A utility representation theorem in economics shows that, under certain conditions on a preference ordering, that ordering can be represented by a real-valued utility function, so that one option is preferred to another exactly when its utility number is larger. This lets a decision-maker's entire preference structure be captured by a single function rather than a full list of pairwise comparisons, though not every preference relation admits such a representation. The best-known instance is the Von Neumann-Morgenstern utility theorem, which shows that a rational agent's preferences over lotteries can always be represented by a utility function of this kind.
Facts
StatementUnder certain conditions, a preference ordering can be represented by a real-valued utility function, such that option A is preferred to option B if and only if the utility of A is larger than that of B. 1 Classification
Statement Form Statement FormCharacterization Theorem 1 Connections
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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.
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. Utility representation theorem - Wikipedia
Introduction, sentence 1Quote, Introduction, sentence 1
under certain conditions, a preference ordering can be represented by a real-valued utility function
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