I understand what steven0461 said. I get the idea too, I just think it's wrong. I've tried to explain why it's wrong numerous times, but I've clearly failed, and don't see myself making much further progress.

In lieu of further failed attempts to explain myself, I'm lodging a gratuitous appeal to Nobel Laureate authority, leaving some further references, and bowing out.

The following quote from Amartya Sen (1979) pretty much sums up my position (in the context of a similar debate between him and Harsanyi about the meaning of Harsanyi's supposed axiomatic proof of utilitarianism).

[I]t is possible to define individual utilities in such a way that the only way of aggregating them is by summation. By confining his attention to utilities defined in that way, John Harsanyi has denied the credibility of "nonlinear social welfare functions." That denial holds perfectly well for the utility measures to which Harsanyi confines his attention, but has no general validity outside that limited framework. Thus, sum-ranking remains an open issue to be discussed in terms of its moral merits-and in particular, our concern for equality of utilities-and cannot be "thrust upon" us on grounds of consistency.

Further refs, if anyone's interested:

• Harsanyi, John (1955), "Cardinal Welfare, Individualistic Ethics and Interpersonal Comparisons of Utility", Journal of Political Economy 63. (Harsanyi's axiomatic "proof" of utilitarianism.)
• Diamond, P. (1967) "Cardinal Welfare, Individualistic Ethics and Interpersonal Comparisons of Utility: A Comment", Journal of Political Economy 61
• Harsanyi, John (1975) "Nonlinear Social Welfare Functions: Do Welfare Economists Have a Special Exemption from Bayesian Rationality?" Theory and Decision 6(3): 311-332.
• Sen, Amartya (1976) "Welfare Inequalities and Rawlsian Axiomatics," Theory and Decision, 7(4): 243-262 (reprinted in R. Butts and J. Hintikka eds., Foundational Problems in the Special Sciences (Boston: Reidel, 1977). (esp. section 2: Focuses on two objections to Haysanyi's derivation: the first is the application of the independence axiom to social choice (as Wei Dai has pointed out), the second is the point that I've been making about the link to utilitarianism.)
• Harsanyi, John (1977) "Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen," in Butts and Hintikka
• Sen, Amartya (1977) "Non-linear Social Welfare Functions: A Reply to Professor Harsanyi," in Butts and Hintikka
• Sen, Amartya (1979) "Utilitarianism and Welfarism" The Journal of Philosophy 76(9): 463-489 (esp. section 2)

Parts of the Hintikka and Butts volume are available in Google Books.

(I'll put these in the Harsanyi thread above as well.)