Әлеуметтік әл-ауқат функциясы: қоғамдық таңдау және қалауларды бағалау

Function that ranks states of society according to their desirabilitya discussion of the same concept in the context of voting and politics
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. 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, 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.

Some authors maintain a distinction between a social choice or ordering function: a choice function selects a single best outcome, while an ordering function ranks all possible outcomes. In the context of elections, a social choice function is a single winner voting system. Every social ordering can be made into a choice function by considering only the highest ranked outcome. Less obviously, though, every social choice function is also an ordering function. Deleting the best outcome, then finding the new winner, results in a runner up who is assigned second place. Repeating this process gives a full ranking of all candidates. Because this construction allows for treating both functions simultaneously, social ordering and choice functions are often conflated by abuse of terminology.

Introducing one additional axiom—the nonexistence of Dutch Books, or equivalently that social choice behaves according to the axioms of rational choice—implies that the social choice function must be the utilitarian rule, i. e. the weighting function must be equal to the utility functions of each individual. This result is known as Harsanyi's utilitarian theorem.