Talk:Arrow's impossibility theorem: Difference between revisions
→Finding EPOV on Arrow
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:: [[Dr. Edmonds]], quick point: STAR is covered by Arrow's Theorem. This is because it satisfies the majority criterion in the two-candidate case and thus fails IIA. So I recommend creating some terminology to cover only Approval and Score (and I think Majority Judgement also?) to ensure people don't get misled into thinking all cardinal methods are not covered by Arrow's Theorem. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 18:29, 18 March 2020 (UTC)
:::[[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] Semantics are important here. Arrow theorem was only for Ordinal systems when originally written. There have been extensions which would apply to majoritarian cardinal systems like STAR. Each of these extensions needs to be considered separately since they all have different assumptions. We should add sections to the arrow's theorem page for each and clearly spell out the differences in axioms to arrrow's theorem. There may be a way to write down a generalized arrows theorem which encompasses all extensions but I have never seen it. The formulation on the electo wiki page is the one for Ordinal systems only. It does not apply to score. --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 18:51, 18 March 2020 (UTC)
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