Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen

Abstract

I shall comment only on Section 2 of Amartya Sen’s contribution, where he discusses a recent paper of mine (Harsanyi, 1975). In this paper, I argued for the utilitarianview that our social welfare function ought to be defined as a linearcombination-and, indeed, as the arithmetic mean—of the different individuals’ von Neumann-Morgenstern (vNM) utility functions. One basis of my arguments was the following mathematical theorem (proved in Harsanyi, 1955). If (a) the individual members of society follow the Bayesian rationality axioms in their behavior; and if (b) our moral choices between alternative social policies likewise follow these rationality axioms; and if (c) we are always morally indifferent between two social policies when we know that all individuals in our society would be indifferent between the effects of these two policies; thenour social welfare function will be, as a matter of mathematical necessity, a linearcombination of all individuals’ vNM utility functions. In the same paper, I also criticized Sen’s views favoring nonlinearsocial welfare functions.