The von Neumann-Morgenstern utility theorem is a foundational result in decision theory showing that rational choice under uncertainty can always be described as maximizing the expected value of a numerical utility function. Proved by John von Neumann and Oskar Morgenstern in 1947, the theorem shows that if an individual preferences over uncertain outcomes satisfy four specific axioms, then there exists a real valued utility function such that the individual preferences are fully captured by maximizing its expected value. The theorem does not claim that a person consciously sets out to maximize this function, only that a rational person choices are equivalent to acting as though they were maximizing it, and the resulting utility function is unique up to adding a constant and multiplying by a positive number. The theorem forms the mathematical foundation of expected utility theory, widely used throughout economics and game theory to model decisions made under risk.
Facts
StatementAny individual whose preferences satisfy four axioms has a utility function whose expected value the individual's choices maximize. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Von Neumann-Morgenstern utility theorem (Wikipedia)
Introduction, statement of the theorem
In 1947, John von Neumann and Oskar Morgenstern proved that any individual whose preferences satisfied four axioms has a utility function.
Introduction, year of proof
In 1947, John von Neumann and Oskar Morgenstern proved that any individual whose preferences satisfied four axioms has a utility function.
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.