PhilGoetz comments on Average utilitarianism must be correct? - Less Wrong

2 Post author: PhilGoetz 06 April 2009 05:10PM

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Comment author: PhilGoetz 08 April 2009 03:56:26AM *  -1 points [-]

As a result, (and this is the crucial part) nothing in the axioms say that f has to have anything to do with the w(i).

Here we disagree. f is the utility function for a world state. If it were an arbitrary function, we'd have no reason to think that the axioms should hold for it. Positing the axioms is based on our commonsense notion of what utility is like.

I'm not assuming that there are a bunch of individual w(i) functions. Think instead of a situation where one person is calculating only their private utility. f is simply their utility function. You may be thinking that I have some definition of "utilitarianism" that places restrictions on f. "Average utilitarianism" does, but I don't think "utilitarianism" does; and if it did, then I wouldn't apply it here. The phrase "average utilitarianism" has not yet come into play in my argument by this point. All I ask at this point in the argument, is what the theorem asks - that there be a utility function for the outcome.

I thikn you're thinking that I'm saying that the theorem says that f has to be a sum or average of the w(i), and therefore we have to be average utilitarians. That's not what I'm saying at all. I tried to explain that already before. Read steven0461's comment above, and my response to it.

Comment author: conchis 08 April 2009 04:39:21AM *  2 points [-]

The claim I am taking exception to is the claim that the vNM axioms provide support to (average) utilitarianism, or suggest that we need not be concerned with inequality. This is what I took your bullet points 6 and 8 (in the main post) to be suggesting (not to mention the title of the post!)

If you are not claiming either of these things, then I apologize for misunderstanding you. If you are claiming either of these things, then my criticisms stand.

As far as I can tell, most of your first two paragraphs are inaccurate descriptions of the theory. In particular, f is not just an individual's private utility function. To the extent that the vNM argument generalizes in the way you want it to, f can be any monotonic transform of a private utility function, which means, amongst other things, that we are allowed to care about inequality, and (average) utilitarianism is not implied.

But I've repeated myself enough. I doubt this conversation is productive any more, if it ever was, so I'm going to forego adding any more noise from now on.

Read steven0461's comment above, and my response to it.

I read both of them when they were originally posted, and have looked over them again at your exhortation, but have sadly not discovered whatever enlightenment you want me to find there.

Comment author: PhilGoetz 08 April 2009 04:51:30AM *  0 points [-]

The claim I am taking exception to is the claim that the vNM axioms provide support to (average) utilitarianism, or suggest that we need not be concerned with inequality. This is what I took your bullet points 6 and 8 (in the main post) to be suggesting (not to mention the title of the post!)

As steven0461 said,

If in all the axioms of the expected utility theorem you replace lotteries by distributions of individual welfare, then the theorem proves that you have to accept utilitarianism.

Not "proven", really, but he's got the idea.

As far as I can tell, most of your first two paragraphs are inaccurate descriptions of the theory. In particular, f is not just an individual's private utility function. To the extent that the vNM argument generalizes in the way you want it to, f can be any monotonic transform of a private utility function, which means, amongst other things, that we are allowed to care about inequality, and (average) utilitarianism is not implied.

I am pretty confident that you're mistaken. f is a utility function. Furthermore, it doesn't matter that the vNM argument can apply to things that satisfy the axioms but aren't utility functions, as long as it applies to the utility functions that we maximize when we are maximizing expected utility.

Either my first two bullet points are correct, or most of the highest-page-ranked explanations of the theory on the Web are wrong. So perhaps you could be specific about how they are wrong.

Comment author: conchis 08 April 2009 05:41:47PM *  1 point [-]

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.)

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