Talk:Arrow's impossibility theorem: Difference between revisions
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: I would not say you are wrong but there are a few things you are missing. Most importantly is that Gibbard-Satterthwaite theorem is not Arrows theorem. Yes they are related but Gibbard-Satterthwaite is way more general. Arrows theorem talks about the specific criteria which will be failed. The importance of arrows theorem is that it shows that Ordinal systems must have one of the bad issues. Gibbard-Satterthwaite shows that all systems has some issue with strategy but it may not be a particularly bad issue. I realize that it is tempting to say all systems have issues but I think that is a misguided narrative because it implies that all issues are equally bad. All systems have trade-offs and some of the trade-offs are not worth it. The question is about what is the optimal balance. Most use Arrow as a way to say that Ordinal systems will not be monotonic and monotonicity is too important to trade away when cardinal systems exist. The narrative "Who cares if IRV is nonmonotonic? Arrows theorem shows that all systems will be nonmonotonic" is pushed by FairVote. It is wrong. Monotonicity is a core concept to fair voting. --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 00:26, 10 January 2020 (UTC)
:: [[User:Dr. Edmonds|Dr. Edmonds]], I think we agree on many things. For example, monotonicity is an important (and underrated) criterion for electoral systems. Furthermore, all systems have trade-offs, and some of the trade-offs are not worth it (we agree on that, too). But, I believe all rhetorical strategies also have trade-offs, and some are not worth it. Trying to jump through a loophole in Arrow's theorem just complicates the discussion in an unhelpful way. The [http://lists.electorama.com/pipermail/election-methods-electorama.com/2020-January/thread.html#2403 EM list discussion in January] (that stretched into February) didn't come to a consensus, but generally was sympathetic to [http://lists.electorama.com/pipermail/election-methods-electorama.com/2020-January/002403.html my original January 9 email]. I particularly appreciated [http://lists.electorama.com/pipermail/election-methods-electorama.com/2020-January/002425.html Forest Simmons' response on January 13], where he improves on my "no perfect car" metaphor. ''Even if'' cardinal methods are not subject to Arrow's theorem, there are plenty of other theorems that close the loophole described. If you still hold this position, could you make your case on [[EM list]]? -- [[User:RobLa|RobLa]] ([[User talk:RobLa|talk]]) 22:56, 16 March 2020 (UTC)
: If I may, I'd like to point out that one of the main reasons imo that it is interesting to say cardinal methods aren't affected by Arrow's Theorem is because this implies cardinal methods pass [[IIA]]. That is an argument some cardinal advocates make in favor of their methods (that this implies their voting methods are free of the spoiler effect, since candidates can enter and drop out of the race without changing the result). While that can be vigorously debated (for example, if any voter changes their scores for candidates who are present both before and after some candidates enter or drop out of the race, then cardinal methods fail IIA), it seems only right to put something on this wiki that helps the debate to happen. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 23:22, 16 March 2020 (UTC)
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