REALITY OF THE CONJUNCTION FALLACY
197
Item 2 attracted 46 fallacies out of 83 participants.Thirty-
Maintainingcoherenceis computationallydifficultin the
nineparticipantscommittedtheconjunctionfallacy on just sense of requiring resources that grow rapidly as a function
one of the two items. Of this group, 32 participants com- of the structural complexity of the judgments in play (see
mitted it for Item 2, and only 7 participants committed it Georgakopoulos,Kavvadias, & Papadimitriou,1988). The
for Item 1.
noteworthyfeature of human judgment,however, is that in-
Experiment 4 induced numerous violationsof the con- coherence strikes even in simple cases, such as comparing
X
Y X
and . Why are we so disinclined to
junction principle. Choice among bets was the depen- the chances of
probability
`
dent variable with no mention of
, so the fal- coordinateprobabilitywith logical structure?
lacy is not likely to result from nonmodern interpretation
One reason might be the separation of neural loci for
of the probability idiom. Moreover, the instruction to the evaluation of logical implication versus empirical
leave only one choice legible for an independent judge plausibility. These two mental activitiesinduce metabolic
can be expected to cancel any pragmatic tendency to in- activity in opposite hemispheres connected by axon bun-
X
X
Y
terpret as ` ¬ . Finally, the fallacy rate was virtu- dles of relativelynarrow bandwidth(for neuroimagingev-
ally the same in the explicitand implicit conditions, sug- idence, see Osherson et al., 1998, and Parsons & Osher-
gesting that the conjunction fallacy does not depend son, 2001). Coordinating assessments of chance with the
and
narrowly on use of
to express conjunction.
DISCUSSION
Faced with evidence of fallacious reasoning about sin-
logical forms of statements may not be facilitated by this
cognitive architecture.
REFERENCES
gle events, some psychologistsdeny that there is anything Bar-Hillel,M. (1991). Commentary on Wolford, Taylor, and Beck: The
conjunction fallacy? Memory & Cognition, 19, 412-414.
Bar-Hillel, M., & Neter, E. (1993). How alike it is versus how likely
it is: A disjunction fallacy in probability judgments. Journal of Per-
sonality & Social Psychology, 65, 1119-1131.
counternormative in attributing greater chance to a con-
junction of such events than to one of the conjuncts
(Gigerenzer, 1991;Gigerenzer, Hoffrage, & Kleinbolting,
chance
1991). Puttingasidesemanticissuesabouttheword
,
Dawes, R., Mirels, H. L., Gold, E., & Donahue, E. (1993). Equating
inverse probabilitiesin implicit personality judgments. Psychological
Science, 4, 396-400.
Dulany, D. E., & Hilton, D. J. (1991). Conversational implicature, con-
scious representation, and the conjunction fallacy. Social Cognition,
9, 85-110.
Earman, J. (1992). Bayes or Bust? Cambridge, MA: MIT Press.
Fiedler,K. (1988). The dependence of the conjunctionfallacy on subtle
linguistic factors. Psychological Research, 50, 123-129.
Fitelson, B. (1999). The plurality of Bayesian measures of confirmation
and the problem of measure sensitivity. Philosophy of Science, 66,
S362-S378.
Georgakopoulos, G., Kavvadias, D., & Papadimitriou, C. (1988).
Probabilistic satisfiability. Journal of Complexity, 4, 1-11.
Gigerenzer, G. (1991). How to make cognitive illusions disappear:
Beyond “heuristics and biases.” In W. Storche & M. Hewstone,
(Eds.), European review of social psychology (Vol. 2, pp. 83-115).
New York: Wiley.
however, it is surely irrational to prefer a reward in case
X
Y
occurs, relative to receiving the
an event of form
`
X
same reward in case occurs (as observed in Kahneman
& Tversky, 1996). And just this pattern occured through-
out our four experiments.
Anotherdefenseof naive judgmentis the claimthat sub-
X
X
Y
X
jects often understand as ` ¬ in the context of `
Y
(Hilton, 1995). This interpretation is said to be consis-
tent with a cooperative attitude about discourse (Grice,
1975). Previous attempts to control for such variables (as
in Tversky & Kahneman, 1983) have been deemed insuf-
ficient. The procedure of Experiment4 will perhaps prove
more persuasive since it invokes a judge who must inter-
X
X
Y
pret outside of the frame provided by ` . Indeed, in-
Gigerenzer,G. (1996). Reply to Tversky and Kahneman. Psycholog-
ical Review, 103, 592-593.
X
X
ability to interpret as in these conditions would cast
doubt on people’s mastery of the very pragmatic princi-
ples used to defend their reasoning about probability.
The general issue brought into focus by the conjunction
problem is the extent to which reasoning about chance is
sensitive to the constraints imposedby the logicalstructure
Gigerenzer, G., Hoffrage, U., & Kleinbolting, H. (1991). Proba-
bilistic mental models: A Brunswikian theory of confidence. Psycho-
logical Review, 98, 506-528.
Grice, H. P. (1975). Logic and conversation. In P. Cole & J. Morgan
(Eds.), Syntax and semantics: Vol. 3. Speech acts (pp. 41-58). New
York: Academic Press.
probabilistic incoherence
of events. Insensitivity leads to
,
Hacking,I. (1975).The emergence ofprobability. Cambridge: Cambridge
and has been documented for events with various logical
structures (e.g., Dawes, Mirels, Gold, & Donahue, 1993;
Osherson, Lane, Hartley, & Batsell,2001). An easy demon-
stration is obtainedby asking one’s colleagueswhether it is
sensible to assign 30% probability to man reaching Mars
by 2020, 80% probability to a sustained economic down-
turn before 2010, and 5% probabilityto the conjunctionof
the two events. In our experience,most peoplefind nothing
objectionable to these estimates, yet they are probabilisti-
cally incoherent (see Neapolitan, 1990, p. 128). Note that
this case seems not to be open to pragmatic interpretation.
University Press.
Hertwig, R., & Chase, V. M. (1998). Many reasons or just one: How re-
sponse modeaffects reasoning in the conjunctionproblem. Thinking&
Reasoning, 4, 319-352.
Hertwig, R., & Gigerenzer, G. (1999). The “conjunction fallacy” re-
visited: How intelligent inferences look like reasoning errors. Journal
of Behavioral Decision Making, 12, 275-305.
Hilton, D. J. (1995).The social contextof reasoning: Conversationalin-
ference and rational judgment. Psychological Bulletin, 118, 248-271.
Horwich, P. (1982). Probabilityand evidence. Cambridge: Cambridge
University Press.
Howson,C., & Urbach,P. (1993).Scientific reasoning: TheBayesian ap-
proach. Chicago: Open Court.