Talk:Instant-runoff voting

Center Squeeze

There seems to be some controversy about whether an old version of the "Instant-runoff voting" article that @Closed Limelike Curves restored (rev 1246893366) or if the current revision (rev 1247569260 as of this writing) is fine. Since I came to understand the center squeeze effect many years ago, it completely changed my perception of IRV. It seems we do a disservice to readers by not even mentioning the term in this article, and it seems to me that not only should it be mentioned, but it deserves at least a small WP:SUMMARY-style section of the article with a hatnote link to "Center squeeze". I may come around in a week or two and add said section, but given that the 2009 Burlington mayoral election seems to be a prime real-world example of center squeeze (not to mention the semi-fictional Tennessee example used in many electoral system articles), it seems difficult to justify a failure to mention "center squeeze" in this article and provide an example that helps explain it. It seems funny that neither version of the article uses the term "center squeeze", though the older version has the examples that help describe the phenomenon. -- RobLa (talk) 22:58, 3 October 2024 (UTC)

@Affinepplan per this section, there was previously agreement among non-canvased talk page participants to discuss center squeeze in the lead. Could you give your reasons for opposing this? – Closed Limelike Curves (talk) 22:07, 29 October 2024 (UTC)

1. I'd hardly say I was "canvassing" given that everybody pinged is already an active participant in this talk page and related articles
2. this topic is one editor without response so I'd hardly call that a positive "consensus"

but anyway, please do not put words in my mouth. I never protested the general idea of including comments about the possibility of center squeeze in the lead. I protested the POV manner in which you did so. To say that I am "opposing discussion of center squeeze" is just plain disingenuous. And you'll see in my latest diff that I did in fact leave the sentence intact "IRV also exhibits a kind of spoiler effect called a center squeeze"

What I am opposing is what you wrote to further go on and say that IRV somehow "favors extremists." While I understand why you think this is true --- largely based on evidence from IC models and spatial models --- that is quite a strong statement that demands a high bar of evidence. And I think given IRV's long history of widespread use, if such a statement is true then you need to provide evidence from *real* elections and *real* cultures rather than what is basically just Monte-Carlo-driven speculation.

And furthermore, you need to show that this is true in aggregate / average and not just cherry pick examples or single case studies. Just because a statement appears in a peer-reviewed work does NOT mean that it is scientific consensus. I have seen studies that suggest IRV disadvantages candidates near the middle of the policy spectrum, but I have also seen some suggesting that it succeeds in enabling candidates to cross-cut partisan cleavages and find new coalitions, and I have also seen some suggesting that it makes little difference in the outcomes of elections one way or the other.

Wikipedia should be 1. neutral 2. technical 3. not original research or opinion blogs. I understand that you have a bone to pick with IRV. I am not exactly its biggest fan either. But the lead of the Wiki article on IRV is not the right place to express those opinions. Affinepplan (talk) 22:18, 29 October 2024 (UTC)

And you'll see in my latest diff that I did in fact leave the sentence intact "IRV also exhibits a kind of spoiler effect called a center squeeze"

Thanks, I'd missed that.

While I understand why you think this is true --- largely based on evidence from IC models and spatial models --- that is quite a strong statement that demands a high bar of evidence. And I think given IRV's long history of widespread use, if such a statement is true then you need to provide evidence from *real* elections and *real* cultures rather than what is basically just Monte-Carlo-driven speculation.

I mean, the main reason I think that's consensus is just the median voter theorem. I think mathematical proof is quite strong evidence.

I understand that you have a bone to pick with IRV. I am not exactly its biggest fan either. But the lead of the Wiki article on IRV is not the right place to express those opinions.

I don't have very strong opinions about IRV. I just like explaining math and economics clearly, and this is the particular math/econ topic I've been working on recently. Prior to this, I did a lot of editing in statistics. (And once I'm satisfied with the quality of this corner of Wikipedia, chances I'll probably go back to that.) – Closed Limelike Curves (talk) 00:39, 30 October 2024 (UTC)

> the main reason I think that's consensus is just the

median voter theorem

.

the median voter theorem doesn't imply "IRV favors extreme candidates" in any way shape or form, and that fact is emphatically

not

scientific consensus.

Affinepplan (talk) 00:45, 30 October 2024 (UTC)

Fully agreed here. The median voter theorem (i) does not tell us anything about IRV and (ii) is not evidence for any behaviour in real world elections as preferences are not typically single-peaked. To go from that to "IRV favors extreme candidates" seems like quite a stretch. Jannikp97 (talk) 06:31, 30 October 2024 (UTC)

Preferences are typically "single-peaked enough". (All models are wrong, but...) – Closed Limelike Curves (talk) 23:41, 31 October 2024 (UTC)

I think one of the reasons there's a lot of pushback for the specific phrasing is that extremist is quite a strong label, and would fall under "value-laden" or "contentious" under our style guide (MOS:CONTROVERSIAL). I would recommend against using it unless there is clear consensus in reliable sources to use the exact term. It's also not very well defined. Like, how extreme is extremist?

Obviously, that depends on the number of candidates, but in a three-competitive-candidate race, after eliminations, the minimum proportion of highest-remaining-preferences after transfers to squeeze a candidate out is 26%, when the electorate is divided 26-25-49 and the first two candidates form a mutual majority. Candidate 1 might be more extreme than candidate 3 or 2 in this case (candidate 2 being the moderate candidate winning 25%, and candidate 3 being a more clearly partisan candidate on the other side) but can we really label candidate 1 extremist when they won 26% support, and also a signifcant portion of candidate 2's next preferences? Alpha3031 (t • c) 07:45, 30 October 2024 (UTC)

TBF I think the Nazis got ~⅓ of the vote in the last somewhat-fair Weimar elections. The term "extremist" is common in the literature, but I agree with your general point that there's probably some better word we could find, that makes it clear we're speaking in relative terms. – Closed Limelike Curves (talk) 23:29, 31 October 2024 (UTC)

The informal mathematical claim that IRV favors extremists seems like a fair summary of various well established results. On the other hand, I have not seen evidence that there is consensus on the frequency of changes in election outcomes due to this or on the correspondence between political and mathematical definitions of extremist. It also seems odd to mention center squeeze without mentioning that other election methods are also susceptible. This makes it seem like at least a controversial claim in political science.

Can we say "Like some other commonly-used systems, IRV also exhibits a kind of spoiler effect called a center squeeze, which can prevent the election of a Condorcet winner"? This seems like it correctly summarizes the mathematical result without making empirical claims. McYeee (talk) 05:54, 30 October 2024 (UTC)

I think that's a good phrasing for it. Alpha3031 (t • c) 07:33, 30 October 2024 (UTC)

> seems like a fair summary of various well established results.

no it does not. Affinepplan (talk) 13:04, 30 October 2024 (UTC)

I like the general idea, but I'd suggest two changes—

1. "Like some other commonly-used systems" should be specific about exactly which systems are meant ("Like plurality & two-round").
2. The reference to a "Condorcet winner" adds an unfamiliar technical term into the lead, and also removes the reference to ideology. While a social choice theorist might be able to pick up on how this relates to the median voter theorem, most people probably won't. This one's a bit trickier to resolve, but one possibility would be to replace "extremist" with a term that's more clearly relative, e.g. talking about "more-extreme candidates".

– Closed Limelike Curves (talk) 23:08, 31 October 2024 (UTC)

Removing the reference to ideology seems like a good thing to me, unless we have sources saying that ideology correlates with voting patterns in the way you imply. McYeee (talk) 02:08, 1 November 2024 (UTC)

I'm a bit confused what you mean by voting patterns here, could you clarify? I think all the papers discussing this issue do actually refer to the winners as "extreme", "extremist", etc., but I don't think we have to adopt some exact wording just because all the sources use it. I think the main issue with "extremist" is it doesn't clearly specify that it means "more extreme than other candidates, relative to the center of public opinion". – Closed Limelike Curves (talk) 03:54, 1 November 2024 (UTC)

Would "more-polarizing" candidates be a better alternative? – Closed Limelike Curves (talk) 17:06, 1 November 2024 (UTC)

> "more-polarizing" candidates be a better alternative?

absolutely not. because polarization and partisanship in elections is

1. something that is studied frequently, in many contexts from many angles, by many scholars, across many types of elections and demographics and
2. said studies have not whatsoever conclusively found that the use of IRV is associated with an increase in polarization and partisanship

Affinepplan (talk) 17:27, 1 November 2024 (UTC)

Increase relative to what? It's been studied a ton, you're right. Generally, the finding (in the American context) has been little-to-no difference from FPP or two-round, like we discussed in the section on empirical research. (i.e. It has roughly the same polarizing effects as those rules.) – Closed Limelike Curves (talk) 18:57, 1 November 2024 (UTC)

> Generally, the finding (in the American context) has been

I'm aware of only one study on partisanship of electoral outcomes under IRV in the US. Maybe you are referring to the same one? I certainly wouldn't conclude "generally" the finding has been. I think the only thing that is fair to say that has been "generally" found is that more research is needed. Affinepplan (talk) 19:20, 1 November 2024 (UTC)

problems with IRV article

IRV is not pluralitarian - its whole goal is to see majority choice elected, even if tht majorty choice has to based on vote tallies after votes are transferred from first choices.

it should not be lumped into same family of systems as FPTP. for one thing in FPTP votes are never transferred so the article is clearly wrong when it says that FPTP is like IRV for that reason.

not all IRV vote counts proceed to where there are only two candidates. they do proceed to point where one candidate has amasssed majority of votes (or majoierty of vots still in play at that point) no matter how many other candidates are still in running. therefore IRV is majoritarian, not pluralitarian.

yes eliminations are based on relative vote tallies - the least-popular, no matter how many votes he or she, has is eliminated, but that hardly makes it same as FPTP.

the imporatance of the elimination of the least-popular is that their votes are transferred but that is not mentioned in first paragraph when eliminations are introduced.

edits (quickly reverted) performed on October 16 tried to make these changes.

68.150.205.46 (talk) 05:10, 17 October 2024 (UTC)

Unfortunately, that line of reasoning has a problem because it can be reduced to absurdity. Consider a version of IRV where the process stops if anybody has more than 67% of the first preference votes, or otherwise keeps going until every candidate but one has been eliminated, at which point the remaining candidate has 100% of the first preferences. The threshold for that method is a 2/3 supermajority. But it seems absurd to say that the method ensures a 2/3 supermajority winner. 2A01:799:1511:E300:D6E9:1083:E302:8CF3 (talk) 11:39, 17 October 2024 (UTC)

You just described why it is not majoritarian and why pluralitarian is a correct word for it.

-What is the elimination based on? plurality (imagine every round as a snapshot of single non transferable vote - yes votes are transfered in between, but that is still first-preference plurality since you don't look at the excluded candidate)

-It doesn't matter if it doesn't go until there are two candidates. That is just making counting quicker. It's a simplification by maths. The 50% is not a meaningful quota like in STV. If it was 40%, that would be another case, but then it would even more so not be majoritarian

-IRV does not fulfil the majority rule of social choice theory

-the fact that it goes to 2 candidates only means it won't elect a majority loser, but that is not the same as electing a majority winner

-it is based on later-no-harm, therefore primacy of first-preferences. This also makes it closer to simple plurality than many other systems.

-nobody said it is the same as FPTP

+the word majoritarian is misleading anyway - people incorrectly use it for plurality, winner-take-all and single winner district based systems. Rankedchoicevoter (talk) 13:24, 17 October 2024 (UTC)

@180 Degree Open Angedre: I'm restoring the prior version for now; if you disagree, you can discuss this here. It seems like the majority opinion on this topic is that A) RCV is best described as non-majoritarian, and B) removing discussion of batch elimination is less likely to confuse people. In particular, there doesn't seem to be any reason not to postpone the discussion of early stopping or batch elimination to later in the article, since RCV can be perfectly well-defined without any mention of it.

(There's also no rule against linking to stubs on Wikipedia, but I've removed the link anyways while I expand the article.) – Closed Limelike Curves (talk) 16:16, 28 October 2024 (UTC)

I agree that generally speaking a description of batch elimination is not really necessary for the intro. That is really just an implementation option. However, is there currently or has there ever been any jurisdiction that used instant runoff that would not immediately elect the candidate that had amassed a majority of the valid (non-spoiled, non-exhausted) top-preference votes, and instead just keep on going? If you can find one counterexample, then sure, but otherwise it would just appear to me that what you call "early stopping" is just a part of the method.

Also primaries and runoffs are not the same thing. At best there is a superficial similarity between a very specific type of primary (the nonpartisan jungle primaries) and a runoff system, but even you should not be dropping in partisan or regular open primaries into comparison, and especially not into the opening paragraph. That's just misleading.180 Degree Open Angedre (talk) 16:28, 28 October 2024 (UTC)

Alaska uses this variant. An example can be found here from the 2020 Democratic primary in Alaska.

I understand you may still disagree with this, but for now the majority view seems to be otherwise. There's also a lot of sources disputing or disagreeing with the idea that RCV represents some kind of majoritarianism, so I'd advise against another revert or it may be counted as edit warring. – Closed Limelike Curves (talk) 02:38, 29 October 2024 (UTC)

Why do you think that your view is the "majority" view? It does not appear so to me. You should probably try to convince, if not me, then the other editors, rather than just assume that everyone else agrees with you. 180 Degree Open Angedre (talk) 12:56, 29 October 2024 (UTC)

Because, in this thread, there are 3 or 4 editors who agree with this change and 1 who disagrees without having been canvased. – Closed Limelike Curves (talk) 15:08, 29 October 2024 (UTC)

Which change specifically? Your edits are so large in scope that there are multiple portions that I take issue with. Like referring to instant runoff as being similar to a primary. Or grouping it under a brand new pluralitarian family article that is based on one source entirely. Amongst many others. If you did your edits in a more organized fashion it would be more productive to discuss, but you've made a lot of significant, misleading changes, many of them in the lede of the article, often within a single edit that it's difficult to keep track of all of the issues in a single discussion. I doubt that you have a real majority for all of them. 180 Degree Open Angedre (talk) 17:01, 29 October 2024 (UTC)

Over at the Talk:Two-round system there was already a discussion about whether to merge two-round runoffs and primaries, and at least there, the result was that there was no consensus on this. So, it appears that no, a majority of editors do not agree with your opinion, for at least that part. 180 Degree Open Angedre (talk) 19:02, 29 October 2024 (UTC)

I'm talking, specifically, about describing RCV as pluralitarian or plurality-rule style.

To a lesser extent, I'm also talking about describing it as going down to 1 candidate, which I think @Rankedchoicevoter and @2A01:799:1511:E300:D6E9:1083:E302:8CF3 seemed to agree with (with both describing the 50% bar as an implementation detail and a special case of batch-elimination, rather than a real threshold). Your comment here suggests the same:

However, is there currently or has there ever been any jurisdiction that used instant runoff that would not immediately elect the candidate that had amassed a majority of the valid (non-spoiled, non-exhausted) top-preference votes, and instead just keep on going? If you can find one counterexample, then sure,

but you seem to have ignored the counterexample I provided. – Closed Limelike Curves (talk) 19:30, 31 October 2024 (UTC)

@Rankedchoicevoter and @2A01:799:1511:E300:D6E9:1083:E302:8CF3—can you verify that I've interpreted your arguments correctly? i.e. the first paragraph should avoid discussing early stopping or batch-elimination (which should be moved to the second section)? – Closed Limelike Curves (talk) 19:12, 1 November 2024 (UTC)

It looks like you're conflating their hypothetical argument for why instant run-off isn't majoritarian, which is a separate debate, with yours that the method should not include "early stopping", which is a part of the method, but which you seem to have some sort of issue with including in the description for some reason. 180 Degree Open Angedre (talk) 19:23, 1 November 2024 (UTC)

I also forgot to add, some of the information that you're adding in the lede that is already covered later on in the article. Copy and pasting it back into the lede is just making the article redundant 180 Degree Open Angedre (talk) 17:15, 29 October 2024 (UTC)

Please see Wikipedia policy on this, which is that the lead follows the information in the body. Often this results in overlap between material in the body and in the header. I agree exact duplication isn't ideal, but the discussion I placed in the lead is already written in a summary format; it should instead be expanded in the body. – Closed Limelike Curves (talk) 19:37, 31 October 2024 (UTC)

If the lede follows the body, then what you're trying to do is exactly backwards. Expand what is covered in the body first before summarizing, instead of copy and pasting. 180 Degree Open Angedre (talk) 19:25, 1 November 2024 (UTC)

I don't think there's any requirement for information in the to be written differently from, and in fact Wikipedia explicitly maintains a transclusion feature for including the same text multiple times in an article. – Closed Limelike Curves (talk) 19:45, 1 November 2024 (UTC)

I think you should try reading over that page again. It seems to me that you've misread it. It refers generally to content appearing multiple times in different pages, templates or references. For Help:Transclusion#Repetition within a page, it makes reference to articles that are already very repetitive, such as ones with lists, and recommends the creation of a template to have the repeating text. I don't think that applies in this context. 180 Degree Open Angedre (talk) 20:01, 1 November 2024 (UTC)

I'm not sure what you think I've misread here. My point is just that, because the lead is a summary of the body, the lead may sometimes repeat text found in the body, and Wikipedia does actually allow for repeating the same text within a page. I don't think there's any issue with editing it to avoid that repetition, but cutting all the information about empirical research on RCV from the lead isn't the right way to do that. – Closed Limelike Curves (talk) 21:40, 1 November 2024 (UTC)

Is it even correct to use the word "majoritarian" to describe a single-winner system? I'm used to hearing it contrasted with, for example, proportional representation. McYeee (talk) 19:38, 28 October 2024 (UTC)

"Majoritarian" is sometimes used as a synonym for winner-take-all representation, particularly in political science. In social choice, "majoritarianism", "majority-rule", or a "majority winner" generally refers to Condorcet's majority-rule principle—someone is a majority-preferred candidate if most voters prefer them to each one of their opponents. – Closed Limelike Curves (talk) 03:11, 29 October 2024 (UTC)

IIA does not imply "vulnerability to strategic nomination / withdrawal"

@180 Degree Open Angedre wrote

> As instant runoff fails independence of irrelevant alternatives, it is vulnerable to some extent of both strategic nomination and strategic withdrawal

I would just say more plainly "Instant runoff voting may be manipulable to some extent via strategic candidate entry and exit." it is not really true IMO that IIA failure implies that strategy is necessarily possible. for example imagine a rule that just picks randomly between every pair of candidates based on some seed that depends on the size of the candidate sets. obviously this is both a failure of IIA and impossible to take advantage of for profitable manipulation via candidate entry/exit Affinepplan (talk) 17:29, 25 October 2024 (UTC)

Thanks for the correction. I'll change it to that if you haven't already 180 Degree Open Angedre (talk) 17:47, 25 October 2024 (UTC)

Can you define what you mean strategic nomination? I would have thought that the strategy of nominating a large number of clones of a Condorcet loser would be a profitable strategic manipulation by candidate entry and that nominating or withdrawing candidates to change the seed would be profitable by entry or exit respectively. See also the definition of strategic nomination given here which I think matches my intuition. McYeee (talk) 18:32, 25 October 2024 (UTC)

this is exactly my point. a statement like "IIA implies vulnerability to [...]" requires significantly more context and conditions and definitions and mathematically proofs etc. than is appropriate for just saying it in passing. Affinepplan (talk) 18:45, 25 October 2024 (UTC)

Does it actually require that context? I can say that given any polynomial f, the integral $\textstyle \int _{0}^{1}f(x)dx$ is well defined without saying whether I mean the complex-valued Riemann integral or the real-valued Lebesgue integral. I wouldn't be opposed to more context in this article, but the lack of context doesn't seem like a reason for removal. More explicitly, I'm not aware of any reasonable set of definitions of those terms that makes the statement false. McYeee (talk) 19:29, 25 October 2024 (UTC)

`A => B` is equivalent to `B or not A`

in this case, `B` is pretty much always true that in some sense every voting rule under most reasonable models of voter behavior admits some opportunities for profitable manipulation via candidate entry/exit.

so `B or not A` is just `B` here. that is to say, "IIA implies vulnerability to strategic manipulation" is only as true in the way that "the sky is blue implies vulnerability to strategic manipulation" is true. Affinepplan (talk) 19:42, 25 October 2024 (UTC)

Every voting rule under most reasonable models of voter behavior admits some opportunities for profitable manipulation via candidate entry/exit

I get it now. To quote Thomas Henry Huxley, "How extremely stupid of me not to have thought of that"! McYeee (talk) 19:56, 25 October 2024 (UTC)

You wouldn't be stupid not to have thought of that, because it's not correct. IIA is very explicitly defined as "the results not changing when a candidate enters/leaves the race". There are a wide variety of voter models where there is no strategic nomination incentive. The article on Arrow's impossibility theorem details these cases, e.g. rated voting rules and the left-right voter ideology model, where Condorcet methods pass thanks to the median voter theorem). (cc @RobLa.) – Closed Limelike Curves (talk) 20:20, 25 October 2024 (UTC)

yes clearly I'm aware of the definition of IIA.

but my statements remain true.

Approval is IIA yet under many "reasonable" models of behavior there are incentives for strategic entry / exit. the randomized rule I gave above is not IIA yet there are not such incentives in expectation.

@Closed Limelike Curves I am trying to be empathetic to the fact that it seems you have zero formal education in this domain, but it's hard to remain empathetic when you come into every discussion with such arrogant-yet-sophomoric statements. Please read beyond Electowiki and a few Tideman papers before declaring that you know everything. Affinepplan (talk) 20:28, 25 October 2024 (UTC)

That's a bit harsh. I'm the one who made the edit this time, in any case. 180 Degree Open Angedre (talk) 20:37, 25 October 2024 (UTC)

to be clear, I'm referring to his reply here. not the original edit. yes, it is harsh, but I'm a bit exasperated with the constant POV pushing and lack of technical expertise. Affinepplan (talk) 20:41, 25 October 2024 (UTC)

Is it a correct summary of your point to say that approval only passes IIA because IIA is defined in terms of fixed ballots rather than fixed reasonable voters? McYeee (talk) 21:01, 25 October 2024 (UTC)

I guess, sure. IIA is a mathematical property of a function. "vulnerable to strategic nomination" is vague & normative statement that relies on a lot of assumptions about the model and context, so I think the two are not very comparable. Affinepplan (talk) 21:08, 25 October 2024 (UTC)

Approval is IIA

Whether or not approval is IIA depends strongly on your model of voter behavior and the precise definition of approval voting. In models where it does satisfy IIA (i.e. the dichotomous preference model or a fixed absolute threshold) there is no incentive for a losing candidate to enter or exit, by the definition of IIA. – Closed Limelike Curves (talk) 21:08, 25 October 2024 (UTC)

it depends on nothing. Approval is IIA full stop. it has a mathematical definition that is satisfied by Approval.

please stop spreading misinformation about technical subjects you do not understand. This idea that IIA somehow depends on voter behavior, beliefs, and strategy is just a common misconception among the amateur election reform community. Affinepplan (talk) 21:12, 25 October 2024 (UTC)

In this I actually agree with CLC. Approval voting with voters who express their honest preferences is IIA. But approval voting, as it is generally defined, has no mechanism to force honest preferences. In the presence of strategic voters (which is to say, always), the relative performance of two candidates in approval voting will depend on the presence or absence of third candidates, so approval voting does not obey IIA. —David Eppstein (talk) 21:30, 25 October 2024 (UTC)

Approval with voters who express any preferences, honest, strategic, whatever is still IIA if we're just considering the typical definition for choice functions.

if we want to use the term IIA more loosely to refer to the principle "A > B should not depend on C" then yes I think we are all in agreement that individuals may alter their response depending on the available alternatives.

this is a case of the codification from loose principle --> formalism being a bit underspecified I suppose? in any case even if using the looser formulation I would not recommend the original wording of the edit, as the technically accurate statement would be that IIA failures mean there exist *any* profiles on which profitable manipulations can occur, but I imagine most readers will interpret "vulnerability to strategy" to at the very least be, say, an efficiently computable strategy that doesn't rely on perfect information. Affinepplan (talk) 21:39, 25 October 2024 (UTC)

Approval only satisfies IIA if the voters are forced to express their preference for each candidate without any knowledge of which other candidates are present. Such a system is impossible: after you have asked the voter's preference for one candidate, that voter will remember that the candidate is present and will be unable to formulate an independent preference for other candidates.

So the system you are calling IIA is a system that does not exist. —David Eppstein (talk) 21:43, 25 October 2024 (UTC)

There's practicalities and menu effects in real life for sure. However, @Affinepplan is talking from a social choice perspective, which abstracts away these kind of details.

In its most highly-generalized sense, a social welfare function is a multivariate function that takes a bunch of k-dimensional, real-number vectors as inputs. Then, it outputs another k-dimensional vector representing each candidate's "final score" or "quality". For example, FPP gives candidate i one point for each voter who gives them the highest rating.

With this formal definition, we can give a formal definition of IIA: it says that if any of the input vectors changes in the i-th place, the output only changes in the i-th place. – Closed Limelike Curves (talk) 22:13, 25 October 2024 (UTC)

this is not how I would define it formally. see the below comment. Affinepplan (talk) 22:20, 25 October 2024 (UTC)

You can give different definitions; I selected this one as the most general possible definition. A somewhat more common definition is given in the article on Arrow's theorem. – Closed Limelike Curves (talk) 22:28, 25 October 2024 (UTC)

Approval voting with voters who express their honest preferences is IIA. But approval voting, as it is generally defined, has no mechanism to force honest preferences.

More than that, the issue is approval voting has no unique definition of "honest voting". Here are at least 5 different ways you could reasonably formalize "honest" approval voting:

1. FPP, but with a tied-at-the-top rule (if two candidates are equal-ranked first, both get a point). In that case, honest approval behaves like FPP.
2. The opposite of that (anti-plurality with a tied-at-the-bottom rule).
3. Anything in-between (there's nothing special about either first or second ranks, we can pick a different cutoff).
4. All candidates with a rating above 50% are given one point.
5. Voters choose some approval threshold at random.

These rules are all the same from the standpoint of mechanism design, because the available strategy profiles are the same. However, they're not equivalent from the standpoint of social choice, so we have to specify which of these 5 "different" rules we're discussing. The last 2 satisfy IIA, the first 3 don't. – Closed Limelike Curves (talk) 21:55, 25 October 2024 (UTC)

Does anyone have a good citation for the formal definition of IIA in this context? It would save us a lot of arguing. McYeee (talk) 21:37, 25 October 2024 (UTC)

see above comment. I think the very crux of the disagreement is the conflation of the formal definition and the broader principle behind that definition. Affinepplan (talk) 21:39, 25 October 2024 (UTC)

I get that, but what is the formal definition of IIA? If you point to a WP:RS that shows that gives the definition you mention, that'll save us a lot of time. McYeee (talk) 21:43, 25 October 2024 (UTC)

Let's take a step back and ask for a formal definition of a voting system. Affinepplan seems to imagine a system that goes from the utilities hidden in voters' heads directly to an outcome via a mathematical function, without the intermediate step of actually voting. I don't think that can be called a voting system. —David Eppstein (talk) 21:50, 25 October 2024 (UTC)

I like the definitions here https://arxiv.org/abs/2008.08451 which includes a discussion on the many forms of IIA

I do not mean to suggest that these are the only axioms reasonable to take. but formalism has been requested and I will provide.

tl;dr

• there exists some infinite set C and X of candidates and voters
• a profile P is a map P: C --> L(X) for C, X finite nonempty subsets of C, X
• L is a linear order
• a voting method is a map F from a profile P to a subset F(P) < P
• f satisfies Independence of Irrelevant Alternatives (IIA) if for any (V, X)-profiles P and P′ and x, y ∈ X, if P|{x,y} = P′|{x,y}, then x defeats y in P according to f if and only if x defeats y in P′ according to f

to your credit, the authors here do specify that L is a strict linear order, whereas I was implicitly assuming an extension to a weak order (and in fact for approval it must be dichotomous); I apologize for making that assumption without clarifying. however, the authors also state that these definitions are straightforward to apply when L must be dichotomous. so after doing so, it is clear that Approval is IIA.

What I am hearing from your argument, please tell me if this is wrong, that Approval cannot be IIA because it is simply not possible to generate dichotomous preferences over a finite set of candidates without knowing the membership of that set. I would agree with that, but I would also not say that makes Approval "fail" IIA I would say that makes IIA "not applicable without further clarification" Affinepplan (talk) 22:19, 25 October 2024 (UTC)

> the authors also state that these definitions are straightforward to apply when L must be dichotomous

correction: they state this about weak orders, not specifically dichotomous Affinepplan (talk) 22:20, 25 October 2024 (UTC)

The article on Arrow's theorem should contain references to Arrow's paper, which includes the original definition of these terms. The definition I gave, which is more general, can be found in Balinski and Laraki's 2011 book on Majority Judgment. – Closed Limelike Curves (talk) 22:25, 25 October 2024 (UTC)

Lede once again has turned into a soapbox

@Closed Limelike Curves please, stop vandalizing social choice articles with your agenda. it's really exhausting to have the same battle over and over again across dozens of articles.

I really don't have the energy to go through a DRN. but I'm going to tag @David Eppstein @180 Degree Open Angedre @Mcyeee @Sarek Of Vulcan @Wotwotwoot for visibility Affinepplan (talk) 18:16, 29 October 2024 (UTC)

They are arguing with me that somehow a majority of editors agree with all the changes made in their 12000+ character dump in the lede, under the "problems with IRV article" talk section, but I find that hard to believe. Quite a bit of what they are trying to add back in bulk has already been either moved around to other parts of the article, reworded or removed, by other editors. In any case, I don't think this is appropriate editing etiquette, especially for an editor already facing an WP:AN/I for this repeated behavioral pattern. 180 Degree Open Angedre (talk) 18:30, 29 October 2024 (UTC)

> majority of editors

is there even one? lol Affinepplan (talk) 18:37, 29 October 2024 (UTC)

The ANI thread is for the unrelated question of whether I made too many page moves. (And I would have started with a talk page discussion, to be honest.)

They are arguing with me that somehow a majority of editors agree with all the changes made in their 12000+ character dump in the lede,

First: calling a revert a "12,000+ character dump in the lede" is extremely misleading.

Second: I said that a majority of editors were in favor of the first paragraph, which places IRV in the context of other plurality-with-elimination rules. If you have disputes with the first paragraph, you can make an RfC to get more external opinions—my impression of the thread at § Problems with the IRV article is that most participants agreed the article should discuss the similarities of IRV with other families in the plurality family (including @Rankedchoicevoter and at least one IP). If you have disputes with the 3rd-5th paragraphs, you can create a new talk page section to discuss these changes. If this doesn't yield a new consensus, you can open a dispute resolution (like I previously attempted) at WP:DRN. – Closed Limelike Curves (talk) 20:36, 29 October 2024 (UTC)

> If you have disputes with the 3rd-5th paragraphs, you can create a new talk page section to discuss these changes.

as you are the one trying to add these, you bear the burden of reaching consensus. feel free to create a talk page section if you like. in the meantime I've removed at least the most egregious POV. Affinepplan (talk) 20:38, 29 October 2024 (UTC)

If you have disputes with the 3rd-5th paragraphs, you can create a new talk page section to discuss these changes.

In the spirit of WP:AGF, I will assume that you simply forgot your initial message pinging me to that problems with IRV article thread and will share it with you here:

@180 Degree Open Angedre: I'm restoring the prior version for now; if you disagree, you can discuss this here.

And I'm sorry, but no, this [1] is not just a minor reversion. At first I tried to discuss some of the things that I disagreed with there, as you had asked me to. But first you fell back on "a majority of editors" siding with your opinion, and now you say that, no, I was just supposed to respond to only your first paragraph and none of the other many, many additions that you've made in this. I don't even disagree with using the description of plurality with eliminations, so that's not even one of my problems here. Now it feels like I have just wasted my time. 180 Degree Open Angedre (talk) 21:11, 29 October 2024 (UTC)

Hi 180, I totally understand why you might be feeling confused or exhausted, and I'm very sorry about that. I think I was unclear about what specifically I was asking for. Communication can be difficult. Right now, the first thing I'm trying to do is break the dispute down into single issues or disagreements, so we can discuss each one separately in its own section. If we jumble everything together, we're probably going to end up arguing in circles.

So far, I've seen you raise objections to describing IRV as belonging to the plurality-rule family, so I directed you to the section where we discussed. I think the talk page section where I pinged you is an appropriate place for discussing that specific question—"Can we describe IRV as falling into a plurality-like family of rules"? The consensus there seems to be yes. That consensus can change, however; particularly if you provide enough reliable sources to convince most other editors this is wrong, or if you suggest some alternate wording that both sides can agree on.

If you have objections to other parts of the article, those should probably go in their own separate sections, so we can keep everything focused on answering a single well-defined question. For example, "How should we describe the rate of spoiled ballots?" or "Should this sentence be removed from the lead and placed in section X"?

On the revert: I've tried restoring Sarek's last version, then breaking my changes down into two disjoint sections. This should make them smaller and easier to read. (Keep in mind that Wikipedia's character counts include citations, and it looks like some of the citations were duplicated when I did this, so the character counts are probably off.)– Closed Limelike Curves (talk) 23:46, 29 October 2024 (UTC)

There's an active ANI at Wikipedia:Administrators'_noticeboard/Incidents#Bold,_or_disruptive? if you'd like to leave a comment there. It might be more of a conduct thing than a content thing anyway. Wotwotwoot (talk) 18:38, 29 October 2024 (UTC)

At the very minimum, Closed Limelike Curves, I'd like you to consider reducing or bundling (WP:CITEBUNDLE) any instances where you have added more than one inline citation to any statement in the lead. mixed reception among political scientists and social choice theorists. has 4 footnotes each, whereas the same text in the body only has two. There is absolutely no reason to do that unless the citations used are terrible (in which case the text probably should not be in the lead in the first place). Also, I see you've pointed it out yourself, but at least try to deduplicate your references before you hit the publish button? Finally, I will be removing the reference to The Hill and rewriting that sentence unless you do so first, no comment yet on any of the other additions. Alpha3031 (t • c) 23:52, 29 October 2024 (UTC)

At the very minimum, Closed Limelike Curves, I'd like you to consider reducing or bundling (WP:CITEBUNDLE) any instances where you have added more than one inline citation to any statement in the lead.

Got it, will do. Are two side-by-side citations OK? Sometimes I give them in pairs of closely-related sources, in which case I think bundling the pairs could work nicely. (e.g. there's a case where I cite the New America Foundation report and then a blog post by one of the authors, Lee Drutman, where he gives his takeaways from writing the report more simply.)

Also, I see you've pointed it out yourself, but at least try to deduplicate your references before you hit the publish button?

Yep, sorry, didn't notice until after I did that—I should've been more careful. (I'm in visual editor, where the only indication of references being duplicated is some tiny numbers changing slightly, and which IME has an annoying tendency to duplicate references at the drop of a hat.)

Finally, I will be removing the reference to The Hill and rewriting that sentence unless you do so first, no comment yet on any of the other additions.

No objections to removing if you want. Another option is bundling it with Atkinson & Ganz 2023, like I'm thinking of doing with Drutman's report (the "fully" reliable source) and blog post. It's basically the same situation (Atkinson & Ganz wrote a paper, then an op-ed describing the key takeaways from their research). – Closed Limelike Curves (talk) 00:27, 30 October 2024 (UTC)

request for page protection

since CLC is seemingly unable or unwilling to stop POV pushing and edit warring, I've filed a request for page protection here Wikipedia:Requests for page protection/Increase#Instant-runoff voting Affinepplan (talk) 00:24, 30 October 2024 (UTC)

Hi, left a comment saying I'd be cool with page protection, especially if we can open a dispute resolution process at the same time. You mentioned not feeling up for starting the procedure right now, so I'm open to postponing the DRN for a week or two in case you're busy. Thanks! – Closed Limelike Curves (talk) 19:23, 30 October 2024 (UTC)

mention of negative responsiveness and no-show paradox is too "cutesy" and POV

> Since then, IRV has been criticized for other mathematical pathologies, which include eliminating candidates who have too much support from some voters and electing candidates if too many voters turn out to oppose them.

1. there's no need to link to mathematical pathologies here. I wouldn't really call this "pathological" in that sense anyway --- those are usually reserved for things like the Cantor function and such
2. I would not say "too much support" or "too many turn out to oppose" as these are less accurate and more opinionated than just simply saying "negatively responsive" and "exhibits no-show paradox"

Affinepplan (talk) 19:41, 1 November 2024 (UTC)

please remember, wikipedia is not a place to persuade readers of your political agenda @Closed Limelike Curves. it is a place to find neutral and accurate information. it's ok if it's a little "boringly" written. In my opinion it's much more appropriate to say objectively that IRV is "negatively responsive" and "no-show" etc. and let the reader form their own opinion about this. It's not really the same thing as "too much opposition turnout" as that is making assumptions about which voters constitute "opposition" or not. the no-show paradox could be achieved via voters who put the eliminated candidate as a very very close second! hardly "opposition" Affinepplan (talk) 19:44, 1 November 2024 (UTC)

the no-show paradox could be achieved via voters who put the eliminated candidate as a very very close second! hardly "opposition"

It can also occur when a candidate is ranked last on a voter's ballot, i.e. very clear opposition, so it's still a fully accurate description of a paradox of IRV.

These are simple, plain-English descriptions of negative responsiveness and no-show paradoxes (both technical terms most readers won't know about). – Closed Limelike Curves (talk) 19:59, 1 November 2024 (UTC)

> It can also occur when a candidate is ranked last on a voter's ballot, i.e. very clear opposition,

yes, it could potentially. but it is not accurate to summarize the failure of no-show this way (by looking at one specific instantiation). Affinepplan (talk) 20:08, 1 November 2024 (UTC)

Unless either the example is a theoretical one where each voter's preferences are known from the outset or voters were compelled to rank all of the candidates, it can't really be said with so much certainty that a candidate being ranked last on a voter's ballot indicates very clear opposition. Outside of those two scenarios, the better indication for opposition would be a candidate not being ranked at all, though even then, that could also just be simple disinterest rather than active opposition. 180 Degree Open Angedre (talk) 20:11, 1 November 2024 (UTC)

I'm not necessarily opposed to Lime's additions, but I feel like it's not summarized well enough, and the lede has gotten cluttered as a result. Quite a bit of it, if it hasn't already been covered in the sections below, probably should be moved down into their relevant sections. I understand that Lime has a POV that they were trying to incorporate into the article, which is why they had made their own separate Draft version earlier, but I think that if they want to make a good lede, they should try to summarize the information that is in the current version of the article instead of just repeatedly inserting their own version over and over again with minimal regard for, well, nearly every other editor's edits. I've tried to keep as much of what I think is valuable information from their additions in it, but until this is cleaned up, honestly, I think I prefer this version of the article, from before Lime started to edit war again, is much better: https://en.wikipedia.org/w/index.php?title=Instant-runoff_voting&oldid=1253823862 180 Degree Open Angedre (talk) 21:08, 1 November 2024 (UTC)

yes, I also prefer that old revision. Affinepplan (talk) 21:32, 1 November 2024 (UTC)

And I prefer the even older revision, prior to any brigading, which can be found here. – Closed Limelike Curves (talk) 21:55, 1 November 2024 (UTC)

I understand you're upset that other editors don't agree with your edits and it's more fun when you get to decide by singular fiat what goes into an article, but I don't appreciate being labeled a "brigader."

That revision is substantially worse than the one 180Degree Open Angedre sent and also substantially worse than the current revision. Affinepplan (talk) 22:05, 1 November 2024 (UTC)

I agree we shouldn't link mathematical pathologies and that. I like the phrasing "exhibits the no-show-paradox", preferably with a link. On the other hand, "negatively responsive" probably doesn't mean anything to most of our readers, and it would be nice if we could phrase it in a way that they'll understand. McYeee (talk) 23:15, 1 November 2024 (UTC)

Probably the phrasing I used before—that a candidate can lose as a result of being "too popular" or receiving "too many votes". This phrasing/explanation is pretty standard in the literature, e.g. Doron and Kronick 1977 describing it as "a candidate could lose an election because he or she received too many votes". – Closed Limelike Curves (talk) 01:19, 2 November 2024 (UTC)

What's the issue with linking "mathematical pathologies", though? I linked it to clear up the term's meaning. – Closed Limelike Curves (talk) 03:35, 2 November 2024 (UTC)

Do reliable sources call it a pathology? It seems like the term is more derogatory here than when applied up the Weierstrass function. McYeee (talk) 06:12, 2 November 2024 (UTC)

I'm sure the word has been used but it's certainly not a common term in this context. and in any sense it means something quite different than the way it's used in mathematics Affinepplan (talk) 13:44, 2 November 2024 (UTC)

Yes, it's a common term from reliable sources, with basically the same meaning as in the rest of math. That said I don't care enough to argue further so I'm fine with replacing it with "paradoxes". – Closed Limelike Curves (talk) 15:42, 2 November 2024 (UTC)