Economic Comparisons of Alternative Theories of Stochastic Dominance

The theory of stochastic dominance applied to financial decisions associates classes of investors with classes of gambles (random payoffs). Each investor resides in a class of mixed risk averters (MRA). Pairs of gambles, say, X and Y are classified according to a collection of mathematical inequalities on moments and integrals of distribution functions. This paper represents these inequalities as statements of preference by a subset of investors B with parametric utility functions, B⊂MRA, where B is a basis for the entire class MRA; gamble X stochastically dominates Y if and only if the basis members unanimously prefer X over Y. We use this representation to compare stochastic dominance to an alternative theory that appears in literature on social welfare, and that relies solely on the distributional inequalities. Our results caution those who might use the test statistics developed for the alternative theory in their studies of financial data