Arrow Social Welfare Function (constitution)
Kenneth Arrow (1963) generalizes the analysis. Along earlier lines, his version of a social welfare function, also called a 'constitution', maps a set of individual orderings (ordinal utility functions) for everyone in the society to a social ordering, a rule for ranking alternative social states (say passing an enforceable law or not, ceteris paribus). Arrow finds that nothing of behavioral significance is lost by dropping the requirement of social orderings that are real-valued (and thus cardinal) in favor of orderings, which are merely complete and transitive, such as a standard indifference-curve map. The earlier analysis mapped any set of individual orderings to one social ordering, whatever it was. This social ordering selected the top-ranked feasible alternative from the economic environment as to resource constraints. Arrow proposed to examine mapping different sets of individual orderings to possibly different social orderings. Here the social ordering would depend on the set of individual orderings, rather than being imposed (invariant to them). Stunningly (relative to a course of theory from Adam Smith and Jeremy Bentham on), Arrow proved the General Possibility Theorem that it is impossible to have a social welfare function that satisfies a certain set of "apparently reasonable" conditions.
Read more about this topic: Social Welfare Function
Famous quotes containing the words arrow, social, welfare and/or function:
“It is easy to dodge a spear in the daylight, but it is difficult to avoid an arrow in the dark.”
—Chinese proverb.
“It’s frightening how easy it is to commit murder in America. Just a drink too much. I can see myself doing it. In England, one feels all the social restraints holding one back. But here, anything can happen.”
—W.H. (Wystan Hugh)
“I have an intense personal interest in making the use of American capital in the development of China an instrument for the promotion of the welfare of China, and an increase in her material prosperity without entanglements or creating embarrassment affecting the growth of her independent political power, and the preservation of her territorial integrity.”
—William Howard Taft (1857–1930)
“Of all the inhabitants of the inferno, none but Lucifer knows that hell is hell, and the secret function of purgatory is to make of heaven an effective reality.”
—Arnold Bennett (1867–1931)