Expected Scott-Suppes utility representation

We provide an axiomatic characterization for an expected Scott-Suppes utility representation. Such a characterization is the natural analog of the von Neumann-Morgenstern expected utility theorem for semiorders and it is noted as an open problem by Fishburn (1968). Expected Scott-Suppes utility representation is analytically tractable and can be used in applications that study preferences with intransitive indifference under uncertainty. Our representation offers a decision-theoretical interpretation for epsilon equilibrium as well.