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Equity, Arrow's Conditions, and Rawls' Difference Principle

Peter J. Hammond

Abstract

An Arrow social welfare function was designed not to incorporate any interpersonal comparisons. But some notions of equity rest on interpersonal comparisons. It is shown that a generalized social welfare function, incorporating interpersonal comparisons, can satisfy modifications of the Arrow conditions, and also a strong version of an equity axiom due to Sen. One such generalized social welfare function is the lexicographic form of Rawls' difference principle or maximin rule. This kind of generalized social welfare function is the only kind satisfying the modified Arrow conditions, the equity axiom, and a condition which underlies Suppes' grading principle.