How probability theory explains the conjunction fallacy

Abstract

The conjunction fallacy occurs when people judge a conjunctive statement B-and-A to be more probable than a constituent B, in contrast to the law of probability that P(B∧A) cannot exceed P(B) or P(A). Researchers see this fallacy as demonstrating that people do not follow probability theory when judging conjunctive probability. This paper shows that the conjunction fallacy can be explained by the standard probability theory equation for conjunction if we assume random variation in the constituent probabilities used in that equation. The mathematical structure of this equation is such that random variation will be most likely to produce the fallacy when one constituent has high probability and the other low, when there is positive conditional support between the constituents, when there are two rather than three constituents, and when people rank probabilities rather than give numerical estimates. The conjunction fallacy has been found to occur most frequently in exactly these situations. © 2008 John Wiley & Sons, Ltd.