Stochastic Choice and Expected Utility

Dagsvik (2008) has recently extended Debreu’s (1958) representation theorem for stochastic choice to the domain of lotteries. Dagsvik provides conditions under which there exists a linear utility function such that the probability of choosing one alternative over another is represented by the di¤erence in their utilities. We give an alternative, simpler proof of Dagsvik’s result. Our proof derives the result as an extension of the Expected Utility Theorem. We also replace Dagsvik’s two continuity axioms with a single alternative.