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:
“... and the next summer she died in childbirth.
That’s all. Of course, there may be some sort of sequel but it is not known to me. In such cases instead of getting bogged down in guesswork, I repeat the words of the merry king in my favorite fairy tale: Which arrow flies for ever? The arrow that has hit its mark.”
—Vladimir Nabokov (1899–1977)
“Without our suffering, our work would just be social work, very good and helpful, but it would not be the work of Jesus Christ, not part of the Redemption.... All the desolation of the poor people, not only their material poverty, but their spiritual destitution, must be redeemed. And we must share it, for only by being one with them can we redeem them by bringing God into their lives and bringing them to God.”
—Mother Teresa (b. 1910)
“Power has only one duty—to secure the social welfare of the People.”
—Benjamin Disraeli (1804–1881)
“Science has fulfilled her function when she has ascertained and enunciated truth.”
—Thomas Henry Huxley (1825–95)