The Conjunction Effect: Fallacy or Bayesian Inference?

Abstract It has been suggested by Wolford, Taylor, and Beck (1990) that the conjunction fallacy is not really a fallacy at all but arises when individuals misconstrue the judgmental problem providing estimates of the kind P(X|A&B) or P(X|B) (reverse probabilities) instead of the actual quantities that are being sought by the experimenter: P(A&B|X) or P(B|X). As pointed out by Wolford and co-workers, while the following judgment, P(A&B|X) > P(B|X), is a violation of the conjunction rule, outcomes such as P(X|A&B) > P(X|B) do not necessarily violate any probabilistic law. In an attempt to de-bias the judgment process, in Study 1 participants were requested to provide both types of probabilities at the same time. The results revealed a drop in the incidence of the conjunction fallacy to 32% averaged over all scenarios compared with 57% for the same scenarios in an earlier study. In each scenario the two sets of estimates, normal and reverse, were significantly different from each other indicating that participants were capable of distinguishing between the two concepts. Despite this fact in two of the four scenarios a significant minority of participants (44 and 49%) continued to commit the fallacy. These combined outcomes cast doubt on Wolfordet al.’s (1990) account of the fallacy. In addition, Studies 2 and 3 showed that under certain conditions, most participants’ judgments of the kind P(X|A&B) > P(X|B), far from being normative, were inconsistent with Bayes’ theorem even in broad terms.