I don’t think the theorem provides support for total utilitarianism, specifically, unless you add extra assumptions about how to deal with populations of different sizes or different populations generally. Average utilitarianism is still consistent with it, for example.
Well, average utilitarianism is consistent with the result because it gives the same answer as total utilitarianism (for a fixed population size). The vast majority of utility functions one can imagine (including ones also based on the original position like maximin) are ruled out by the result. I agree that the technical result is “anything isomorphic to total utilitarianism” though.
I just want to second the point that some others have made that it seems more accurate to say only that Harsanyi’s result supports utilitarianism (rather than total utilitarianism). Adding the word “total” suggests that the result rules out other version of utilitarianism (e.g. average, critical-level and critical-range utilitarianism), which as you point out is not correct. More generally, I think “utilitarianism” (without the “total”) nicely signals that Harsanyi’s result concerns fixed-population settings.
It is also worth noting that Harsanyi himself accepted average utilitarianism rather than total utilitarianism in variable-population settings (see the letter exchange between him and Yew-Kwang Ng reported in the appendix of Ng, Y. K. (1983). Some broader issues of social choice. In Contributions to Economic Analysis (Vol. 145, pp. 151-173). Elsevier.).
Thanks!
Well, average utilitarianism is consistent with the result because it gives the same answer as total utilitarianism (for a fixed population size). The vast majority of utility functions one can imagine (including ones also based on the original position like maximin) are ruled out by the result. I agree that the technical result is “anything isomorphic to total utilitarianism” though.
I had not seen that, thanks!
I just want to second the point that some others have made that it seems more accurate to say only that Harsanyi’s result supports utilitarianism (rather than total utilitarianism). Adding the word “total” suggests that the result rules out other version of utilitarianism (e.g. average, critical-level and critical-range utilitarianism), which as you point out is not correct. More generally, I think “utilitarianism” (without the “total”) nicely signals that Harsanyi’s result concerns fixed-population settings.
It is also worth noting that Harsanyi himself accepted average utilitarianism rather than total utilitarianism in variable-population settings (see the letter exchange between him and Yew-Kwang Ng reported in the appendix of Ng, Y. K. (1983). Some broader issues of social choice. In Contributions to Economic Analysis (Vol. 145, pp. 151-173). Elsevier.).
Anyway, thanks for this post!
[Edited comment to remove grammatical error]