Each of the five mutually inconsistent principles in the Third Impossibility Theorem of Arrhenius (2000) is, in isolation, very hard to deny.
This post/paper points out that lexical total utilitarianism already satisfies all of Arrhenius’s principles in his impossibility theorems (there are other background assumptions):
However, it’s recently been pointed out that each of Arrhenius’s theorems depends on a dubious assumption: Finite Fine-Grainedness. This assumption states, roughly, that you can get from a very positive welfare level to a very negative welfare level via a finite number of slight decreases in welfare. Lexical population axiologies deny Finite Fine-Grainedness, and so can satisfy all of Arrhenius’s plausible adequacy conditions. These lexical views have other advantages as well. They cohere nicely with most people’s intuitions in cases like Haydn and the Oyster, and they offer a neat way of avoiding the Repugnant Conclusion.
Also, for what it’s worth, the conditions in these theorems often require a kind of uniformity that may only be intuitive if you’re already assuming separability/additivity/totalism in the first place, e.g. (a) there exists some subpopulation A that satisfies a given condition for any possible disjoint unaffected common subpopulation C (i.e. the subpopulation C exists in both worlds, and the welfares in C are the same across the two worlds), rather than (b) for each possible disjoint unaffected common subpopulation C, there exists a subpopulation A that satisfies the condition (possibly a different A for a different C). The definition of separability is just that a disjoint unaffected common subpopulation C doesn’t make a difference to any comparisons.
So, if you reject separability/additivity/totalism or are at least sympathetic to the possibility that it’s wrong, then it is feasible to deny the uniformity requirements in the principles and accept weaker non-uniform versions instead. Of course, rejecting separability/additivity/totalism has other costs, though.
This post/paper points out that lexical total utilitarianism already satisfies all of Arrhenius’s principles in his impossibility theorems (there are other background assumptions):
Also, for what it’s worth, the conditions in these theorems often require a kind of uniformity that may only be intuitive if you’re already assuming separability/additivity/totalism in the first place, e.g. (a) there exists some subpopulation A that satisfies a given condition for any possible disjoint unaffected common subpopulation C (i.e. the subpopulation C exists in both worlds, and the welfares in C are the same across the two worlds), rather than (b) for each possible disjoint unaffected common subpopulation C, there exists a subpopulation A that satisfies the condition (possibly a different A for a different C). The definition of separability is just that a disjoint unaffected common subpopulation C doesn’t make a difference to any comparisons.
So, if you reject separability/additivity/totalism or are at least sympathetic to the possibility that it’s wrong, then it is feasible to deny the uniformity requirements in the principles and accept weaker non-uniform versions instead. Of course, rejecting separability/additivity/totalism has other costs, though.