Stochastic Dominance Analysis Without the Independence Axiom

We characterize the consistency of a large class of nonexpected utility preferences (including mean‐variance preferences and prospect theory preferences) with stochastic orders (for example, stochastic dominances of different degrees). Our characterization rests on a novel decision theoretic result that provides a behavioral interpretation of the set of all derivatives of the functional representing the decision maker’s preferences. As an illustration, we consider in some detail prospect theory and choice‐acclimating preferences, two popular models of reference dependence under risk, and we show the incompatibility of loss aversion with prudence. This paper was accepted by James Smith, decision analysis.