Josiah Lopez-Wild

Expected utility theory seeks to define rational choice behavior. Given a collection of acts available to some decision maker, expected utility theorists commonly identify the “rational” act as the act which _maximizes expected utility_ (where the expectation is taken with respect to some probability measure). The mathematical core of expected utility theory is a representation theorem. These theorems link expected utility maximization to a qualitative description of an agent’s choice behavior, captured in a preference relation. We say that an agent’s preferences are _represented_ by a utility function and/or probability measure which is derived from the representation theorem. Representation theorems only prove that such a function exists, but do not show how to find it. Thus one may ask: given an agent’s preference relation, when can we compute a representing utility function? In this paper I prove a computable version of the von Neumann-Morgenstern representation theorem, answering this question in the affirmative.