Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of σ-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper the authors present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions the authors present sufficient conditions for the existence of a probability measure P with ∫fdC=∫fdP for all increasing functions f when C is a given capacity. Examples include n-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function.
