Mixture independence foundations for expected utility
将冯·诺依曼-摩根斯坦独立性公理分解为四个逻辑独立的性质，结合完备性、传递性和连续性，为期望效用提供了新的偏好基础。
An alternative preference foundation for expected utility is provided. Our segregated approach considers four logically independent implications of the classic von Neumann-Morgenstern independence axiom. The monotonicity principle is, for a transitive relation, equivalent to monotonicity with respect to first-order stochastic dominance. Rank-dependent separability is similar to the comonotonic sure-thing principle used in the ambiguity literature. The remaining two properties are weak formulations of the independence principle which invoke the latter only for probability mixtures with the extreme, that is the best, respectively, the worst outcome. These four implications of independence, together with completeness, transitivity and continuity of a preference relation, characterize expected utility. Furthermore, if rank-dependent separability is dropped, expected utility still holds on each subset of three-outcomes lotteries that give positive probability to both the best and the worst outcomes.