How alike is it versus how likely is it: A disjunction fallacy in probability judgments.

Abstract

One event cannot be more probable than another that includes it. Judging P(A & B) to be higher than P(A) has been caIled the conjunction fallacy- This study examined a disjullctioll fallaQ< Ss received brief case descriptions and ordered 7 categories according to 1 of 4 criteria: (a) probability of membership, (b) wiIlingness to bet on membership, (c) inclination to predict membership, and (d) suitability for membership. The list included nested pairs of categories (e.g., Brazil-South America). Ranking a category more probable than its superordinate, or betting on it rather than its superordinate, is fallacious. Prediction, however, may be guided by maximizing informativeness, and suitability need conform to no formal rule. Hence, for these 2 criteria, such a ranking pattern is not fallacious. Yet ranking of categories higher than their superordinates was equally common on all 4 criteria. The results support representativeness against alternative interpretations. The extension rule in probability theory states that if A is a subset ofB, then the probability of A cannot exceed that ofB. A special case of the extension rule is the conjunction rule, which states that the probability of A&B can exceed the probability of neither A nor B, since it is contained in both. Tversky and Kahneman (1983) demonstrated that, under certain circumstances, people predictably and systematically violate the conjunction rule. In one study, they gave subjects the fof ng description: lda is 31 years old, single, outspoken, and very bright. She maed in philosophy. As a student, she was deeply concerned with les of discrimination and social justice, and also participated in :i-nuclear demonstrations. (p. 297) This was followed by a list of eight possible outcomes, each describing possible activities of at the present time (her job, her interests, or both). Subjects were asked to rank order the outcomes by the probability that they describe Linda's current activities. Of the eight, one was representative of (Linda is active in the feminist movement), one was unrepresentative of (Linda is a bank teller), and one was a conjunction of these two (Linda is a bank teller and is active in the feminist movement). A large majority of the subjects (85%) rated the conjunctive outcome, Linda is a bank teller and is active in the feminist movement, more probable than Linda is a bank teller. This result was predicted from the representativeness hypothesis: Representativeness is an assessment of the degree of correspondence between a sample and a population, an instance and a category, an act and an actor or, more generally, between

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