Transitive regret over statistically independent lotteries

Preferences may arise from regret, i.e., from comparisons with alternatives forgone by the decision maker. When each outcome in a random variable is compared with the parallel outcome in an alternative random variable, regret preferences are transitive iff they are expected utility. In this paper we show that when the choice set consists of pairwise statistically independent lotteries and the regret associated with each outcome is with respect to the entire alternative distribution, then transitive regret-based behavior is consistent with betweenness preferences and with a family of preferences that is characterized by a consistency property. Examples of consistent preferences include CARA, CRRA, and anticipated utility.