Talk:Arrow's impossibility theorem

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My removal of the electionmethods.org link[edit source]

In the edit summary, Psephomancy added a link to an archived version of something posted on electionmethods.org:

* Discussion of Arrow’s Theorem and Condorcet’s method

...with the summary:

did you just remove it because it's a dead link?

Well, it was mainly that. The author (Russ Paielli) pulled the website down. It seems to me that we're not doing readers of this wiki much of service by offering an unannotated link to an archive of a webpage from 2005.

I agree with much of what that particular web page says. At some point, I'd like to perform a plagiarism-free restatement of some of the important arguments made on that page, rather than redirecting people to an old archived snapshot of a long defunct website. I think there was plenty of discussion about IIAC on the EM list when this page was first published. If I recall correctly, there was an essay or two on the old electionmethods.org that I contributed some prose to, but I can't remember which ones, and it might even be this essay. I'd have to dig up the very old email backups to find what I wrote.

In general, I've always been careful not to dismiss Arrow's result as irrelevant to my preferred method. As we've seen with w:Gibbard's theorem, the core principle of Arrow's theorem (i.e. there is no "perfect" voting system because many important criteria are mutually exclusive) holds true no matter the system. If I recall correctly, some of Russ's restatement of my writing implied I was dismissive of Arrow, and I didn't want to be associated with a dubious effort to declare Arrow's theorem irrelevant.

So thanks for digging up the archive link to that page. A little bit of annotation around that link would be wonderful. Hopefully an active Electowiki editor can perform the plagiarism-free restatement I was hoping for. -- RobLa (talk) 05:04, 8 January 2020 (UTC)

EPOV on Arrow and cardinal methods[edit source]

Just a bit ago, I posted a message to the EM list about Arrow's theorem and cardinal methods. I'll quote a little bit of the message here:

Many Score voting[1] activists claim that cardinal methods somehow dodge Arrow's theorem. It seems to me that *all* voting systems (not a mere subset) are subject to some form of impossibility problem. Arrow's impossibility theorem deserved great acclaim for subjecting all mainstream voting systems of the 1950s to mathematical rigor, and it's clear that his 1950 paper and 1951 book profoundly influenced economics and game theory for the better. His 1972 Nobel prize was well deserved. It seems that it has become fashionable to find loopholes in Arrow's original formulation and declare the loopholes important. Even if the loopholes exist, talking up those loopholes doesn't seem compelling, given the subsequent work by other theorists broaden the scope beyond Arrow's version.

I expand on these points quite a bit in my email. The full message is archived here: "(EM) Arrow's theorem and cardinal voting systems". I'm eager to read what the membership there thinks on this topic, since that group of people has frequently been successful at changing my mind on a particular topic. I'm also eager to read your response to my message (privately or publicly, via whatever mode of communication you prefer). -- RobLa (talk) 23:47, 9 January 2020 (UTC)

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. --Dr. Edmonds (talk) 00:26, 10 January 2020 (UTC)