Absolute versus relative likelihood

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Fox, C. R., Levav, J. * In this paper we investigate how people construct absolute and relative likelihood judgments. We document systematic violations of two fundamental probability axioms that can occur when evidence for an event H and its complement not-H are stronger than evidence for another event L and its complement not-L. First, H is judged “more likely” than L, while L is assigned a higher probability than H, violating procedure invariance. Second, H is judged more likely than L, while not-H is also judged more likely than not-L, violating ordinal complementarity. We attribute these “belief reversals” to complement neglect—a tendency to underweight evidence for complementary events (i.e., not-H and not-L when H and L are focal)—in relative but not absolute likelihood judgment. To explain these belief reversals we advance the Contingent Weighting of Support (CWS) model that embeds support theory within the contingent weighting model, and derive conditions under which each type of belief reversal is expected to occur. We then fit this model to data in two experiments, and provide direct evidence of complement neglect in relative but not absolute likelihood judgment. We conclude with a discussion of additional forms of belief reversal and their implications concerning the construction of belief.

Fox, C. R., Levav, J. Absolute versus relative likelihood. Working Paper, UCLA Anderson School, Revise & Resubmit, Psychological Review.