Conditions for Expected Utility Maximization: The Finite Case

Abstract

A decision is a mapping from states of nature to consequences. Given a utility $u$ on the set of consequences and a measure $\nu$ on the set of states, the expected utility of a decision $f$ is $\int u(f(e)) d\nu(e)$. By the "expected utility hypothesis" on a set of choices made by an individual we mean that there exists a utility and a measure such that the individual always chooses the decision of highest expected utility. We present a set of necessary and sufficient conditions that a set of choices between two decisions be consistent with the expected utility hypothesis. We assume the set of states and the set of consequences to be finite and we do not assume the ordering, given by the choices, to be complete. Our conditions require the individual to make new choices, between decisions which involve repetitions of states, in a consistent way. There are finitely many new choices and they do not involve utility.