utilitetsrepresentation

Utilitetsrepresentation is a concept in economics and decision theory describing the representation of preferences by a utility function. In this approach, each possible outcome or choice is assigned a real number, such that more preferred outcomes receive higher utility. This formalizes qualitative orders of preference into a quantitative tool that enables comparative and probabilistic analysis.

There are two primary notions of utility representation: ordinal utility and cardinal utility. An ordinal representation preserves only the ranking of options—any increasing transformation of the utility function yields the same preference ordering. Cardinal (or von Neumann–Morgenstern) utility uses a scale in which differences are meaningful, and, for risky choices, utility is defined up to positive affine transformations, allowing statements about risk attitudes and expected utility to be meaningful.

Axioms and foundational results underpin utilitetsrepresentation. Common assumptions include completeness, transitivity, and continuity of preferences. Under suitable conditions, a utility function that represents the preference relation exists (representation theorems). For risk, the von Neumann–Morgenstern utility theorem shows that if a decision maker’s preferences over lotteries satisfy independence and continuity, they can be represented by an expected utility function. Debreu’s and related representation theorems formalize when such representations exist in broader settings.

Applications span welfare economics, where social welfare functions rely on underlying utility representations; in decision theory and economic design, where mechanisms and contracts depend on measurable utilities; and in cost–benefit analysis, where outcomes are assessed through utility-based criteria. Limitations include issues of interpersonal comparability, measurement challenges, and ethical concerns about aggregating utilities.