Thanks – this is a very important point and I am glad that you raised it! Overall, I think we should be very uncertain about what the long-run population dynamics might be after a catastrophe. I am not sure how much we disagree, but I tried to add some thoughts below (Note: Maya might not necessarily agree with my thoughts on this issue).
As you point out, we write in the paper that Malthusian population dynamics may reemerge in the long run and that evolutionary pressures are one of the main reasons to expect that this might happen. We do not directly argue that such reemergence won’t happen, but in the footnote that follows immediately after that passage you quoted we write:
“In contrast, Arenberg et al. (forthcoming) argue that “empirical facts and models of heritability do not provide reason to conclude that positive population growth is bound to continue via the dynamics of a higher-fertility type making up an ever-increasing share of the global population”.
Here’s an attempt to quickly explain Arenberg et al.’s argument: Arenberg et al. point out that we “should not conflate higher fertility within a heterogeneous population with high or above-replacement fertility: it is an empirical question whether future higher-fertility sub-populations will have above replacement fertility”. They then argue that “there is strong historical and global evidence that even higher-fertility groups will eventually trend to near or below replacement fertility”. Drawing on these insights, they introduce a model indicating that “long-term population growth can be negative even with both strong heritability and an above-replacement-fertility sub-population”.
Now, it could reasonably be argued that evolutionary pressures will nonetheless determine fertility rates on 100,000+ year timeframes. However, even if this is correct, such timeframes are only relevant if there is at least a decent probability that humanity will still be around in 100,000 years (conditional on surviving this century). This is not obvious; for instance, if the background probability of human extinction is 1% in each century, then the probability that humanity is still around after 100,000 years is only 0.004%. It is therefore not clear to me that the Malthusian model is correct, so it seems sensible to take other models of fertility seriously.
Thanks again for engaging with the paper!
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]