Ellsberg Revisited: A New Look at Comparative Probability

摘要: Suppose you are given the opportunity of guessing whether it will snow or not in Chicago next Christmas. If guess correctly, win $1,000; if not, nothing. Which event, no snow, would bet on? It is widely accepted among decision theorists that your answer reveals which two events deem more probable. Furthermore, choices over a field obey certain postulates coherency and consistency, then there probability measure P on reflects choices: regard A as probable than B if, only P(A) > P(B). Numerous experiments have shown people often'violate those postulates, so they lack full descriptive validity. Moreover, because systematic persistent violations one postulates-an independence axiomthe theory has been questioned its normative adequacy guide to wellreasoned judgments choices. The purpose present paper examine weaker set avoids axiom well usual assumption fully transitive preferences. Despite this weakening, assumptions imply unique normalized functional p pairs preserves sense p(A, B) 0. several nice mathematical properties, including "conditional additivity," reflect vestiges numerical probability, related conventional by = P(B) when omitted coupled other postulates.