A note on almost stochastic dominance

Both the expected-utility maximization and the hierarchy property are very important properties in stochastic dominance. For almost stochastic dominance, Leshno and Levy (2002) propose a definition and Tzeng et al. (2013) modified it to give another definition. This note provides more information on the two definitions. The former has the hierarchy property but not the expected-utility maximization, whereas the latter has the expected-utility maximization but not the hierarchy property.