Stochastic Dominance for Incomplete Preferences

Abstract According to Stochastic Dominance, it is rationally obligatory to prefer one gamble to another if it gives you the same chances of getting final outcomes you prefer. According to Statewise Maximality, it is rationally permissible not to disprefer a gamble if it is guaranteed not to result in a final outcome you disprefer. These principles conflict in cases involving incomplete preferences, known as Opaque Sweetening cases. In this paper, we argue for Stochastic Dominance and against Statewise Maximality in Opaque Sweetening cases. First, we rebut two standard arguments for statewise maximality, which we call the Argument from Full Information and the Argument from the Primacy of Final Outcomes. We then provide an argument for the verdict of Stochastic Dominance in Opaque Sweetening cases. This argument appeals to the principle of Transitivity, the Sure-Thing Principle, and the claim that stochastic reasoning is appropriate at least for choices which do not involve incomparability.