Abstract
Leshno and Levy (2002) established almost stochastic dominance (ASD) to reveal a preference for most decision makers, but not for all of them.Although almost stochastic dominance is widely used to find the efficient investment sets,Tzeng et al. (2013) found that almost stochastic dominance established by Leshno and Levy (2002) does not have expected-utility maximization.Therefore, Tzeng et al. (2013) revised almost stochastic dominance.Almost stochastic dominance defined by Tzeng et al. (2013) has hierarchy property but not the expected-utility maximization. Therefore,we give a new definition for almost stochastic dominance and revised the utility function.The new almost stochastic dominance has both hierarchy property and the expected-utility maximization.We further provided the algorithm which let almost stochastic dominance can be executed in data analysis.