Social welfare function

In welfare economics, the social welfare function is a function that ranks social states pick complete descriptions of the society as less desirable, more desirable, or indifferent for every possible pair of social states. Inputs of the function include any variables considered to impact the economic welfare of a society. In using welfare measures of persons in the society as inputs, the social welfare function is individualistic in form. One usage of a social welfare function is to represent prospective patterns of collective selection as to alternative social states. The social welfare function provides the government with a simple guideline for achieving the optimal distribution of income.

The social welfare function is analogous to the consumer theory of indifference-curve–budget constraint tangency for an individual, except that the social welfare function is a mapping of individual preferences or judgments of programs in the society as to collective choices, which apply to all, whatever individual preferences are for variable constraints on factors of production. One bit of a social welfare function is to establish howthe analogy is to an ordinal utility function for an individual with at least minimal restrictions suggested by welfare economics, including constraints on the number of factors of production.

There are two major distinct but related vintage of social welfare functions:

Arrow social welfare function constitution

general impossibility theorem which says that it is impossible to realize a social welfare function that satisfies aset of "apparently reasonable" conditions.