Binary Regret for Statistically Dependent Risks

Abstract

Unlike the traditional normative decision theories under risk, we are concerned with a unary relation, interpreted as subjective acceptability judgment, on the set of all joint probability distributions over two-attributed decision outcomes, where the first attribute describes final wealth levels the chosen alternative may yield and the second foregone wealth levels which may be given by the abandoned alternative. We show axioms of the unary relation for the existence of a general binary regret model. Then, we develop and provide two axiomatic characterizations of a simple regret model which additively separates expected intrinsic-utility and regret-rejoicing scale. Our model generalizes Bell's and Loomes and Sugden's classical simple regret model.