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.
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StatementAny individual whose preferences satisfy four axioms has a utility function whose expected value the individual's choices maximize. 1 Classification
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Source Von Neumann-Morgenstern utility theorem (Wikipedia)
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Source Von Neumann-Morgenstern utility theorem (Wikipedia)
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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.
In Branch: Game Theory, Lead
In decision theory, the von Neumann-Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function.
Proved By: John von Neumann, Lead
In 1947, John von Neumann and Oskar Morgenstern proved that any individual whose preferences satisfied four axioms has a utility function, where such an individual's preferences can be represented on an interval scale and the individual will always prefer actions that maximize expected utility.
In Group: Decision Theory and Utility, Lead paragraph
In decision theory, the von Neumann-Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function.
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