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 makers 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