Between First- and Second-Order Stochastic Dominance
构建了一阶到二阶随机占优之间的连续谱规则，适用于决策者既偏好更多又可能接受部分风险的情境，如存在目标或局部凸效用时，并通过实例展示其应用。
We develop a continuum of stochastic dominance rules, covering preferences from first- to second-order stochastic dominance. The motivation for such a continuum is that while decision makers have a preference for “more is better,” they are mostly risk averse but cannot assert that they would dislike any risk. For example, situations with targets, aspiration levels, and local convexities in induced utility functions in sequential decision problems may lead to preferences for some risks. We relate our continuum of stochastic dominance rules to utility classes, the corresponding integral conditions, and probability transfers and discuss the usefulness of these interpretations. Several examples involving, e.g., finite-crossing cumulative distribution functions, location-scale families, and induced utility, illustrate the implementation of the framework developed here. Finally, we extend our results to a combined order including convex (risk-taking) stochastic dominance. This paper was accepted by Manel Baucells, decision analysis.