A computable von Neumann-Morgenstern representation theorem. - Lopez-Wild, Josiah (Synthese, 2025)
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.