Talk:Arrow's impossibility theorem: Difference between revisions
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: 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)
:: The Stanford article I linked, mentions some of the extensions. I think we should add sections to the page detailing these. It is important to say that these are not Arrow's theorem but extensions. They all have their own assumptions and limitations. As [[User:Kristomun|Kristomun]] says they come down to " majority plus something at least as powerful as ranked universal domain violates IIA". This means Score passes and so do several multimember score systems. It is really a restriction on majoritarian systems so maybe the title of the section should be "extensions to majoritarian systems". [[User:Psephomancy]] added a change to the page to clear up the wording and he added some references. --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 16:03, 20 March 2020 (UTC)
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