Stochastic dominance, regret dominance and regret-theoretic dominance

It is well known that stochastic dominance alone is insufficient for ensuring preferences when individuals experience regret. In this paper, we study two additional notions of dominance: (a) regret-theoretic dominance, which characterizes preferences in regret theory and (b) regret dominance, which characterizes preferences in mean-risk models with regret-based risk measures. We (a) extend our understanding of preferences in regret theory to problems with multiple choices under an infinite number of scenarios, (b) highlight that some notions of regret in the normative literature, specifically relative regret, can lead to unreasonable preferences within a mean-risk framework and (c) illustrate how regret dominance can help reduce the size of conventional efficient sets. Conditions where stochastic dominance, regret dominance and regret-theoretic dominance are equivalent are also presented.