SMU SOE Seminar (Apr 5, 2018): Representativeness and Similiarity

We provide a framework for analyzing a range of well-documented non-Bayesian behaviors including base rate neglect, conjunction fallacy and disjunction fallacy. The model that we propose formally links the concept of similarity in theoretical psychology with belief updating. We follow Kahneman and Tversky (1974) and assume that when attempting to respond to the question “how likely is A given B”, people mistakenly respond to the question “how similar are A to B”. With a similarity-based updating rule the posterior of A ∪ C given B may be less than the posterior of A given B, simply because A ∪ C differs more from B than A does when B ∩ C = Ø. Our axioms yield a Cobb-Douglas weighted geometric mean of μ(A|B) and μ(B|A) as the behavioral conditional probability of A given B, where μ is the correct subjective probability and μ(·|·) is the Bayesian conditional of μ. That is, our decision makers confuse these two conditional probabilities but have correct unconditional beliefs. This combination of correct priors and incorrect updating occurs often since in many experiments subjects are explicitly given the relevant prior probabilities.

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