Talk:Arrow's impossibility theorem: Difference between revisions
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:::[[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)
:: [[User:Dr. Edmonds|Dr. Edmonds]], I find your selected quote unconvincing, for reasons that I described in [http://lists.electorama.com/pipermail/election-methods-electorama.com/2020-January/002408.html my January 9 response to "fdpk69p6uq"]. Note that "fdpk69p6uq" [http://lists.electorama.com/pipermail/election-methods-electorama.com/2020-January/002415.html replied to me on January 10] and then [http://lists.electorama.com/pipermail/election-methods-electorama.com/2020-January/002429.html Kristofer Munsterhjelm replied to both of us on January 14]. It may be worth bringing [[User:Kristomun]] into this conversation, but regardless, that particular interview didn't persuade me. -- [[User:RobLa|RobLa]] ([[User talk:RobLa|talk]]) 07:15, 19 March 2020 (UTC)
::: I think my vote here would be simple: we should let a mention of the possible/likely evasion of cardinal methods of Arrow's Theorem go to the top of the cardinal voting methods page, and then include a disclaimer "see below for controversy and discussion" linking to a more detailed section section. It doesn't seem right to not have this be very close to the top, since it's one of the major vectors of comparison between ranked and rated methods, and one of the biggest reasons someone would consider abandoning traditional voting theory results. Also, RobLa, I'm still interested in hearing why you took out the sentence saying "all pure cardinal methods pass the participation criterion", since you presumably don't have an objection to that. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 07:49, 19 March 2020 (UTC)
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