Ordinal utility

Ordinal utility represents preferences by ranking alternatives, without assigning significance to the numerical distances between them. Any increasing transformation of a utility representation preserves the same preference ordering.

Preference relation: A relation that represents how an agent ranks alternatives, including whether one is preferred, dispreferred, or equally preferred to another. Ordinal utility encodes this ranking rather than measuring satisfaction.
Monotonic transformation: A transformation that preserves or reverses order; a strictly increasing transformation preserves the ordering of values. Applying a strictly increasing transformation changes utility numbers without changing preferences.
Cardinal utility: A utility representation in which numerical differences or ratios carry meaning under specified transformations. Unlike ordinal utility, cardinal utility can make some comparisons of utility magnitude meaningful.
Revealed preference theory: An approach that infers preference rankings from observed choices among available alternatives. Observed choices can test or recover the rankings represented by ordinal utility.
Rational choice theory: A framework that models choices as outcomes of consistent preferences subject to available alternatives and constraints. Ordinal utility is a standard way to represent preferences within this framework.
Utility representation theorem: A mathematical result establishing conditions under which a preference relation can be represented by a utility function. Representation theorems state when an ordinal ranking can be encoded numerically.
Expected utility hypothesis: The hypothesis that choices under risk can be represented as maximizing expected values of a utility function. Expected-utility models require more structure than an ordinary ranking of certain alternatives.
Consumer theory: The economic study of how consumers choose goods and services under constraints. Consumer theory commonly describes choices using ordinal preferences and indifference curves.
Completeness (preference relation): A property requiring that, for any two alternatives, an agent can rank one at least as highly as the other. A complete ranking lets utility assign an order to every pair of alternatives.
Weak order: A complete and transitive relation that allows alternatives to be ranked, including ties. A weak order is the preference structure an ordinal utility function can represent.

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