Probabilistic Choice and Stochastic Dominance

Abstract

This paper presents an axiomatic model of probabilistic choice under risk. In this model, when it comes to choosing one lottery over another, each alternative has a chance of being selected, unless one lottery stochastically dominates the other. An individual behaves as if he compares lotteries to a reference lottery - a least upper bound or a greatest lower bound in terms of weak dominance. The proposed model is compatible with several well-known violations of expected utility theory such as the common ratio effect and the violations of the betweenness. Necessary and sufficient conditions for the proposed model are completeness, weak stochastic transitivity, continuity, common consequence independence, outcome monotonicity, and odds ratio independence.