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:::3. The sentence seems redundant, given the already-existing sections covering limitations caused by human psychology and philosophical disagreements about interpersonal utility comparisons.
:::4. The sentence makes it sound like rated methods are exempt under a technicality, or there's a similar result applying to rated methods under a different name (like how Satterthwaite technically doesn't apply to cardinal methods, but Gibbard's theorem proving only a slightly weaker result still does). Arrow, Vickrey, and Harsanyi would all disagree with the claim, and argue these kinds of numeric scores are meaningful in a way that allows score voting to avoid independence failures (up to practical failures). (Sen also might agree, since I've seen him argue elsewhere that interpersonal utility comparisons are possible.) Balinski and Laraki also showed cardinal utilities or grades proportional to aren't actually needed for IIA, so long as voters are allowed to rate candidates independently (median ratings only require ordinal information). –[[User:Closed Limelike Curves|Maximum Limelihood Estimator]] 02:01, 21 April 2024 (UTC)
::::If you're using this citation to show that Arrow has changed his mind to that cardinal methods evade (i.e. aren't affected by) his own results, then it does not seem relevant to use this citation when discussing Sen's generalization. "Sen showed X, Arrow had an informal argument along these lines too, but later in life he changed his mind", makes it sound like the "later in life he changed his mind" part is relevant to the informal argument, which it isn't.
::::That's distinct from using the citation to reference that Arrow says that his own impossibility theorem does not apply to cardinal voting.
::::I now see you have removed the "informal argument" clause entirely, but I would like to restore it.
::::As for the rest, I've already given a summary above (under "Spoiler effects and IIA"), but I would like to add a few more points.
::::I am not proposing that the lead ''discuss'' the generalizations, only that it makes the reader aware that they exist. Actual discussion would take place in a separate section, not in the lead. If you'd like, we could add a contingency and say something like "generalizations exist that do apply to rated elections ''given additional assumptions''".
::::My point is basically the converse of yours.
::::There are many places on Wikipedia where a footnote or caveat about rated voting says "the IIA result only holds if voters don't change their scales", or something to that effect. These exist because the consensus seems to be that some people do change their scales. The generalizations formalize the argument that if they do, then the broader election does fail IIA, giving a theoretical backing relevant to the theorem for what's being informally expressed in the caveats (as well as elsewhere, in Approval papers discussing how to vote, mean utility, etc.; or even right here on this page with CRGreathouse saying "I grant that there are normalization issues with cardinal voting systems").
::::So your concern is that discussing generalizations in the lead would risk people thinking that the standard Arrow's theorem applies to rated voting. Mine is that not doing so would risk them thinking that rated voting ''elections'' pass, just because the systems do.
::::The reasons I gave under "Spoiler effects and IIA" give the theoretical relevance of the generalizations to Arrow's theorem. And the behavior seeming natural enough that there are caveats to this effect elsewhere indicate that it's practically relevant as well. Thus for two different reasons it deserves a more broad discussion than just a passing remark in the interpersonal comparison section. [[User:Wotwotwoot|Wotwotwoot]] ([[User talk:Wotwotwoot|talk]]) 11:17, 21 April 2024 (UTC)
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