Talk:Arrow's impossibility theorem: Difference between revisions

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:::::: RobLa, I think it may be worth adding a point in response to yours. The goal of a wiki, imo, should be to capture all the sides of a debate to a good degree somewhere; otherwise, there is no resource left where readers can find unbiased information (or even, perhaps, know that there are any disputes about a certain thing). So in that regard, it is absolutely a good idea for us to document what different people say about cardinal methods in relation to Arrow's Theorem, why, and what each argument implies for the quality of the systems. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 02:46, 20 March 2020 (UTC)

:::: [[User:BetterVotingAdvocacy]] I think I more-or-less agree with your proposal. The "see below" bit is implied, so it may not be needed; everything in the summary should be covered in more detail in the latter part of the article. I removed the bit about the participation criterion because of the context that it was stated; it implied that cardinal methods don't violate any important criteria and minimized the significance of [[universality criterion]]. We don't have to have an exhaustive list of all criteria for the reader of the summary, but I don't want to leave the impression that cardinal methods pass all criteria. We still need to trim the introduction by quite a bit; we may need a general "criteria passed by cardinal methods" section (or some other similar name). -- [[User:RobLa|RobLa]] ([[User talk:RobLa|talk]]) 02:39, 20 March 2020 (UTC)

: Trying to think of my own position, I think mine is that under reasonable assumptions, cardinal voting violates IIA, and that this can be proven by arguments that lie very close to Arrow's theorem. (Basically, majority plus something at least as powerful as ranked universal domain violates IIA.) However, you can't use the literal Arrow's theorem, because Arrow's definition of universal domain ''restricts'' the voting method to be ordinal. On the one hand, people who say "Arrow doesn't apply to Range, so we can have IIA" are strictly speaking right. But unless the ratings are independently calibrated (as my EM post refers to), you get an IIA violation. "Arrow's theorem doesn't apply" simply says that the exact theorem can't be used on cardinal methods, but it doesn't prove that the method avoids IIA failure. There's a more general theorem hiding somewhere, but Arrow's is not it. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 12:26, 20 March 2020 (UTC)