Revisiting Almost Second-Degree Stochastic Dominance
指出Leshno和Levy关于几乎二阶随机占优的主要定理存在反例，重新定义了该条件，证明新定义是排除病态凹偏好后所有决策者排序分布的必要充分条件，并推广到高阶占优。
Leshno and Levy [Leshno M, Levy H (2002) Preferred by “all” and preferred by “most” decision makers: Almost stochastic dominance. Management Sci. 48(8):1074–1085] established almost stochastic dominance to reveal preferences for most rather than all decision makers with an increasing and concave utility function. In this paper, we first provide a counterexample to the main theorem of Leshno and Levy related to almost second-degree stochastic dominance. We then redefine this dominance condition and show that the newly defined almost second-degree stochastic dominance is the necessary and sufficient condition to rank distributions for all decision makers excluding the pathological concave preferences. We further extend our results to almost higher-degree stochastic dominance. This paper was accepted by Peter Wakker, decision analysis.