Talk:Negative responsiveness/Archive 1

In the example of a violation of the Monotonicity Criterion, it says that candidate C would be the Condorcet winner. However, it seems that there is no Condorcet winner in this case. In pairwise matchups C would beat A, A would beat B and B would beat C, meaning all three would be in the Smith Set. The winner would then depend on what form of Condorcet voting would take place. I would suggest solving this problem by either

1) Changing the second preference of A's voters to C (this will create 4 categories in the second election, but still result in a violation of monotonicity). Then in pairwise voting we would have C beats A and C beats B, meaning C is not the Condorcet winner.

2) Remark that there is no Condorcet winner and choose an appropriate resolution scheme, such as Minimax Condorcet, to choose a winner.

--Anon. 18:25:07, December 3, 2005 (UTC)

I cut the sentence completely. Why discuss what Condorcet methods will do instead of, say, Bucklin voting? It seems irrelevant to the article. KVenzke 17:46, 4 December 2005 (UTC)

Because condorcet methods pass the monotonicity criterion, that's why. You're right that Bucklin voting should be mentioned as well. The article could use more examples, such as a sentence explaining why Bucklin passes too. Scott Ritchie 18:35, 4 December 2005 (UTC)

Condorcet methods don't necessarily pass the monotonicity criterion. Consider Raynaud, Borda-Elimination (Nanson), or Smith//IRV. That's why it doesn't make sense to point out who the Condorcet winner is. KVenzke 04:16, 6 December 2005 (UTC)

Can you point out an example demonstrating that? It would be relevant to the article to show how they can fail. Scott Ritchie 00:10, 7 December 2005 (UTC)

Suppose that the method is Raynaud (wv), so that we repeatedly eliminate the candidate who has the most votes against him in a single pairwise contest.

36 abc
34 bca
30 cab
C is eliminated and A wins.

Now raise A on 5 bca ballots:

41 abc
29 bca
30 cab
B is eliminated and C wins.

I hope that's what you were looking for. KVenzke 22:58, 7 December 2005 (UTC)

I have deleted the following sentence: "Most versions of the Single Transferable Vote which simplify to Instant Runoff when there is only one winner are not monotonic, however variants of STV such as CPO-STV and the Quota Borda system are." To the best of my knowledge, there is no STV method that has been proven to satisfy monotonicity. And the Quota Borda system has been proven to violate monotonicity. See example 3. Markus Schulze 09:22, 31 December 2005 (UTC)

Why not CPO-STV, or other methods that simplify to monotonic systems when there is one winner? Scott Ritchie 04:07, 2 January 2006 (UTC)

The Quota Borda system does simplify to a monotonic system when there is only one winner. Markus Schulze 09:50, 2 January 2006 (UTC)

It is possible that I am missing something, but I am confused. It seems to me that the example given is not an example of a violation of the Monotonicity Criterion.

The Definition:

Douglas Woodall, calling the criterion mono-raise, defines it as:

A candidate x should not be harmed [i.e., change from being a winner to a loser] if x is raised on some ballots without changing the orders of the other candidates.

The Example:

1st Election
39 A,B
35 B,C
26 C,A
C is eliminated, and A wins.

2nd Election
49 A,B
25 B,C
26 C,A
B is eliminated, and C wins.

The Example shows that A is the winner in the first election, but in the second election, A has a raised position yet loses, which seems to violate monotonicity. However, the Definition also states that candidate x should be harmed if x is raised without changing the orders of the other candidates. I guess I am confused because in the Example the orders of the candidates change. C is in 3rd place in the first election and changes to 2nd place in the second election. This, to me, is an example of a change in order of the candidates. If this is the case, then either another example is needed or the definition of the MC needs to be clarified. Otherwise, based on my current interpretation, I am not convinced that IRV, for instance, fails the MC.

You are misunderstanding. "without changing the orders of the other candidates" means that votes which ranked y > z still rank y > z. In the example we start with 39 A > B > C, 35 B > C > A, and 26 C > A > B for the first election. We then take 10 of the B > C > A and change them to A > B > C, i.e. some voters increase their preference for A without changing the orders of the other candidates, all those votes still rank B > C. After the change we have 49 A > B > C, 25 B > C > A, and 26 C > A > B, which causes A to lose the election and IRV to violatate the monotonicity criterion. I'll be correcting the main article shortly. 206.104.161.170 (talk) 18:56, 20 June 2008 (UTC)

Now, it could be interpretation is wrong and that the "changing the orders of the other candidates" means something else. It could mean a change in the secondary votes (for example, if the primary voters of C have secondary votes of A in the first election and change their secondary votes to B in the second election).

My point is that this article is confusing to someone who is not on expert on voting methods or voting system criterion. I am suggesting that this article could be clarified a little, but I do not consider myself knowledgeable enough to do so myself. Can someone either clarify the article or at least clarify this to me? Bryanmode 16:20, 6 November 2006 (UTC)

The reference to order changing is about the order of candidates on the ballot, not in some final ranking. Note that not all voting methods even produce a full ordered ranking -- the algorithm can simply halt when a winner (or N winners) are selected. And no, basic IRV is definitely not monotonic.

Say you have an IRV election with three candidates ("A", "B", "C") and the votes are as follows:

2 C > B > A

6 A > B > C

5 B > A > C

4 C > B > A

The first group and fourth group look the same, but they're separated because we're going to explore what happens when the first group changes their vote.

First round: 6 votes for A, 5 for B, 6 for C. B is eliminated.

Second round: 11 votes for A, 6 votes for C. A wins.

Now, A does such a good job that the two voters in the first bloc decide they were wrong about A. So, in the next election, with all the same candidates, the votes are:

2 A > C > B

6 A > B > C

5 B > A > C

4 C > B > A

First round: 8 votes for A, 5 for B, 4 for C. C is eliminated.

Second round: 8 votes for A, 9 for B. B wins.

By ranking A higher, these two voters caused A to lose when A would've otherwise won.

Note that the relative order of the other candidates on the ballot in the first bloc (C > B) is unchanged. That's what was required by the condition you were discussing.

Ka-Ping Yee created an excellent graphical representation of IRV's monotonicity failure. Rmharman 06:40, 28 November 2006 (UTC)

The following sentence is incorrect:

Tactical voting in this way presents an obvious risk if a voter's information about other ballots is wrong, however, and there is no evidence that voters actually pursue such counter-intuitive strategies in non-monotonic voting systems in real-world elections.

I don't have the time or indeed the expertise to edit the section properly, but somebody should. The second clause ("there is no evidence" etc.) has been quite plainly wrong since the German federal election of 2005, in which conservative voters in Dresden deliberately voted against their party of choice (the CDU) in order to maximize that party's number of seats in the federal parliament. This was possible due to Germany's voting system (mixed member proportional with overhang seats) and the fact that the vote in Dresden took place a week after the rest of the country due to the death of a candidate, enabling voters in Dresden to vote tactically in full knowledge of the results already achieved elsewhere. As a result of this, the German Constitutional Court ruled on July 3 2008 that the German voting system must be reformed to improve its monotonicity.

For more, see: [1] (in English) or various German wikipedia articles such as [2] —Preceding unsigned comment added by 210.84.53.32 (talk) 04:19, 26 July 2009 (UTC)

I altered the section on probability, chiefly because it read like someone making a case, rather than an NPOV statement of the available resources, some bits sounded like OR (The section asked for a citation on still reads a little OR, but I think it deserves a chance to be substantiated).--Red Deathy (talk) 13:57, 7 June 2011 (UTC)

The stated IRV example is not very realistic, because it contains a Condorcet cycle among the three Candidates in election one, with a very strong support for any of the three majorities in the cycle. I also criticize, that the example assumes a huge swing of the voters preferences. I suggest another example, without a Condorcet cycle, and just a small swing: Three candidates are running, a left, a right, and a center candidate. Hundred voters casting their ballots:

Number of votes 1st Preference 2nd Preference

28 Right Center

5 Right Left

35 Left Center

32 Center

The IRV-winner in that election would be Left, because Center gets eliminated first, and Left wins against Right according to the remaining preferences. But if the five voters, who voted 1st (削除) Left (削除ここまで)(追記) Right (追記ここまで) and 2nd (削除) Right (削除ここまで)(追記) Left (追記ここまで), switch their 1st and 2nd choice, then Right gets eliminated first, and Center wins against Left, so Left loses due to the new votes in favor of Left. -- Richard 13:45, 13 May 2011 (UTC)

Maybe I do not understand something, but nothing matches in the calculations in the article and in the talk page as well. "But if the five voters, who voted 1st Left and 2nd Right" - there are no such voters in the table given as the example. Also, in the article, given examples fail to prove the thesis they were brought for. Changing ranks from Right to Left entrenches the Left, not sets them down.

Robs777 (talk) 18:54, 11 October 2012 (UTC)

I corrected the error in the description of the example that's given here. In the article I used a different example. The two additional votes for Left in the article example (switching Right, Left, Center to Left, Right, Center) show a greater support for Left. That hurts Right in the first round, cause it no longer reaches the 2nd round. But Center, now entering 2nd round, beats Left. So the greater support for Left causes Left to lose, the result changes from Left winner, Right 2nd to Center winner, Left 2nd. Center is least prefered by the Left, Right, Center voters. Best, --Richard (talk) 10:53, 24 April 2014 (UTC)

I've removed text which stated that Single Transferable Vote can be non-monotonic depending on the methods used. No counting method (not even Meek's method) eliminates the non-monotonicity of STV - all counting methods reduce to IRV in single winner elections, and IRV is non-monotonic. Some counting methods, such as Meek's method, reduce the potential for tactical voting with STV, but they do not completely eliminate the non-monotonicity.

I amnot sure I agree with the removal. It is not enough to say that Meek's method cannot be montonic because 'STV' is never monotonic. That argument is circular. I will post a fuller answer at the STV talk page when I have researched it. Alan 09:46, 17 May 2005 (UTC).

When I added that text ("STV may or may not be monotonic, depending on the method used") I was actually thinking of Condorcet-STV, not Meek. Meek can be non-monotonic, though in real-world elections it is rare; see [3]. Since Condorcet-STV doesn't actually tabulate vote transferral directly, it is not susceptible to the same analysis that indicts other STV systems; in some sense, Condorcet-STV is STV in effect, not in implementation. TreyHarris 15:25, 17 May 2005 (UTC)

Is there any proven statement that 'any' STV-method isn't monotonic? Like "any method that fulfills ... (which we call a 'STV-method') ... is not monotonic". Otherwise the most rigid statement should be "satisfaction of monotonicity criterion hasn't been proven for any known STV method". To write "all known STV methods are not monotonic" requires to show counter-examples for all of them. Please show me e.g. an example that Schulze STV is not monotonic. It reduces to the monotonic Schulze method in single winner elections, so any proposed counter-example must have at least two seats to be filled. Best, --Richard (talk) 11:52, 24 April 2014 (UTC)

If a voting system can be non-monotnic then it is fair to say that the system is a monotonic. Clearly any voting system is non-monotic sometimes. For example if there is unanamouse agreement about who the best candidate is. So when someone says that a system is non-monotonic they mean that there are circumstances where ranking someone higher can hurt them, given a certain pattern of votes. —Preceding unsigned comment added by 144.82.93.19 (talk) 09:47, 1 April 2011 (UTC)

"Clearly any voting system is non-monotic sometimes.". This is simply wrong. You might have written "Any voting system may be redesigned in some way (resulting in a different system), such that it becomes monotonic, or loses this property". Best, --Richard (talk) 11:33, 24 April 2014 (UTC)

First, I'm going to discuss the definition of the Monotonicity criterion. That article equates the term to what Woodall termed "mono-raise" in [4]. STAR very clearly does not violate this criterion, and Markus Schulze's example above is not germane.

Woodall himself gives 7 different monotonicity criteria, of which mono-raise is only the first. Of those, STAR passes only mono-raise. I've seen other more-complete lists of monotonicity criteria which include other ones that Woodall missed and STAR passes, such as mono-add-plump (which does not imply and is not implied by mono-raise).

Is mono-raise the canonical monotonicity criterion, as the relevant wikipedia article currently states? Let's look at the other, more recent references cited by that article:

• [5] ... this considers only strictly ordinal rules; by the definition there, STAR is not even a voting method. Does not directly apply. However, within the limits of this constraint, the given definition of "monotonicity" is equivalent to mono-raise.
• [6] Ditto.
• [7] In formal terms, this has the same problem as the two articles above; it considers only fully-ranked voting methods. However, it does include the following less-formal (English) definition of monotonicity: "An election profile P exhibits an upward monotonicity failure if there exists a profile P� that is identical to P except that candidate A [the winner under P] is ranked higher by a subset of voters, but candidate A is not the IRV winner." Schulze is in essence arguing that the word "ranked" in this definition is absolutely key even for rated voting methods; Nardopolo is in essence arguing that this word should be replaced by "rated" when discussing rated methods. Since this definition is equivalent to mono-raise for ranked methods, I think it's evidence that unqualified "monotonicity" is generally understood to mean mono-raise; in other words, I think this should count as evidence in Nardopolo's favor.
• [8] This article gives only the following incomplete definition of monotonicity: "...a condition known as non-monotonicity. This has a complex definition, but is most easily explained as a condition where a candidate can increase their chances of victory by lowering their first preference count." It's clear that Antony Green does not consider this the only meaning of monotonicity, but it's also clear that STAR passes by this definition.

So all in all, I'd say that "monotonicity" is generally understood as "mono-raise", which STAR passes. Homunq (࿓) 11:22, 20 August 2018 (UTC)

I decided to take this further; I searched "monotonicity voting cardinal" on Google Scholar and clicked on the 6 links in the first page of results that appeared potentially relevant. These include: (sorry, Harvard proxy in urls)

• [9] Discusses how ordinal voting methods work for cardinal agents. Does not define "monotonic" for cardinal voting methods.
• [10] Doesn't mention monotonicity, don't know why it came up. (Also, a whole paper on voting dedicated to proving Pareto dominance is Unclear On The Concept. The class of situations where Pareto dominance applies has no overlap with realistic voting scenarios.)
• [11] Doesn't actually mention cardinal voting methods; unrelated use of "cardinal".
• [12] Uses cardinal mono-raise as the primary definition of monotonicity, though other definitions are discussed.
• [13] Defines monotonicity for ordinal methods and for approval voting. Both definitions are special cases of cardinal mono-raise.
• [14] Doesn't define monotonicity (only reference to it is a citation of one of Schulze's papers).

So, though I still don't have a slam-dunk proof that cardinal mono-raise is the best definition of "monotonic" to use here, I think this evidence further tends to support that proposition. In particular, the definition of monotonicity for approval voting is a clear counterexample to Schulze's argument that only the ordinal definition is accepted. Homunq (࿓) 14:46, 20 August 2018 (UTC)

The Muller–Satterthwaite Theorem relies on a definition of monotonicity that appears to be slightly different than the one presented here. Being more strict, it gives a much stronger result. Should the distinction be mentioned in this article? 2605:A601:A927:1900:257D:1C19:DCAC:E3EF (talk) 07:12, 17 November 2021 (UTC)

It sounds relevant to the page, so yes. --Erel Segal (talk) 14:39, 18 November 2021 (UTC)

Currently this section is misleading, a single election can't be used to show that a method violates monotonicity, therefore I propose to change this section as follows: When the ballots of a real election are released, it is fairly easy to proof, if it was possible

• to defeat the winner by raising him on some of the ballots
• to push a looser by lowering him on some of the ballots

This could be called a real-life monotonicity violation.

The ballots (or information allowing them to be reconstructed) are rarely released for instant runoff elections, which means there are few recorded monotonicity violations for real IRV elections. -- Richard 13:45, 13 May 2011 (UTC)

But any real-life election can be modelled in examples. I calculated figues given here as an examples and they do not confirm lack of monotonicity. I just want to understand how it really works. I seems that everybody talk about this but nobody can fetch any examples. Robs777 13:02, 15 October 2012 (UTC)

They do confirm, as they show that when X is winner, upranking X on some ballots causes X to lose. It's worthless for X to have a greater support in the first round, and it's harmfull if that is causing X to lose. If the actual ballot tallies are not available, a real-life election can't be modelled in examples. Guessing what the actual votes could have been is fiction and not real-life. Best, --Richard (talk) 11:08, 24 April 2014 (UTC)

The current version is hard to understand, but not very informative, I propose also to change this subsection as follows: A real-life monotonicity violation was detected in the 2009 Burlington, Vermont mayor election under instant runoff voting, where the necessary information is available. In this election, the winner Bob Kiss could have been defeated by raising him on some of the ballots. E.g. if all voters who ranked Kurt Wright over Bob Kiss over Andy Montroll, would have ranked Kiss over Wright over Montroll, and additionally some people who ranked only Wright, would have ranked Kiss over Wright, then these votes in favor of Kiss would have have made him lose! ^[1] The winner in this scenario would have been Andy Montroll, who was also the Condorcet winner according to the original ballots.

If there are no complaints or suggestions to these three changes, I would change the article accordingly -- Richard 13:45, 13 May 2011 (UTC)

Richard's version seemed to have lived for a few years, but was changed by Tbouricius in diff #760704116 in January 2017. Adding the names and parties of the candidates is helpful, but it also states that instead of a real-life monotonicity violation "... was detected" it is now "...could have occurred". It also adds the sentence "This hypothetical monotonicity violating scenario, however, would require that right-leaning voters switch to the most left-wing candidate." This wording is confusing to me; I may take a crack at rephrasing it, but it'd be wonderful if someone else who understands this better did the work. -- RobLa (talk) 21:30, 11 October 2017 (UTC)

Sorry that my reply is really late. I just reworded the section again and kept the information about the candidates' party affiliations, as it may be useful for readers in assessing how relevant they consider the example. But I removed the last sentence "This hypothetical monotonicity violating scenario, however, would require that right-leaning voters switch to the most left-wing candidate."

The alleged left-to-right order of candidates is subjective and a decisive left-to-right-sorting K,M,W isn't supported by the actual voting data (among fully ranked votes: app. 1⁄4 of votes for Wright had Kiss 2nd and Monroe 3rd, i.e. among these app. 1⁄4 didn't state a "right-to-left preference" W>M>K). Also added that Kiss was incumbent, and incorporated that it's a comparison of a real world election outcome to a hypothetical mono-raise alteration.

as alleged left-to-right order of candidates is subjective and a decisive left-to-right-sorting K,M,W isn't supported by the actual voting data (among fully ranked votes: app. 1⁄4 of votes for Wright had Kiss 2nd and Monroe 3rd, i.e. among these --Richard (talk) 18:39, 31 August 2023 (UTC)

I have a problem with the section "Real-life monotonicity violations" and the 2009 Burlington description. AFAIK it is not a violation of monotonicity if you could adjust the vote tallies to affect the result, even if such examples show the latent possibility of such an outcome. To observe real life monotonicity you need to show change in votes between two elections. IIRC from reading the lit some years ago, that's why it's hard to find a real life example, precisely because changing patterns of votes are not so easy to detect, and it's impossible to know whether voters were switching from one candidate to another, ceteris parebus.--Red Deathy (talk) 13:44, 7 June 2011 (UTC)

No, you can't argue on the base of two different elections, because you can't say that voter V changed it's preferences if ballot submission is secret (what it always should be!). And you won't most likely (almost for sure) find any two real elections that fit into the mono-raise criterion ("... without changing the orders of the other candidates.", only raise one candidate, no other changes in all ballots). Best, --Richard (talk) 12:12, 24 April 2014 (UTC)

I want to question the whole existing of a "real-life monotonicity violation." Monotonicity is a mathematical property but not something that happens. If the issue is that non-monotonicity invites certain kinds of tactical voting, then state the kind of tactical voting incentives that may occur and link to the appropriate sections of the Tactical voting article. Monotonicity involves an election and a hypothetical alternative election, so it can't happen, per se, in real-life. Progressnerd (talk) 22:48, 19 November 2017 (UTC)

Hi, you're right in monotonicity being a property that an election method either possesses or not, and "real-life monotonicity violation" is kind of a misnomer. In the Burlington example, I now tried to phrase it better, i.e. non-monotonicity of IRV can be exemplified based on real world election data, showing it's not just some abstract mathematical property, but something which can have actual real world implications (like not having any kind of alternative votes obviously has also real life implications. And funny enough, if the Wikipedia article about the election is right, then the city switched back to a two round runoff system, which has the same type of monotonicity violations as IRV).

Maybe the section should be renamed to something like "monotonicity violations exemplified with real-life data".

But I don't consider it a good fit to just link to Tactical Voting, as the section is explicitly about how a lack of monotonicity can be exemplified when real world data is provided. And the subsection about Burlington's mayoral election exemplifies a lack of monotonicity for the most common voting system IRV.

illustration of IRV's lack of monotonicity using real world data (for the most common ranked voting system IRV). --Richard (talk) 19:08, 31 August 2023 (UTC)

Backers of single winner reforms that violate later-no-harm criteria like to focus their ire on instant runoff voting. But in fact traditional runoff elections are more likely to generate nonmonotonic outcomes than IRV because the field abruptly is reduced to just two candidates for the runoff. In typical fashion in articles developed primarily by IRV critics, the focus of this article is much more on IRV than on runoff elections. Anyone interested in providing balance by examining the huge number of runoffs around the world (most presidential elections are chosen by runoffs, for example) would be doing disinterested readers a favor. RRichie (talk) 22:13, 11 October 2012 (UTC))

Hi, you have a point in IRV being hypothetically less prone to monotonicity violations, yet it's even harder to exemplify it for two-round runoffs with real world data, as the information how voters would rank candidates is usually not collected. So any ranked voting system is easier to criticise, as it collects more information. And first past the post is perfect regarding monotonicity, it just fails in basically every other aspect except simplicity / ease of use (although partitioning into voting districts may spoil even the latter).

Two round systems with a top-two runoff are mathematically equivalent to IRV if only three candidates are running, so simple examples match both systems. My example in section "Instant-runoff voting and the two-round system are not monotonic" seems to have survived, so it's mentioned since many years.

Btw. there are also runoffs with up to three candidates, which possess actually an interesting feature: do not eliminate all choices except for two (with a decent chance polar opposites). Even IRV could be stopped with three candidates left, and having a second round runoff.

With just three candidates left, even rather complicated Descending Coalition methods (DSC&DSQ) are rather easy to describe and implement.

And with just three candidates, even Descending Coalitions methods (DSC/DSQ) are rather easy to describe and impleme (t. --Richard (talk) 19:48, 31 August 2023 (UTC)

Thank you @Closed Limelike Curves: for beginning to edit this article. I think it is currently not in a good state. I however, do not quite see the reason to revert my revertion. The Frequency of Violation Section is currently not in a good state. rangevoting.org is not a source that should appear on wikipedia WP:RELIABLE. Just take a look at the Australia article, you will see that it is not a good scientific source. Further, I added an actual academic source which studied the frequency of IRV monotonicity violations, I think that would be beneficial for the article. Finally, I do not understand the figure. Either it needs some proper explanation or should be deleted. A typical four-candidate election is not a valid explanation though. Jannikp97 (talk) 07:08, 22 March 2024 (UTC)

I don't have any objections to also including the academic article. That said, the work of both the Center for Range Voting and Dr. Warren D. Smith are well-known and respected in the electoral system design community. (Despite the... unusual, 2009-era web design.) Closed Limelike Curves (talk) 07:30, 22 March 2024 (UTC)

Sorry to say this, but I do not think this is really true. They are surely well-known, but well-respected only marginally. If we look at say WP:REPUTABLE we should cite articles that are reliable, independent, published sources with a reputation for fact-checking and accuracy. The rangevoting page satisfies none of these criteria, especially not independence and accuracy. Hence, I would prefer, if possible, to rather use reliable sources, as otherwise this might give the false impression of acknowledging the page as a wikipedia worthy source. In this article, for instance, the citation for the Burlington election can easily be replaced by the Graham-Squire and McCune paper. Further, the discussion and especially methodology on the pages on Louisiana and Australia do not seem very scientific to me, so I am not too sure about including them here. Jannikp97 (talk) 08:19, 22 March 2024 (UTC)

I'm not sure what makes you say the Center for Range Voting (now Center for Election Science) isn't reliable, independent, or doesn't have a reputation for fact-checking or accuracy?

The work they put out is pretty good, and WDS is a PhD mathematician with years working in the field. The work isn't published in a peer-reviewed journal, but preprints by scholars are commonly cited on Wikipedia. Closed Limelike Curves (talk) 21:35, 22 March 2024 (UTC)

The quality on the rangevoting website is notoriously low and Smith seems to put more effort into insulting established researchers, e.g., Arrow or Saari, than making his work readable. Further, the site seems to be very much focused on promoting range voting, which itself makes it not independent, but instead quite biased.

Smith having a PhD in math isn't really relevant (even though his old non voting work seems quite good).

Yes preprints are commonly cited on Wiki (whether that is a good thing is different question). However, I think usually only preprints of established researchers. For instance compare to WP:SELFPUB Jannikp97 (talk) 08:32, 23 March 2024 (UTC)

The figure is a Yee diagram, description here:

https://electowiki.org/wiki/Yee_diagram

Improved descriptions welcome! Closed Limelike Curves (talk) 07:32, 22 March 2024 (UTC)

If I had to be honest, if this article does not even manage to properly describe what this image visualizes, I am not too sure, it would be possible in an image caption. The image is certainly pretty, but at least to me it seems more-so confusing than actually helpful. Jannikp97 (talk) 08:54, 22 March 2024 (UTC)

As an alternative, I have this diagram which colors the win region depending on where candidate C is placed. Is this clearer?

Closed Limelike Curves (talk) 18:00, 22 March 2024 (UTC)

This is a bit clearer, however I am not too sure if it perfectly symbolizes monotonicity. In the figure, we are not really talking about the preferences of the voters, but the locations of the candidates or am I missunderstanding something here? Jannikp97 (talk) 18:03, 22 March 2024 (UTC)

Yes, you're right, although you can see it by "squinting" (the blue hole in the middle is where candidate C loses despite being the most popular candidate, but they can win by moving towards the wings). It's not as good as the current image for representing monotonicity violations, though. Closed Limelike Curves (talk) 18:19, 22 March 2024 (UTC)

Yeah. Probably it is fine to leave it for the time being. There are worse things to fix in voting articles :D Jannikp97 (talk) 20:24, 22 March 2024 (UTC)

The redirect More-is-less paradox has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 August 2 § More-is-less paradox until a consensus is reached. Steel1943 (talk) 20:08, 2 August 2024 (UTC)

The redirect Less-is-more paradox has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 August 2 § Less-is-more paradox until a consensus is reached. Steel1943 (talk) 20:11, 2 August 2024 (UTC)

this article is about positive responsiveness and monotonicity in general, so why is so much discussion specifically about IRV? surely there are plenty of other examples to draw from including party-list elections, participatory budgeting, non-political contexts, etc.

I would almost nominate this article for deletion entirely. it seems like it is taking a mathematical concept and using it as a pretext for politically-motivated soapboxing

tagging @David_Eppstein and @Jannikp97 for feedback as I have seen you provide many high-quality edits on related pages. Affinepplan (talk) 16:41, 23 October 2024 (UTC)

The section on frequency of violations focuses on IRV because additional support paradoxes are only very common in IRV/two-round systems. However, I'd have no objections to retitling the section to reflect the focus on IRV, or to adding a brief discussion of other rules. – Closed Limelike Curves (talk) 18:36, 23 October 2024 (UTC)

> additional support paradoxes are only really common in IRV/two-round systems.

this is not true whatsoever. as the article even mentions, quota based apportionment rules can fail monotonicity, and I would be willing to be there have been far more of these elections exhibiting nonmonotonicity affecting a far greater number of seats and constituents than there are for IRV, for which there are at best a few dozen examples so far in modern history.

although it should be noted that this is (population) monotonicity aka positive/negative involvement or "participation", which is distinct from (support) monotonicity, which itself is distinct from Positive Responsiveness. as a side note, this article should be much more clear and technical about which exact forms of monotonicity are being reference for any given statement

I want to be clear that I am not trying to whitewash IRV's behavior on certain preference profiles, most notably (and as you have made sure to repeat over and over on every single wiki article relating to IRV, spoiler effects, Arrow's theorem, and monotonicity) center squeeze. It is certainly an objective truth that center squeeze & nonmonotonicity can and does happen sometimes with IRV, and is a notable behavioral defect that Wikipedia should not censor. But all that being said, I really don't think it is appropriate for every technical article about what are in essence mathematical algorithms to be constantly barking about this failure. Affinepplan (talk) 18:46, 23 October 2024 (UTC)

this is not true whatsoever. as the article even mentions, quota based apportionment rules can fail monotonicity, and I would be willing to be there have been far more of these elections exhibiting nonmonotonicity affecting a far greater number of seats and constituents than there are for IRV, for which there are at best a few dozen examples so far in modern history.

If you're aware of statistics on this, please go ahead and add them. But as the person who added the information on quota methods, I'm very doubtful that monotonicity failures are more common than in IRV.

although it should be noted that this is (population) monotonicity aka positive/negative involvement or "participation", which is distinct from (support) monotonicity,

No, it's about positive responsiveness. The voters in this case switched their votes from the CDU/CSU to the FDP. (I've never heard the term "support monotonicity", and if it's different from Arrow's positive association/responsiveness I'm not sure what it is.) – Closed Limelike Curves (talk) 19:03, 23 October 2024 (UTC)

I think one other reason why there might be a lot of literature on IRV specifically is that it's a very commonly proposed reform to FPTP. It's like, the vanilla icecream of voting reforms, so to speak. Alpha3031 (t • c) 08:18, 25 October 2024 (UTC)

Hi Closed Limelike Curves, I see you've moved this from monotonicity criterion a few weeks back, which by the edit summary seems to be because you wanted to reflect a focus on violations of the criterion. While this is a valid reason to boldly move a page, the new title may not necessarily fit our WP:CRITERIA as well. For example, piecemeal moves cause the series of articles in the category do no longer be WP:CONSISTENT. Ignoring naming conventions, having paradox at the end of the title may also be WP:OVERPRECISION, and negative responsiveness seems to have no other page relevant to it, meaning that it is sufficient to identify this subject.

Since you seem to be interested in moving multiple pages in the topic (I see Majority loser criterion was also moved, but reverted) I would highly recommend reverting and opening an WP:RM discussion instead, so that the naming conventions of the category can be discussed as a group (which would help maintain consistency). Thanks! Alpha3031 (t • c) 12:25, 23 October 2024 (UTC)

I agree that this renaming probably should not have occurred. "Monotonicity" is a bit of a subtle word in social choice and deserves a full article beyond just being a "paradox" Affinepplan (talk) 14:42, 23 October 2024 (UTC)

No objections to considering other names. Decent potential titles that have all been used in the literature would be:

1. Positive/negative responsiveness/response
2. Less-is-more paradox
3. Additional support paradox

I lean towards one of the latter two, both for consistency with no-show paradox and multiple districts paradox, and because I'd rather use small/familiar words instead of complicated ones. – Closed Limelike Curves (talk) 18:47, 23 October 2024 (UTC)

I think "Monotonicity" was fine and descriptive. although I would not call it neither a "criterion" nor a "pathology" nor "paradox".

IMO I would title the article something like "Monotonicity (Social Choice)" and write an exposition on all the various definitions of monotonicity of which there are several, maybe nearing a dozen, subtly-but-meaningfully different variations Affinepplan (talk) 18:50, 23 October 2024 (UTC)

You're right that there's a lot of different kinds of monotonicity floating around, which is part of why I changed the title. Lots of these "criteria" titles, like "Monotonicity criterion", are due to EM-list contributors and differ from some of the more-common names in the literature. "Positive response" and "positive association" are the terms I'm more familiar with from my economics background, and I believe are more common in published literature, whereas "monotonicity criterion" is common on the EM list and has been used in Voting Matters . However, that term can easily clash with others like "population monotonicity" and "Maskin monotonicity" from social choice and mechanism design. This article is about "Positive responsiveness/association", which is unambiguously used for cases where increasing the utility/rating of X, holding all else constant, causes X to lose. – Closed Limelike Curves (talk) 22:27, 23 October 2024 (UTC)

that's fine, but then the article should be titled `Positive responsiveness` and not `Negative responsiveness paradox`

also in that case it is not true that all quota apportionment rules fail. D'Hondt is (technically) a quota rule... Affinepplan (talk) 23:38, 23 October 2024 (UTC)

I know Gallagher pointed out somewhere that "Divisors" in highest averages methods have the same interpretation as the "Quota" in quota rules, but "Quota method" generally refers to rules that keep both the quota and the house-size fixed. – Closed Limelike Curves (talk) 23:59, 23 October 2024 (UTC)

as defined by Quota method, which is what this page links to, D'Hondt is unambiguously a quota method; it is in fact characterized as the only divisor rule which is also a quota rule.

at the absolute bare minimum, the language in this article should be qualified to "some" quota rules or "many" quota rules. Affinepplan (talk) 00:05, 24 October 2024 (UTC)

I suppose we could make the title "positive responsiveness", but I went for "negative responsiveness paradox" to be consistent with other articles (namely no-show paradox and multiple districts paradox). If the issue is WP:OVERPRECISION, "Negative responsiveness" is fine. I generally suggest the negative interpretation because I find in my classes/explanations, most people have an easier time grasping paradoxes than "criteria". If I give the definition of positive responsiveness they have a lot of trouble understanding it, but when I show people an example of how increasing a candidate's score can make them lose, everyone suddenly jolts up in their seats and goes "What?" – Closed Limelike Curves (talk) 00:06, 24 October 2024 (UTC)

tbh I'd rename both of those as well to "Participation (social choice)" and "Consistency (social choice)"

thinking in terms of "paradoxes" just comes across as amateurish to me. maybe I'm alone in that though. Affinepplan (talk) 00:12, 24 October 2024 (UTC)

Given there are multiple good options, I am inclined to move the page back to the old title until things can be narrowed down to two or three, after which an RM can decide things. Alpha3031 (t • c) 08:20, 25 October 2024 (UTC)

works for me Affinepplan (talk) 12:29, 25 October 2024 (UTC)

As I said before, I don't think the old title is a great idea, because it's ambiguous. ("Monotonicity" is used for a bunch of things, and it's already easy to conflate with the pages Monotonicity (mechanism design) and Maskin monotonicity.) Affinepplan seems to be ok with "Positive/negative responsiveness", and I'd be fine with "Negative responsiveness" too. – Closed Limelike Curves (talk) 20:52, 26 October 2024 (UTC)

To be honest I can't be bothered reverting the move, I'm just going to start the RM while the page is at the current title, though if there's no consensus it normally gets reverted back. Alpha3031 (t • c) 04:42, 27 October 2024 (UTC)

In true voting nerd fashion, can I submit a ranked ballot ordering my name suggestions? :p It would save us multiple rounds of voting.

The vote can close with the majority-preferred candidate as winner (or close as "no consensus"/"relist" in the unlikely event there isn't one). – Closed Limelike Curves (talk) 04:27, 30 October 2024 (UTC)

You can write whatever you like in a bolded comment, but the more complicated it is the more likely it will confuse the closer. Technically, it's not a vote, so you should explain how well your suggestions fit WP:CRITERIA as well, as that would be taken into account. Alpha3031 (t • c) 07:57, 30 October 2024 (UTC)