Arrhenius on welfarist axiologies

What do we know about Arrhenius's impossibility theorems about welfarist axiologies?

Here’s the short version of what Arrhenius shows about welfarist axiologies (theories that rank populations only by the welfare of the people who’d live in them):

• Core 2000 theorem. Any welfarist axiology that satisfies three very plausible conditions — Dominance (if A and B have the same number of people and everyone in A is better off than everyone in B, then A is better), Addition (if adding some worse-off people is bad, adding more and even worse-off people is at least as bad), and a mild Minimal Non-Extreme Priority (very large gains for many can outweigh a slight harm to one) — must accept at least one of three counter-intuitive results: the Repugnant Conclusion, the Sadistic Conclusion, or an Anti-Egalitarian Conclusion (preferring an unequal population with lower average welfare to an equal one). (Institutet för framtidsstudier)

• What “welfarist axiology” means in the paper. It’s an “at least as good as” ordering over all possible populations, based solely on welfare, assumed reflexive, transitive, and complete; Arrhenius notes Dominance is stronger than simple Pareto. (Institutet för framtidsstudier)

• The three “bad” conclusions defined. Arrhenius explicitly formulates Repugnant, Sadistic, and Anti-Egalitarian conclusions and proves the incompatibility result above. (Institutet för framtidsstudier)

• Escape routes he considers (and worries about). You could drop completeness (allow incommensurability), or go non-welfarist/pluralist; but Arrhenius argues these moves are costly or unmotivated within a welfarist frame. (Institutet för framtidsstudier)

• Later impossibility results. Arrhenius also proved “one more” theorem using slightly different, often weaker, conditions (e.g., Egalitarian Dominance, General Non-Extreme Priority, Non-Elitism, Weak Non-Sadism, Weak Quality Addition) to show no axiology can meet them all; this strengthens the case even if one rejects some premises from 2000. (Institutet för framtidsstudier)

• Ongoing debate. Recent work argues some proofs rely (implicitly) on a Finite Fine-Grainedness assumption about the welfare scale; critics propose “lexical” views to evade certain theorems, while others “riskify” the conditions (population prospects under uncertainty) to restore impossibility without that assumption.

If you want, I can sketch the three adequacy conditions and three conclusions in plain English with a tiny diagram of how the proof structure forces the clash.