Revisiting Almost Second-Degree Stochastic Dominance

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Abstract
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.

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