Cardinal Utility

In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations. Two utility indices are related by an affine transformation if for every value of one index u, occurring at quantity of the goods bundle being evaluated, the corresponding value of the other index v satisfies a relationship of the form

,

for fixed constants a and b. Thus the utility functions themselves are related by

The two indices differ only with respect to scale and origin.

Cardinal utility is mostly considered to be an outdated idea. Only within specific contexts such as decision making under risk, utilitarian welfare evaluations, and discounted utilities for intertemporal evaluations, is cardinal utility usually accepted. Elsewhere, such as in general consumer theory, ordinal utility is preferred.