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# steven0461 comments on Average utilitarianism must be correct? - Less Wrong

5 06 April 2009 05:10PM

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Comment author: 07 April 2009 04:47:40PM *  5 points [-]

Oh! I realized only now that this isn't about average utilitarianism vs. total utilitarianism, but about utilitarianism vs. egalitarianism. As far as I understand the word, utilitarianism means summing people's welfare; if you place any intrinsic value on equality, you aren't any kind of utilitarian. The terminology is sort of confusing: most expected utility maximizers are not utilitarians. (edit: though I guess this would mean only total utilitarianism counts, so there's a case that if average utilitarianism can be called utilitarianism, then egalitarianism can be called utilitarianism... ack)

In this light the question Phil raises is kind of interesting. 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. People who place intrinsic value on inequality would deny that some of the axioms, like maybe transitivity or independence, hold for distributions of individual welfare. And the question now is, if they're not necessarily irrational to do so, is it necessarily irrational to deny the same axioms as applying to merely possible worlds?

(Harsanyi proved a theorem that also has utilitarianism follow from some axioms, but I can't find a good link. It may come down to the same thing.)

Comment author: 08 April 2009 12:21:55AM *  2 points [-]

FWIW, this isn't quite Harsanyi's argument. Though he does build on the von Neuman-Morgenstern/Marschak results, it's in slightly different way to that proposed here (and there's still a lot of debate about whether it works or not).

Comment author: 08 April 2009 05:50:16PM *  2 points [-]

In case anyone's interested, here are some references for (a) the original Harsanyi (1955) axiomatization, and (b) the subsequent debate between Harsanyi and Sen about it's meaning. There is much more out there than this, but section 2 of Sen (1976) probably captures two key points, both of which seem equally applicable to Phil's argument.

(1) The independence axiom is seems more problematic when shifting from individual to social choice (as Wei Dai has already pointed out)

(2) Even if it weren't, the axioms don't really say much about utilitarianism as it is is commonly understood (which is what I've been trying, unsuccessfully, to communicate to Phil in the thread beginning here)

• Harsanyi, John (1955), "Cardinal Welfare, Individualistic Ethics and Interpersonal Comparisons of Utility", Journal of Political Economy 63.
• Diamond, P. (1967) "Cardinal Welfare, Individualistic Ethics and Interpersonal Comparisons of Utility: A Comment", Journal of Political Economy 61 (especially on the validity of the independence axiom in social vs. individual choice.)
• 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. (1977) Foundational Problems in the Special Sciences (Boston: Reidel). (esp. section 2)
• 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.

Comment author: 07 April 2009 10:03:43PM *  2 points [-]

As far as I understand the word, utilitarianism means summing people's welfare; if you place any intrinsic value on equality, you aren't any kind of utilitarian.

Utilitarianism means computing a utility function. It doesn't AFAIK have to be a sum.

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. People who place intrinsic value on inequality would deny that some of the axioms, like maybe transitivity or independence, hold for distributions of individual welfare. And the question now is, if they're not necessarily irrational to do so, is it necessarily irrational to deny the same axioms as applying to merely possible worlds?

(average utilitarianism, that is)

YES YES YES! Thank you!

You're the first person to understand.

The theorem doesn't actually prove it, because you need to account for different people having different weights in the combination function; and more especially for comparing situations with different population sizes.

And who knows, total utilities across two different populations might turn out to be incommensurate.