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. Furthermore, if you don’t count the interests of people who exist until after they exist or unless they come to exist, it probably won’t look like total utilitarianism, although it gets more complicated.
You might be interested in Teruji Thomas’ paper “The Asymmetry, Uncertainty, and the Long Term” (EA Forum post here), which proves a similar result from slightly different premises, but is compatible with all of 1) ex post prioritarianism, 2) mere addition, 3) the procreation asymmetry, 4) avoiding the repugnant conclusion and 5) avoiding antinatalism, and all five of these all at the same time, because it sacrifices the independence of irrelevant alternatives (the claim that how you rank choices should not depend on what choices are available to you, not the vNM axiom). Thomas proposes beatpath voting to choose actions. Christopher Meacham’s “Person-affecting views and saturating counterpart relations” also provides an additive calculus which “solves the Non-Identity Problem, avoids the Repugnant and Absurd Conclusions, and solves the Mere-Addition Paradox” and satisfies the asymmetry, also by giving up the independence of irrelevant alternatives, but hasn’t, as far as I know, been extended to deal with uncertainty.
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 for writing this!
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. Furthermore, if you don’t count the interests of people who exist until after they exist or unless they come to exist, it probably won’t look like total utilitarianism, although it gets more complicated.
You might be interested in Teruji Thomas’ paper “The Asymmetry, Uncertainty, and the Long Term” (EA Forum post here), which proves a similar result from slightly different premises, but is compatible with all of 1) ex post prioritarianism, 2) mere addition, 3) the procreation asymmetry, 4) avoiding the repugnant conclusion and 5) avoiding antinatalism, and all five of these all at the same time, because it sacrifices the independence of irrelevant alternatives (the claim that how you rank choices should not depend on what choices are available to you, not the vNM axiom). Thomas proposes beatpath voting to choose actions. Christopher Meacham’s “Person-affecting views and saturating counterpart relations” also provides an additive calculus which “solves the Non-Identity Problem, avoids the Repugnant and Absurd Conclusions, and solves the Mere-Addition Paradox” and satisfies the asymmetry, also by giving up the independence of irrelevant alternatives, but hasn’t, as far as I know, been extended to deal with uncertainty.
I’ve also written about ex ante prioritarianism in the comments on the EA Forum post about Thomas’ paper, and in my own post here (with useful feedback in the comments).
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]