More generally, Arrhenius proves an impossibility result that applies to all possible population ethics (not just person-affecting views), so (if you want consistency) you need to bite at least one of those bullets.
That result (The Impossibility Theorem), as stated in the paper, has some important assumptions not explicitly mentioned in the result itself which are instead made early in the paper and assume away effectively all person-affecting views before the 6 conditions are introduced. The assumptions are completeness, transitivity and the independence of irrelevant alternatives. You could extend the result to include incompleteness, intransitivity, dependence on irrelevant alternatives or being in principle Dutch bookable/money pumpable as alternative “bullets” you could bite on top of the 6 conditions. (Intransitivity, dependence on irrelevant alternatives and maybe incompleteness imply Dutch books/money pumps, so you could just add Dutch books/money pumps and maybe incompleteness.)
There are some other similar impossibility results that apply to I think basically all aggregative views, person-affecting or not (although there are non-aggregative views which avoid them). See Spears and Budolfson:
The results are basically that all aggregative views in the literature allow small changes in individual welfares in a background population to outweigh the replacement of an extremely high positive welfare subpopulation with a subpopulation with extremely negative welfare, an extended very repugnant conclusion. The size and welfare levels of the background population, the size of the small changes and the number of small changes will depend on the exact replacement and view. The result is roughly:
For any positive welfare population and negative welfare population, there exists some background population + small average welfare changes to it such that the negative welfare population + the changes to the background population are preferred to the positive welfare population (without the changes to the background population).
This is usually through a much much larger number of small changes to the background population than the number of replaced individuals, or the small changes happening to individuals who are extremely prioritized (as in lexical views and some person-affecting views).
(I think the result actually also adds a huge marginally positive welfare population along with the negative welfare one, but I don’t think this is necessary or very interesting.)
You could extend the result to include incompleteness, intransitivity, dependence on irrelevant alternatives or being in principle Dutch bookable/money pumpable as alternative “bullets” you could bite on top of the 6 conditions.
That result (The Impossibility Theorem), as stated in the paper, has some important assumptions not explicitly mentioned in the result itself which are instead made early in the paper and assume away effectively all person-affecting views before the 6 conditions are introduced. The assumptions are completeness, transitivity and the independence of irrelevant alternatives. You could extend the result to include incompleteness, intransitivity, dependence on irrelevant alternatives or being in principle Dutch bookable/money pumpable as alternative “bullets” you could bite on top of the 6 conditions. (Intransitivity, dependence on irrelevant alternatives and maybe incompleteness imply Dutch books/money pumps, so you could just add Dutch books/money pumps and maybe incompleteness.)
There are some other similar impossibility results that apply to I think basically all aggregative views, person-affecting or not (although there are non-aggregative views which avoid them). See Spears and Budolfson:
https://philpapers.org/rec/BUDWTR
http://www.stafforini.com/docs/Spears & Budolfson—Repugnant conclusions.pdf
The results are basically that all aggregative views in the literature allow small changes in individual welfares in a background population to outweigh the replacement of an extremely high positive welfare subpopulation with a subpopulation with extremely negative welfare, an extended very repugnant conclusion. The size and welfare levels of the background population, the size of the small changes and the number of small changes will depend on the exact replacement and view. The result is roughly:
This is usually through a much much larger number of small changes to the background population than the number of replaced individuals, or the small changes happening to individuals who are extremely prioritized (as in lexical views and some person-affecting views).
(I think the result actually also adds a huge marginally positive welfare population along with the negative welfare one, but I don’t think this is necessary or very interesting.)
Yeah, this is what I had in mind.