Revisiting Almost Second‐Degree Stochastic Dominance

Leshno and Levy (2002) 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.