Social welfare function

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In welfare economics and social choice theory, a social welfare function—also called a social ordering, ranking, utility, or choice function—is a function that ranks a set of social states by their desirability. A social welfare function takes two possible outcomes, then combines every person's preferences to determine which outcome is considered better by society as a whole. Inputs to the function can include any variables that affect the well-being of a society.^[1]

Social choice functions are used in collective decision-making by economists to rigorously identify which outcome should be considered more desirable for society as a whole, e.g. to identify the optimal distribution of income,^[2] as well as by democratic governments to choose between several options based on the preferences of the voters.

The notion of social welfare is analogous to the utility function of consumer theory, but with the key difference being the social welfare function is a mapping of individual preferences or judgments of everyone in a society where collective choices apply to all, whatever individual preferences are for (variable) constraints on factors of production.

There are two, slightly different, kinds of social welfare functions used by economists:

• Ordinal (or ranked voting) functions determine only which of two options is better.
• Cardinal (or rated voting) functions attempt to compare different options numerically, to determine how much better one choice is compared to another.