Nonlinear social welfare functions

Abstract

It is argued that Bayesian decision theory is a solution of an important philosophical problem, viz. the problem of how to define rational behavior under risk and uncertainty. The author has shown in earlier papers that if we take the Bayesian rationality postulates seriously, and take an individualistic point of view about social welfare, then our social welfare function must be a linear function of individual utilities: indeed, it must be their arithmetic mean. The present paper criticizes Diamond's and Sen's contention that one of the Bayesian postulates (viz. the sure-thing principle) does not apply to social decisions, even though it may apply to individual decisions. It also criticizes Sen's proposal of making social welfare a nonlinear function of individual utilities. The social welfare function proposed by the author depends on interpersonal utility comparisons. The use of such comparisons is defended. It is also argued that anybody who feels that the utilitarian (i.e., linear) form of the social welfare function is not egalitarian enough, should reject the author's individualism axiom, instead of trying to reject the Bayesian rationality axioms. However, this would be equivalent to giving egalitarian considerations a priority in many cases over humanitarian considerations. Finally, the paper discusses the reasons why even full agreement on the mathematical form of the social welfare function would not give rise to a Utopian state of moral consensus: moral controversies arising from disagreements about what predictions to make about future empirical facts would still remain.