A note on superadditive probability judgment.

Abstract

Recent studies have demonstrated subadditivity of human probability judgment: The judged probabilities for an event partition sum to more than 1. We report conditions under which people's probability judgments are superadditive instead: The component judgments for a partition sum to less than 1. Both directions of deviation from additivity are interpreted in a common framework, in which probability judgments are often mediated by judgments of evidence. The 2 kinds of nonadditivity result from differences in recruitment of supporting evidence together with reduced processing of nonfocal propositions. Suppose that an event, E, has been partitioned into two or more mutually exclusive subevents and that probability assessments are made for E and for each of these subevents. The assessments are said to be additive if the probability assigned to E is approximately equal to the sum of the probabilities of the subevents. They are subadditive if the probability assigned to E falls short of the subevent sum, and they are superadditive if the assignment to E exceeds the subevent sum. Superadditivity is a feature of Shafer's theory of evidence (Shafer, 1976) and has been found previously for evidence judgments (Briggs & Krantz, 1992) but not for probability judgments. Subadditive probability judgment has been widely reported in the literature and helped to motivate Support Theory (Rottenstreich & Tversky, 1997; Tversky & Koehler, 1994). The purpose of the present article is to document the existence of superadditive probability judgment in special conditions. Our findings suggest modifications of Support Theory. Tversky and colleagues (Rottenstreich & Tversky, 1997; Tversky & Koehler, 1994) pointed out that subadditivity is common in both nonexpert and expert probability judgments. In a dramatic example (Redelmeier, Koehler, Liberman, & Tversky, 1995), physicians were asked to provide probabilities for the following events, with respect to a particular hospitalized patient whose case had been summarized to them: