Stochastic Dominance Without Transitive Preferences

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Abstract
Traditional definitions of stochastic dominance assume that the decision agent's preference-or-indifference relation on outcomes of risky decisions is transitive. This paper proposes a stochastic dominance relation for the comparison of risky decisions that is applicable to any complete and reflexive preference-or-indifference relation, or to any asymmetric preference relation. The new dominance relation possesses a number of intuitively desirable properties and is equivalent to the usual stochastic dominance relation when preferences are transitive.

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