Linda problem. Fully 82.4% of the same group failed to solve a
nondeontic selection task problem.

^14 A reviewer has pointed out that the discussion here is not
necessarily tied to the mental models approach. The notion of
searching for counter-examples under the guidance of some sort of
control process is at the core of any implementation of logic.

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