Talk:Arrow's impossibility theorem/GA2

GA Review

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Nominator: Closed Limelike Curves (talk · contribs) 20:46, 27 May 2024 (UTC)

Reviewer: Randomstaplers (talk · contribs) 19:04, 18 August 2024 (UTC)

First off, I noticed a bunch of references in the lead. Ideally, they should be kept to a minimum to conform to the other GAs on Wikipedia.⸺(Random)staplers 19:07, 18 August 2024 (UTC)

• There are also a couple of broken references, which will have to be fixed.⸺(Random)staplers 19:33, 18 August 2024 (UTC)

Readability

I noticed you just linked to rational choice in the lead, and straight off the bat, you present mathematical proofs to the reader.

• People who read encyclopedias may not be well versed in the jargon: you have to keep in mind that readers won't know all the context related to voting theory.
• Anecdotally, I can tell you that most people won't click on any of the blue links.
• You might want to condense reactions to the theorem to its own section. Place it toward the front, so people will be engaged enough to read further in.

Now, although Warren D. Smith runs a very opinionated site, he has put out a pretty easy-to-follow explanation for Arrow's Impossibility Theorem. You might want to use that as a guide when rewriting this article.

• I have a feeling this might take some time, so I'll close it if no one has anything else to add.⸺(Random)staplers 19:24, 18 August 2024 (UTC)

Hi @Randomstaplers, I thought@Mathwriter2718 was handling the review? Besides that:

1. I'm happy to fix any broken references; which ones are you referring to?
2. I'm not sure what you mean by presenting proofs straight off the bat—the proof is a few sections later.
3. I think knowing what the words "rational" and "choice" mean should be good enough, since the article explains IIA; the link is just there for readers who want to learn more.
4. What do you think I should take from WDS's explanation?

Closed Limelike Curves (talk) 02:52, 19 August 2024 (UTC)

@Closed Limelike Curves well, apparently nobody took up the GAN review, so... you got me reviewing I guess.

• I believe the second reference is broken atm.
• Arrow's impossibility theorem#Preferences. The background is quite short, and there's a lot of blue links to other articles.
• If you open a physical copy of Encyclopedia Britanica, you won't have the luxury of blue links to other articles. And in fact, references to other articles are used sparingly. That's another reason why you should avoid blue links.
• The WDS link is there to show you that, IMO, it could be possible to simplify the intro a little bit, so you can get your point across in a clear manner.

You still have to fix up the lead though, so don't get ahead of yourself...⸺(Random)staplers 02:58, 19 August 2024 (UTC)

• @Closed Limelike Curves I guess I should clarify: blue links should be relied on sparingly. Links are cheap, we could put them anywhere we want, but we should make sure readers can deduce their meaning. The links are there so readers know where to look if they want more background information.

In my opinion... the examples, as much as reasonably possible, should be able to stand on their own.⸺(Random)staplers 03:22, 19 August 2024 (UTC)

@Closed Limelike Curves sorry it took me this long to reply to your August 13th message. I never intended to formally be a reviewer, since I think I am too involved in editing the page to be a reviewer. My hope was more just to help resolve issues I saw in the page. We have worked together to resolve nearly all of the issues I brought up. I personally still think my NPOV concerns about Arrovian IIA should be resolved before this page is a GA, but that's really for GA reviewers to decide. The current wording on the page is much milder and makes me feel much less concerned than I was a bit ago. I assume people won't want to parse that massive thread, so I will summarize my concern with the intention for it to be helpful for editors other than us. Please correct me if you feel I have misrepresented you.

Summary of concern: the first sentence of the current version of the article states that "Arrow's impossibility theorem is a key result in social choice showing that no rank-order method for collective decision-making can satisfy the requirements of rational choice". However, CLC and I disagree about whether this is accurate. I say that many economists explicitly disavow one of the "requirements of social choice" alluded to by this sentence, and there is not a literary consensus that that potential requirement should actually be considered a "requirement of social choice". CLC says that it really is a "requirement of social choice" even though some people disavow it, as the disavowers are casting about for second-best solutions now that it has been aknowledged that satisfying the real requirements is impossible. Part of this debate is whether Arrovian IIA should be conceptually merged with VNM IIA, which essentially everyone accepts. Mathwriter2718 (talk) 01:10, 20 August 2024 (UTC)

Readability ideas

@Closed Limelike Curves

Currently, the third paragraph of the lead says:

Arrow's impossibility theorem is a key result in social choice showing that no rank-order method for collective decision-making can satisfy the requirements of rational choice. Specifically, any such rule violates independence of irrelevant alternatives, the principle that a choice between A and B should not depend on the quality of a third, unrelated option C.
...
Despite this, some ranked methods are much more susceptible to spoilers than others. Plurality-rule methods like first-past-the-post and ranked-choice voting (RCV) in particular are highly sensitive to spoilers, manufacturing them even in center squeezes (where they are not forced). By contrast, majority-rule methods uniquely minimize the possibility of spoilers, limiting them to rare situations called Condorcet paradoxes. Under plausible models of voter behavior, such as the left-right political spectrum assumed by the median voter theorem, the spoiler effect can vanish entirely for Condorcet methods, though not for most other systems. As a result, the practical consequences of the theorem are debatable, with Arrow noting "Most [ranked] systems are not going to work badly all of the time. All I proved is that all can work badly at times."

This could be condensed down to something like:

In an election with three or more candidates, for example with candidates A₁, A₂, A₃, etc. and B, Arrow's impossibility theorem dictates that, should B drop out, voters cannot depend on the final rankings of the A candidates being the same as when B was in the race. Inexplicable shuffling of the A candidates when B drops out violates IIA...

A short description of plurality vs. Score/approval vs. RCV/IRV description (this one probably should not go in the lead, IMO, but might be helpful when trying to explain the voting methods in context of the theorem):

Plurality voting dictates that one opinion must be given to one candidate per voting ballot...

Score/approval allows the voter to give independent opinions to as many candidates as desired per voting ballot, in the form of voting for or against all or as many of the candidates on the ballot, or in the case of score voting, independently scoring each candidate on an arbitrary scale. In this example...

RCV/IRV dictates that one opinion must be given, unless the the opinion is to a candidate at risk of losing. In which case, the rank-order ballot instructs the tallier to transfer the one opinion the voter's second-liked candidate.

Opinions constitute the information received by the tallier, be it for one candidate, multiple, or one candidate with instructions on how to move it.
(And with this last example, the reader says: I get it now! Or not. Who knows, but at least we tried...)

Feel free to italicize as needed. Also, we should probably replace the words like "preference" with a word more universally known: "liked". "Most-liked", "second-most-liked", etc. Continued simplifications and good descriptions should make reading the article significantly easier.⸺(Random)staplers 04:24, 19 August 2024 (UTC)