Cardinal Welfare and Individualistic Ethics: A Comment

M OST of Dr. Harsanyi's paper "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility"' I find very convincing. I fear, however, that his claim that one of the postulates he uses to establish an additive cardinal social welfare function is "weaker" (less restrictive) than those employed for the same purpose in my paper, "A Cardinal Concept of Welfare,"2 may lead some readers to assume that, taken as a whole, his postulates are weaker than mine. On the contrary, Harsanyi's postulates, though personally I find them unobjectionable, are in combination somewhat more restrictive than my own. In the paper in question I sought to show (roughly speaking) that all ethical systems which (a) permit social welfare to be expressed as a single-valued increasing function of (arbitrarily chosen) indicators of individual utility and (b) conform to the postulate described below will permit social welfare to be expressed as the sum of (suitably adjusted) indicators of individual utility. The crucial postulate-my so-called Postulate E-I will express, as does Harsanyi, in the form of finite differences rather than, as in my original paper, in the form of infinitesimals. Postulate E. (1) There are at least three individuals. (2) Suppose that Individual A's utility is the same in situation X as in situation X' and is the same in situation Y as in situation Y' but is higher in X or X' than in Y or Y'. Suppose further that Individual B's utility also is the same in X as in X' and is the same in Y as in Y' but is higher in Y or Y' than in X or X'. Suppose also that all other individuals have the same utility in X as in Y and the same utility in X' as in Y'. (This situation is illustrated in Figure 1 for the three-person case of Individuals A, B, and C, where the vertical lines represent the respective utility indicators and the lines linking them represent the different "situations.") Then, if social welfare is the same in X as in Y, it must be the same in X' as in Y'. In other words, whether one man's utility loss is deemed to outweigh another man's utility gain depends solely on these