Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utilities: A Note

Abstract

In 1955 John Harsanyi proposed three appealing postulates for social choice under uncertainty and tried to show (Theorem V, p. 314) that these postulates lead to a social welfare function which is a weighted sum of the utility functions of the individuals. The importance of this result is that it shows that a rather weak and plausible ethical postulate (Postulate C below) suffices to establish a cardinal social welfare function which is a weighted sum of the individuals' cardinal utility functions. However, as presented by Harsanyi, his conclusion can be applied only to a restricted class of cases which we do not consider broad enough to incorporate many important situations of social choice that may appear in the real world. In this paper we will attempt to improve Harsanyi's result in two directions. First, instead of his Postulate C we will use a new Postulate C', which is even weaker than Postulate C. Second, our proof of the existence of a cardinal social welfare function that is a weighted sum of the individual utility functions will not depend on certain restrictive assumptions utilized in Harsanyi's proof, and consequently our result can be applied to a broader spectrum of situations. Finally, we want to note that the mathematics employed in our proof is very simple indeed. We now present Harsanyi's postulates and Theorem V. Then, Postulate C' will be introduced and our stronger theorem (Theorem V') proved. Harsanyi's three postulates are: Postulate A.-Social preferences R satisfy Marschak's (1950) Postulates I, II, III', and IV. Postulate B. Individual preferences Rj(i = 1, . . ., n) satisfy the same four postulates. Postulate C.-If two prospects P and Q are indifferent from the standpoint of every individual, they are also indifferent from a social standpoint.