Social Welfare Function

In economics, a social welfare function is a real-valued function that ranks conceivable social states (alternative complete descriptions of the society) from lowest to highest. Inputs of the function include any variables considered to affect the economic welfare of a society (Sen, 1970, p. 33). In using welfare measures of persons in the society as inputs, the social welfare function is individualistic in form. One use of a social welfare function is to represent prospective patterns of collective choice as to alternative social states.

The social welfare function is analogous to an indifference-curve map for an individual, except that the social welfare function is a mapping of individual preferences or judgments of everyone in the society as to collective choices, which apply to all, whatever individual preferences are. One point of a social welfare function is to determine how close the analogy is to an ordinal utility function for an individual with at least minimal restrictions suggested by welfare economics. Kenneth Arrow proved a more basic point for a set of seemingly reasonable conditions.