Talk:Comparison of voting rules

Top-level Comparison of Proportional vs Majoritarian

The main article "Electoral Systems" primarily contrasts Majoritarian vs Proportional. It seems to me the primary subject of this article would therefore be the tradeoffs between proportional vs majoritarian - i.e. local representation.

For example, problems with proportional representation, such as the debate of extremist legislators:

http://www.tandfonline.com/doi/abs/10.1080/00344890408523252?journalCode=rrep20

On the hand, proportional representation greater representation of women and minorities:

http://www.kasyp.net/fileadmin/kasyp_files/Documents/reused/documents/party%20organistation_karen%20bird%20amidpaper.pdf

Filingpro (talk) 01:09, 16 April 2017 (UTC)

The content of this article and the "electoral system" article are still being worked out. This separation is not an ideal arrangement. Therefore, please do not assume that what is in one of these two articles is really an indication of what should be in the other article. If you want to add detail on this topic, I suggest adding (to this comparison article) a section titled something like "majoritarian versus proportional voting methods", but please insert it below the mathematical-criteria content -- because the concept of proportional results is more complex and less mathematical (i.e. more subjective) than the comparison between majoritarian (single-winner) methods. VoteFair (talk) 03:11, 16 April 2017 (UTC)

I have to disagree here. There are single-winner positions such as the presidency, mayoralty, governorship, etc, which fundamentally can only be held as a single-winner, majoritarian election. Furthermore, "majoritarian" is not necessarily bad, as all good voting systems are inherently majoritarian even if they can elect compromise candidates. It is only for large committee elections such as for congress/parliament where proportional representation becomes relevant, and then it's only "vs" local representation, not "majoritarianism". In any situation there are only appropriate and inappropriate voting systems, which may or may not be something that we want to put in this article. It may be convenient since we have so much data here and we are doing a comparison, but on the other hand it may be more appropriate in the main article on electoral systems. MarcT 107.129.249.144 (talk) 03:42, 13 May 2019 (UTC)

Schulze and LIIA - IIA

If you click on the LIIA heading in the table, it takes you to a wiki page which says, in part,

> LIIA is weaker than IIA because satisfaction of IIA implies satisfaction of LIIA, but not vice versa.

Note that on this table, Schulze is marked as satisfying IIA but not LIIA. Something is wrong here. — Preceding unsigned comment added by 100.14.179.139 (talk) 11:55, 24 July 2018 (UTC)

I have to agree here. I think the fact that IIA and LIIA can only be met fully by random systems makes the data on a lot of the voting systems suspect. Since the IA situations imply that any candidate can be justified arbitrarily, no democratic system should be able to meet them (thus why only random systems pass). Systems which allow people to strategically manipulate their candidates into winning is not exactly satisfaction of those criteria, at least not in any meaningful way. Some of the other footnotes are absurdly wrong as well, although it may take a while of digging through google scholar to sort all that out properly. MarcT 107.129.249.144 (talk) 03:47, 13 May 2019 (UTC)

"no democratic system should be able to meet them (thus why only random systems pass)"

This is incorrect—score, range, approval, and highest medians all pass IIA. Closed Limelike Curves (talk) 04:19, 6 April 2024 (UTC)

Unexplained terms

"Semi-honest" and "No favorite betrayal" are two terms that this article uses, seemngly without any clear explanation. They should either be linked to an article or article section that explains them, or else there should at least be a footnote that clearly explains them. (There may well also be other terms in need of explanation). Tlhslobus (talk) 05:14, 1 September 2018 (UTC)

"No favorite betrayal" was explained in the Favorite betrayal criterion article before it was deleted:

• Articles for deletion/Favorite betrayal criterion
• Articles for deletion/Favorite betrayal criterion (2nd nomination)
• Articles for deletion/Favorite betrayal criterion (3rd nomination)
• Articles for deletion/Favorite betrayal criterion (4th nomination)
• Articles for deletion/Favorite betrayal criterion (5th nomination)
• Articles for deletion/Favorite betrayal criterion (6th nomination)
• Articles for deletion/Favorite betrayal criterion (7th nomination)

Given the multi-year edit war over that topic, I'm not terribly eager to get involved. But you're right: "favorite betrayal" needs a better explanation in this article. -- RobLa (talk) 17:19, 1 September 2018 (UTC)

What happened to Proportional Voting in this article?

I am so sorry to describe here that I am totally flabbergasted that this article is not what the title purports it to be. Where is the true comparison of systems? Where is the heart of the matter?

Who wrote this? What is going on in the mind of people that wrote/supported this page as it exists now?

I am going to make a few edits. Please help me turn this page into something worth reading.

FredrickS

What you call "proportional" methods is an ambiguous category. Here the term "multi-winner" is used because it is not ambiguous. My guess is that you are thinking of party-based proportional representation, but that's just one sub-category of multi-winner methods.

What changes do you have in mind? This article is very carefully edited by multiple experts on this topic. It is important that academic terminology, not ambiguous terms, be used.

Yes, this article really should be better connected to the Electoral Systems article, but this field does not yet have the academic terminology to fully integrate the two articles.

Real improvements would be great, but please first indicate what you think needs to be improved. VoteFair (talk) (unsigned) 19:44, 29 January 2019 (UTC)

"Multi-winner" is not unambiguous. k-winner elections and proportional elections are two completely different things, even though k-winner voting methods may be used to get a "proportional" result as in STV. For example renormalized range voting can be used for direct proportional elections, but is pretty terrible when applied to k-winner elections. In proportional elections people vote on a distribution where in single and k-winner elections the result is ultimately a ranking. MarcT 107.129.249.144 (talk) 03:21, 13 May 2019 (UTC)

The Comparison Table is Misleading

When I first started digging around here, I was, like most people probably are, taken in by the nice pretty green strips across the comparison table which some of the different voting systems produce. You would naturally assume that a voting system that meets more of the criteria must be "better", however it has come to my attention that this may be far from the case.

Point in case: https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf

He demonstrates clearly, using a relatable example, of how the commonly accepted "desirable" criteria may lead to nonsensical results in practical terms, and how violating those properties under specific conditions can lead to superior results. Apparently Tideman (the creator of the Ranked Pairs method) has also raised similar objections. It's amazing the kind of things you can stumble across on google scholar. :P

Anyway I think we may want to reconsider how the information is presented and add notes about the controversy surrounding some of the criteria. Some methods fail at certain criteria in a bad way, or when they have no theoretical reason to (ie a non-condorcet method failing participation), while others fail the criteria only in specific situations, and do so beneficially, and we should probably make finer distinctions about that.

I should also mention that I've noticed a few errors in the table, as well as important criteria which are missing (ie the weak condorcet criterion) that really ought to be fixed/included. MarcT 107.129.249.144 (talk) 07:37, 15 May 2019 (UTC)

It also says score voting methods pass IIA, with a note that score voting methods only pass IIA if voters don't rate some of the candidates or, in some cases, abstain from voting entirely. That is: if all voters vote honestly, score voting is not IIA. That just means it doesn't pass IIA. I use similar logic with ranked systems, caveat that if in practice they don't trigger IIA then *that specific election* has been IIA, and notably any election where the Condorcet winner wins and the Smith set is only 1 candidate is in practice IIA for that instance, as what determines that there is a Condorcet winner is that you ranked a candidate higher. This doesn't make the *method* IIA; nor does showing that score is IIA if certain voters who trigger IIA failure don't vote prove score is IIA. John Moser (talk) 01:40, 19 February 2021 (UTC)

I agree with MarcT’s substantive point, even though I’m not convinced that his reference provides adequate support. (Most of Darlington’s arguments reject criteria as conflicting with one he himself prefers, which doesn’t really undermine the supposition that they are inherently desirable.) Somehow the implication creeps into articles on voting theory that a method which satisfies a given criterion is ceteris paribus better than one which doesn’t. Without being stated, this assumption is implied by the green colouring and the statement that voting methods may be assessed according to a weighted count of the criteria they satisfy.

I have a particular bugbear about resolvability. It seems to me that given a certain set of ballots, it is possible that one reasonable assumption about what’s going on in voters’ minds will imply that A is the collective preference, and that another will imply that B is; but that the ballot papers by themselves do not provide sufficient information to determine which is the right assumption. In this case it seems to me that a voting system which leaves the choice between A and B unresolved is better than one which makes a decision which ultimately can’t be justified. Has anyone got a proof to the contrary? (And if you say that ulitmately an election needs a result, I might agree; but there are still no grounds for presenting a coin toss as an algorithmically elucidated expression of the collective will.)

At which point does Wikipedia decide that resolvability is desirable? In the resolvability criterion article itself? It merely states the criterion with no implication of desirability. In this page? It mentions the criterion without saying that all criteria are desirable. In the comparison table? By that point resolvability has certainly been identified as advantageous. Colin.champion (talk) 10:32, 28 May 2021 (UTC)

can 'vulnerability to free riding' be a criteria in the table for multi-winner methods? not a simple yes/no answer but there are papers comparing different methods through simulation. 2A02:C7D:8A9:6700:4082:5C5:DABF:ADCE (talk) 18:22, 15 November 2022 (UTC)

Incompatibility between clone independence and proportionality

Douglas Woodall shows that clone independence is incompatible with the Droop proportionality criterion here: http://www.votingmatters.org.uk/ISSUE3/P5.HTM

As such, the clone independence column should be removed from the "Compliance of non-majoritarian party agnostic multi-winner methods" section because it would be uninformative: every Droop-proportional method fails it, and probably so does every proportional method in general. The gist of Woodall's observation is that suppose some coalition X has fielded too few candidates (e.g. it has 80% support but only a single candidate in a 10-winner election). Then cloning X will always make both X and the clone win, and that happens at the expense of some other candidate, hence a violation of clone independence.

Woodall suggests replacing clone independence with three criteria (clone-no-harm, clone-no-help and clone-in), but I don't know any sources that have done so.

In addition, that every method is claimed as being clone-proof despite Woodall's impossibility observation suggests that more of the data may be suspect as well, and so the claims made could use more references in general. 82.164.37.138 (talk) 12:26, 23 August 2019 (UTC)

I assumed that "adding irrelevant (non-winning) clones should not be able to change the election results" was an obvious generalization of the Independence of Irrelevant Clones criterion to multi-winner races because clones are no-longer irrelevant if they win. I thought that this generalization was obvious since candidates are no-longer irrelevant if they win seats. The ICC criterion was also modeled after the IIA criterion and this is also how it is defined: adding irrelevant (non-winning) alternatives should not be able to change the election results. While it seems that the independence of irrelevant alternatives is technically a single winner criterion was originally a single-winner criterion as described in your link, monotonicity was also originally only defined for ordinal methods though this wiki page uses the most reasonable extension of the criterion to cardinal methods as well: https://www.electionscience.org/library/monotonicity/ (though unlike the monotonicity extension, there doesn't seem to be as much of an effort to extend ICC in this way). I want to hear from other editors: for the sake of clarity, are you OK with using this definition of ICC for the multi-winner table? ParkerFriedland (talk) 05:58, 28 August 2019 (UTC)

That doesn't work even for single-winner clone independence. Suppose we're using Borda and Y wins, then we add a clone of X, called X2; and after the cloning, X2 wins. If "clones are no longer irrelevant if they win", then the candidate X2 is not a clone, and so that is not a clone failure. The deeper problem, though, is that just generalizing criteria (even if obvious) can get into original research territory unless there's a published source that can be used to reference that particular generalization. So apart from notability concerns, there's no problem with, e.g. replacing multiwinner ICC with Woodall's clone-no-help. But because there are no sources showing that e.g. Schulze STV passes or fails clone-no-help, all that would lead to is a column full of blank values. Simply saying "clearly, Schulze STV must pass clone-no-help because single-winner Schulze does so" could, besides being original research, easily be wrong. Indeed, Woodall shows that although AV is clone-proof, STV fails clone-no-help. The point is that we don't know. 46.66.178.159 (talk) 13:58, 5 September 2019 (UTC)

"That doesn't work even for single-winner clone independence". Well kind of. Each example in which it "doesn't" work contains an example in which it does work. Whenever you can clone X such that X2 wins a single winner election, you can also clone X such that the original X wins. As a result, even though this modified criterion disagrees with the original ICC about which single winner elections violate ICC, it still agrees with ICC 100% of the time about which single winner voting methods do or do not contain violations of ICC so it is still technically equivalent to IIC in the single winner case (if you view criteria as simply pass/fail tests). Though I do agree that it is awkward that this extension doesn't always agree with IIC in individual elections for single winner positions. Perhaps there is a way for this extended criteria can be worded to also agree with IIC in individual single winner elections as well without having an impact on what methods ultimately pass/fail the criteria. As for Woodall's clone-no-help criteria, I don't see that criteria as being desirable. Consider the fallowing election:

2 voters approve of A and S

2 voters approve of A and B and S

1 voter approve of B and S

2 voters approve of B and C and S

2 voters approve of C and S

If there are 3 winners, one of the winners is obviously S and for the other two it makes the most sense for a proportional voting method to chose A and C since that outcome leads to far more voters being represented, but if S is cloned then after you assign a seat to both S candidates the obvious choice for the third candidate becomes B, though if you pick SSB and you picked SAC in the previous example, you would be violating clone-no-help since the clone is causing candidate B to win and clone-no-help states that cloned candidate cannot help any non-clone candidates win seats. A better alternative might be Warren's clone-imunity criteria (https://rangevoting.org/QualityMulti.html#psibest) though that criteria is only defined for voting methods that use a quality function to grade each outcome (Harmonic, PAV, Monroe, Elbert, etc.) ParkerFriedland (talk) 09:50, 6 September 2019 (UTC)

It sounds like more research is needed. Once that's done, we can refer to it. Alternatively, the clone criteria may be useful to judge nonproportional methods like Minmax Approval but not proportional ones. 46.66.178.159 (talk) 13:45, 20 September 2019 (UTC)

The term "Monroe's method"

Quoting the original paper by Burt Monroe:

"Let us first establish some definitions. We assume that we can quantify the misrepresentation of voter v_a when represented by candidate x_i; call this mu_ia. Further assume that for reasons of voter equality, the scale of mu_ia across voters can be normalized and then compared."

(under "The Pure Fully Proportional Representation Concept")

"For m = 1, the pure FPR system is equivalent to the Borda count. In this example, the Independent is the clear Borda winner. All of the advantages and disadvantages of the Borda rule are inherent in ordinal FPR (...)"

(under "An Example")

In the abstract of Brams and Potthoff's paper "Proportional Representation: Broadening the Options", the authors write:

Under Monroe's system and our generalizations of it, one minimizes total misrepresentation, where misrepresentation is based on approval votes, the rankings of candidates, or other ballot information.

Monroe's method can thus be applied to any weighted points system, and in fact, Monroe uses Borda in his example. Calling only the particular version that uses Approval or Range scores "Monroe" is like saying that Minmax must always use pairwise opposition and thus that Minmax always passes the Favorite Betrayal criterion.46.66.178.159 (talk) 08:38, 6 September 2019 (UTC)

References

Comparison chart color scheme

Could one of you add an explanation or chart for the color scheme in the comparison charts? There are 2 colors for "No" and 2 colors for "Yes". HSukePup (talk) 23:26, 17 October 2019 (UTC)

I think the general idea is that the more bold shades meet the criteria more strictly, while the lighter shades may have some exceptions or require further explanation. 170.135.176.108 (talk) 13:17, 5 November 2019 (UTC)

Highest median and resolvability

The article claims that highest median satisfies resolvability. Could please someone elaborate this claim? Markus Schulze 18:09, 13 December 2020 (UTC)

Clearly the highest median from a finite scale does not satisfy this property. It must be completed in one way or the other in order to distinguish between candidates with the same median evaluation. See the wikipedia article Highest median voting rules.--Tiritigi (talk) 16:47, 21 July 2021 (UTC)

Inconsistent color scheme in comparison

The color scheme in the comparison table indicates the following scale:

• Scores: Best
• Approvals/Rankings: Second best
• No mark (dictatorship, random): Second worst
• Single mark: Absolute worst

This implies that score-based voting systems are superior to ranked voting systems. In the literature, Approvals are considered a floor/ceiling score based system; and score systems are considered highly vulnerable to strategy and generally unable to provide good electoral outcomes in practice. Strictly speaking, the literature suggests score-based systems are among the worst systems, barring single-mark systems. I am uncertain if general consensus as such is representative of what may be considered facts, or if presentation is suggested to be neutral in such a way that Wikipedia would present global warming skepticism as equally valid as the mainstream scientific consensus on climate change; but as it stands, the color scheme—which has now been rolled back from an earlier edit to clarify—gives the automatic impression that global warming is fake news, so to speak, regarding scored versus ranked systems.

Given the literature and the use of a four-scale color scheme, I suggest the below is more scientific and less blatantly biased:

• Rankings: Best
• Approvals/Scores: Second best
• Single mark: Second worst
• No mark (dictatorship, random): Absolute worst

Even this is generous to scores, and only because approvals are considered scores in the literature and are reasonably so. The literature isn't the problem on Wikipedia, though; between FairVote and the few Score vote supporters who started their own barely-existent advocacy groups, there is a lot of subtle tweaking to cover up flaws and elevate the status of one voting system over another as an ongoing propaganda campaign. It is perfectly reasonable and in fact important to discuss some systems as being better than others, so long as this can be backed up with literature weighted for methodological quality and general consensus, and fits with consistent normative values Wikipedia assumes are used for such evaluation or else with declared criteria constituting "better." It is also reasonable to expect presentation will be interpreted by the reader and so can convey things the words don't strictly say. Tables are quite nice, as it's hard to twist bare facts when presented without interpretation (even though these tables don't give weighting to the importance of criterion or their probabilistic failure rates and practical considerations); but apparently there are ways to manipulate that as well. John Moser (talk) 15:10, 14 March 2021 (UTC)

@Bluefoxicy I have recently removed claims that cumulative voting and quadratic voting are cardinal methods, per discussion https://wiki.riteme.site/wiki/Talk:Cumulative_voting#Cumulative_voting_is_a_cardinal_voting_system,_right? and https://wiki.riteme.site/wiki/Talk:Cardinal_voting#Cumulative_voting_seems_to_be_a_cardinal_voting_system

I was thus confronted by the question of what category cumulative and quadratic belong to, if not cardinal nor ordinal. The table you reference, as well as your post, indicates 'mark(s)' as a distinct category. (In my mind, I was thinking 'points' or 'coins'). Do you have any link to a reliable reference for this 'third category'?

Sorry for not answering your question. DougInAMugtalk 11:01, 27 May 2022 (UTC)

That's an odd one. Approval voting is like a ranked system in which only two ranks are allowed, but equal ranking is allowed. Some literature describes approval voting as a score voting system where the score can be only 0 or 1. I have been somewhat inclined to accept this description, although my description of approval as an ordinal system with certain restrictions (and of multiple non-transferable vote as condensing the top 3 preferences to rank 1 and the remainder to rank 2) highlight a larger lack of information (it's also one of the situations in which cardinal systems are considered to have less information under any theory).

Cumulative voting, like approval and MNTV, only allows a coarse-grained vote; but it takes it as a score, making it more similar to a cardinal system, if an implicit one. Notably, cumulative voting doesn't use a cardinal ballot. Ordinal systems take into account ordered preferences; Borda is both an ordered preference system and a score system (seriously, this is relevant in voting theory). The term "score" is more common than "cardinal" in voting theory literature, and I'm unclear on if they are considered the same; Marchant seems to describe Borda's cardinal properties in a discussion on whether the Borda score is cardinal or is only used as an ordinal to determine a ranking.

Single-mark, score, and rankings are different types of ballots. It seems to me the literature considers a system as cardinal or ordinal based on different properties. We might consider single-mark systems as cardinal, although candidates aren't really independently scored, if we consider Borda to be cardinal, since Borda is also not independently scored (score is based on positional ranking). In fact, Hillinger describes first-past-the-post as cardinal, so I guess cumulative would also fall under cardinal. John Moser (talk) 05:44, 7 August 2022 (UTC)

They aren't the same; the papers you link seem to be confused as to what "cardinal" means. "Cardinal" means cardinal utility—a cardinal number measures how much support you give a candidate. Cumulative voting is therefore a cardinal system, and it does use a cardinal ballot (because you mark a number next to each candidate, which says how much support you're giving to a candidate).

The articles you list confuse cardinal utility with point-summing methods, i.e. anything that uses addition. This would include score voting and cumulative voting (cardinal systems), but exclude other cardinal systems like highest medians. Point-summing methods would include the Borda count (another ranked/ordinal system). Closed Limelike Curves (talk) 22:29, 11 March 2024 (UTC)

Serious issues with this article

If I were a Wikipedia editor I would be put the "This article has multiple issues..." health warning at the top. However, I am not a Wikipedia editor and I say instead that this article contains some serious, industrial strength, claptrap.

I came here (to this article) for enlightenment - and I do know a thing or two about electoral systems. But this article does not enlighten me. So far I have got as far as the section, "Direct comparisons between first-past-the-post and proportional voting" and I make the following comments--

1. The statement, "With proportional voting, virtually every voter can point to the representative they voted for" is just plainly not true. That the opposite is true is the main drawback of proportional voting.

2. The statement,

"if a seat is obtained with 20 percent of the vote (which can occur), and a decision is subsequently made with 40 percent of the council members, then the voters' input can be declared as diminished, since about 12 percent of voters have indirectly made the winning decision. If decisions made in proportional voting are won with an absolute majority of the votes by the people who got their seats based on the direct distribution of the constituents' votes, then there is at worst a 50 percent weakening in the representation of voters' opinions, in the sense that a decision represents (indirectly, via the representatives) at least 50 percent of the voters"

needs some serious clarification. How on earth do these numbers tie together? There is no reasoning to support the figures and no reference to seek further clarification.

3. The statement,

"This shows how one system is more accustomed to having a more vertical power structure whereas the other is more collaborative or horizontal in nature."

is nonsense. Please clarify what vertical and horizontal power structure are.

4. The statement,

"In general, the two major parties will have no problem absorbing third-party issues as their own, covering any gaps both forgot to cover collectively. Both parties may therefore deliver close to what the voters want."

is pure unalloyed claptrap - it is a statement of opinion that no third party in the UK (for example) would agree with.

If this section is indicative of the rest of the article it will not be worth reading. — Preceding unsigned comment added by 146.200.235.218 (talk • contribs)

The comparison tables at the bottom are the important part of this article. Yes the introductory sections need revisions, but most of us who are election-method experts skip over those to focus on the comparison tables.

A big issue is that the "electoral systems" article only covers vote-counting methods that are in use by governments. That excludes vote-counting methods that are used but not yet used within governments. These methods need to be compared. Part of the issue is that the term "election methods" has different meanings, and the in-use-by-governments meaning is the one that editors have imposed on the "electoral systems" article.

You are welcome to improve the wordings in the beginning sections. However, please don't criticize the entire article without looking at the entire article. VoteFair (talk) 18:51, 22 June 2021 (UTC)

I find the entire article (not just the mini-essay at the beginning) unenlightening. I will see if I can make some changes. And I would encourage the anonymous complainant to create an account, if only so that his or her criticisms get taken more seriously. Colin.champion (talk) 13:40, 24 June 2021 (UTC)

Well, I did some edits; I hope people find them acceptable. There were some surprising gaps in the literature. The rightful winner under a spatial model is universally identified as the candidate optimising a quantity whose absolute optimum is the geometric median of the voter distribution: this fact is neither obscure nor controversial, yet no paper I consulted mentioned it (and Tideman and Plassmann seem to confuse median with mean at one point).

I’m fairly sure there’s a significant numerical error in the Green-Armytage et al 2015 paper. Table 2 shows Hare’s method to be 94.45% accurate and Minimax 95.19% accurate. I find it incredible that the results should be so close, given the known failures of Hare’s method to elect the consensus candidate. Darlington’s evaluation gives a much wider gap between the two methods. I wasn’t able to get to the bottom of this. Unfortunately it casts doubt on the most interesting conclusion of the paper, which is the impressive performance of ‘Condorcet-Hare’. Colin.champion (talk) 08:52, 12 July 2021 (UTC)

Acknowledgement. In the attempt to close some of the gaps I found (particularly from the direction of the median voter theorem), I took advice from Valerio Dotti of Ca' Foscari University of Venice. Obviously he has no responsibility for the faults which remain. Colin.champion (talk) 06:51, 23 July 2021 (UTC)

I can offer a possible explanation of the questionable figures in Green-Armytage et al. The results quoted for Hare are perfectly believable for Coombs. Perhaps the authors had an implementation with a flag to switch between Hare and Coombs, and performed the evaluation with the flag wrongly set. Colin.champion (talk) 08:28, 1 August 2021 (UTC)

Condorcet's title

My translation was correct, as is confirmed by published sources (eg. Szpiro’s book: “Essay on the application of probability analysis to majority decisions”). The title in the Condorcet article seems to have been copied from Google translate by someone with no knowledge of the language. Is duck à l’orange “duck to the orange”? Colin.champion (talk) 13:32, 22 July 2021 (UTC)

Results table

I’ve added a table showing the relative accuracies of a few ranked voting methods. I originally intended it for the ranked voting article, where there was some discussion (see the talk) but I got cold feet and thought that it was better to put it somewhere which provides more context. Colin.champion (talk) 10:36, 9 August 2021 (UTC)

Jury models and social utility efficiency

n method	5	25	125
FPTP	55.6	52.3	51.2
AV/IRV	61.9	60.1	60.2
Coombs	66.6	61.8	60.8
Borda	71.9	71.2	71.2
Minimax	65.7	65.1	65.1
Copeland	67.9	65.7	65.4

The article previously devoted a lot of space to a discussion of metrics. This seemed misguided to me – the metrics are almost wholly presentational whereas the substance of a comparison lies in the model. A pattern emerged from Bordley’s and Merrill’s evaluations of utilitarian metrics favouring the Borda count over Condorcet methods.

Bordley’s result is genuine but nothing to do with metrics: he essentially used a jury model, and it has been known for some time that the Borda count is approximately optimal under it. I coded up Bordley’s evaluation for σ²=0 and varying numbers of voters; some results are shown here. (There are 5 candidates. The numbers in the table are the percentages of cases in which the best candidate is elected. The Copeland tie-break is to choose the Copeland winner with the largest number of first and second preferences combined.)

I’ve added a brief discussion of jury models to the article since they’re interesting in their own right. The arctan formulae for p play no part in the argument; they make use of an integral which will be found on stackechange.

Merrill’s results are based on a spatial model. So far as I can see his margin between Borda and Condorcet is less than experimental error, and maybe much less, so it probably doesn’t mean anything. I find it incredible that a small change in metric should overturn the superiority of Condorcet methods, and when I look into the question myself in one dimension I find that Condorcet methods continue to outperform the Borda count. I illustrate this by a mini-table in the article. It requires a few extra lines in my software, which follows. The formula for the metric uses the fact that the average distance from x to a point in a standard Gaussian distribution is $x(2\Phi (x)-1)+{\sqrt {\tfrac {2}{\pi }}}e^{-{\tfrac {1}{2}}x^{2}}$.

C program

#include <math.h> #define pi 3.141592653589793 double rtlnorm(double),gaussv() ; static double qk = sqrt(2/pi) ; int fptp(int **bal,double *qwt,int nbal,int m) { double q,*score=vector(m) ; int t,winner ; for(t=0;t<nbal;t++) score[bal[t][0]] += qwt[t] ; for(q=winner=t=0;t<m;t++) if(t==0||score[t]>q) { winner = t ; q = score[t] ; } free(score) ; return winner ; } int borda(int **bal,double *qwt,int nbal,int m) { double q,*score=vector(m) ; int balno,t,winner,*b ; for(balno=0;balno<nbal;balno++) for(q=qwt[balno],b=bal[balno],t=0;t<m-1;t++) score[b[t]] += q * ((m-1)-t) ; for(q=winner=t=0;t<m;t++) if(score[t]>q) { winner = t ; q = score[t] ; } free(score) ; return winner ; } int minimax(int **bal,double *qwt,int nbal,int m) { double q,*qmin=vector(m),**r=matrix(m,m),qmax ; int i,j,balno,t,winner,*b ; for(balno=0;balno<nbal;balno++) for(q=qwt[balno],b=bal[balno],i=0;i<m-1;i++) for(j=i+1;j<m;j++) r[b[i]][b[j]] += q ; for(i=0;i<m;i++) for(qmin[i]=1,j=0;j<m;j++) if(i!=j&&r[i][j]<qmin[i]) qmin[i] = r[i][j] ; for(qmax=winner=t=0;t<m;t++) if(qmin[t]>qmax) { winner = t ; qmax = qmin[t] ; } free(qmin) ; freematrix(r) ; return winner ; } int av(int **bal,double *qwt,int nbal,int m) { int t,tau,balno,winner,loser,mleft,**b=imatrix(nbal,m) ; double qmin,*score=vector(m) ; for(balno=0;balno<nbal;balno++) for(t=0;t<m;t++) b[balno][t] = bal[balno][t] ; for(mleft=m;mleft>0;mleft--) // mleft is the number of remaining candidates { for(balno=0;balno<m;balno++) score[balno] = 0 ; for(balno=0;balno<nbal;balno++) score[b[balno][0]] += qwt[balno] ; for(qmin=loser=t=0;t<mleft;t++) if(t==0||score[b[0][t]]<qmin) { loser = b[0][t] ; qmin = score[loser] ; } for(balno=0;balno<nbal;balno++) for(tau=t=0;t<mleft;t++) if(b[balno][t]!=loser) b[balno][tau++] = b[balno][t] ; } winner = b[0][0] ; free(score) ; freeimatrix(b) ; return winner ; } int main(int argc,char **argv) { int (*alg[])(int **,double *,int,int) = { borda , fptp , minimax , av , 0 } ; char *algname[] = { "borda" , "fptp" , "condorcet" , "av" , 0 } ; int testno,i,j,t,l,r,ntests=1000000,nalg,rightful,winner ; for(nalg=0;alg[nalg];nalg++) ; int m = (argc>=2?atoi(argv[1]):3) , m2 = (m*(m-1)) / 2 ; double offs=(argc>=3?atof(argv[2]):0) ,ql,qr,q ; int *win = ivector(nalg) , *ballot = ivector(m) , **bal = imatrix(m2+1,m) ; double *c = vector(m) , *qwt = vector(m2+1) , *qdist = vector(nalg) ; xi *cm = xivector(m2) ; for(testno=0;testno<ntests;testno++) { for(i=0;i<m;i++) c[i] = gaussv() + offs ; realsort(c,m) ; for(t=i=0;i<m-1;i++) for(j=i+1;j<m;j++,t++) cm[t] = xi((c[i]+c[j])/2,(i<<8)|j) ; xisort(cm,m2) ; for(i=0;i<m;i++) ballot[i] = i ; for(ql=1,i=0;i<=m2;i++,ql=qr) { if(i==m2) qr = 0 ; else qr = rtlnorm(cm[i].x) ; qwt[i] = ql - qr ; for(t=0;t<m;t++) bal[i][t] = ballot[t] ; if(i==m2) break ; l = cm[i].i >> 8 ; r = cm[i].i & 255 ; for(t=0;t<m-1&&ballot[t]!=l;t++) ; swap(ballot[t],ballot[t+1]) ; } for(q=rightful=t=0;t<m;t++) if(t==0||fabs(c[t])<q) { rightful = t ; q = fabs(c[t]) ; } for(t=0;t<nalg;t++) { winner = alg[t](bal,qwt,m2+1,m) ; if(rightful==winner) win[t] += 1 ; q = c[winner] ; qdist[t] += q*(1-2*rtlnorm(q)) + qk*exp(-q*q/2) ; } } printf("m=%-2d, x=%.2f",m,offs) ; for(t=0;t<nalg;t++) printf(" | %s: %4.1f",algname[t],win[t]*100.0/ntests) ; printf("\n") ; for(t=0;t<nalg;t++) printf(" | %s: %5.3f",algname[t],qdist[t]/ntests-qk) ; printf("\n") ; }

Unencyclopedic content

The table at the start of the article, in which 22 experts were asked which voting methods they would each endorse, does not qualify as encyclopedic content and should be removed.

If there were a well-conducted survey of a large number of voting theorists, representative of the overall opinion of the academic field, the results of that survey would be encyclopedic content and would deserve its own section in this article.

However, the table simply conveys the opinions of 22 people who just happened to be attending the same workshop as each other. The source of the table (Laslier, "And the Loser is... Plurality Voting", 2011) does not claim to be the consensus opinion of the academic field. Without additional context, the table could easily be misinterpreted as such.

Ancophosep (talk) 18:40, 27 September 2021 (UTC)

I respectfully disagree. 'Participants of the workshop were specialists in voting procedures and, during the wrap-up session at the end of the workshop, it was decided to organize a vote among the participants to elect “the best voting procedure”.' It's NOT 22 people selected at random. It has since been published an a collection of research papers:

Jean-François Laslier (2011). And the loser is... Plurality Voting. ISBN 978-3-642-42955-2. ISSN 2267-828X. Wikidata Q108664719. {{cite book}}: |journal= ignored (help)

Chapter 13 in Dan S. Felsenthal; Moshé Machover, eds. (2012). Electoral Systems: Paradoxes, Assumptions, and Procedures. Springer Publishing. ISBN 978-3-642-42955-2. OL 34499598M. Wikidata Q108732568.

DavidMCEddy (talk) 13:51, 28 September 2021 (UTC)

Thanks for your comment Ancophosep. Can I say a word in defence of the stackexhange reference? The Wikipedia policy on reliable sources is intended to ensure verifiability, but mathematical results can be confirmed by validating the reasoning leading to them – this is explicitly permitted. In the present case the necessary substitution doesn’t leap to the eye, so the reference gives the reader a hint as to how to perform the derivation. Nothing rests on the reliability of stackexchange posts. (But I confess to not having checked the reasoning myself... I don’t think that’s the point.) Colin.champion (talk) 16:43, 28 September 2021 (UTC)

I was not aware of Wikipedia's policy on mathematical results. Thank you Colin.champion for informing me. I have removed the Better Sources Needed tag that I added earlier.

Ancophosep (talk) 17:11, 28 September 2021 (UTC)

Thank you DavidMCEddy for your reply.

I agree with what you've said. The vote was between 22 experts in voting theory (not 22 random people). The vote was to decide the best voting rule to elect a local mayor. The original paper (Laslier, 2011) is notable enough to be included in a collection (Felsenthal/Machover, 2012). My original comment was not intended to dispute any of these facts; I apologize if I gave that impression.

The root of my concern is that an ordinary Wikipedia reader is likely to misunderstand what the vote represents. The current framing is: "A panel of 22 experts on voting procedures were asked in 2010 to say which of 18 representative single-winner voting methods they endorsed." This phrasing makes is seem like 22 experts, who were representative of their field, carefully considered 18 different voting methods, and decided which of the voting methods were better in general. Introducing the vote results like this is wildly misleading.

If the table is to be included in the article, it MUST be framed correctly. The 22 experts constituted a nonrandom nonrepresentative subset of all voting experts; there is no reason to believe that these 22 people can speak on behalf of their entire academic field. The vote was for a system to elect a local mayor; Lasier (2011) makes it clear that different voting rules would be preferable in different circumstances, so this IS NOT a vote on "What is the best voting rule, in general?" The introductory paragraphs of Appendix I of Laslier (2011) indicate that the vote was informal and that the 22 experts did not have time to consider their votes beforehand, meaning that the results of the vote do not reflect the careful considerations of experts, but rather the gut reactions of experts.

My second point is that when the results of the vote are placed in context, they are not significant enough to be included in this article. The preface to Felsenthal/Machover (2012) states that if the vote were repeated, the circumstances would be different, and we could expect different results. So if repeating the vote would give different results, what is the significance of the original results? Felsenthal/Machover (2012) answers this by labeling it as the "first and last naïve vote on voting rules by voting theorists". This special status is relevant to the comparison of electoral systems, and certainly the fact that this vote occurred must be mentioned somewhere in the article. However, because the results of the vote represent the "naïve" gut reactions of a nonrandom nonrepresentative subset of voting experts, I would argue that they are not particularly relevant or helpful to the ordinary Wikipedia reader. Wikipedia is intended to be a summary; it should not contain every detail of a topic.

Ancophosep (talk) 18:42, 28 September 2021 (UTC)

Mention added of STAR

@JusticeShampoo: added a sentence to the lead para mentioning that STAR had been first proposed in 2014, presumably as an explanation for its absence from the table of methods assessed by Laslier et al. It would be very cumbersome if every method invented since 2010 needed to be mentioned in this way. On the other hand the table isn’t presented as authoritative on the relative values of voting systems, and I don’t think any reader would interpret it otherwise.

There are similar tables elsewhere on Wikipedia. There have been surveys of economists trying to find what common ground exists between them (“is government spending a stimulus?”) and these have not been caveated more heavily than the table in this article. Colin.champion (talk) 08:51, 16 October 2021 (UTC)

I haven’t seen any specific Wikipedia guidance on surveys of expert opinion, but there is guidance on including biased statements. It seems to me that an informal survey is less questionable than a potentially biased source, and that the caveats present in the article go beyond what Wikipedia calls for when there is a risk of bias. Colin.champion (talk) 12:23, 16 October 2021 (UTC)

Summability

It seems to me that the summability criterion needs to be added to the table comparing various methods. Who's going to take that on? -- RobLa (talk) 04:22, 9 February 2022 (UTC)

Unreliable sources

@Closed Limelike Curves: Which sources cited in this article are not reliable? Jarble (talk) 15:33, 13 March 2024 (UTC)

For instance, the "Compliance of non-majoritarian party-agnostic multi-winner methods" table massively links to the "rangevoting" Page or even to a google groups chat or just random pdfs. Jannikp97 (talk) 16:18, 18 March 2024 (UTC)

Delete the Multiwinner part

Hi,

the multiwinner part of the article currently seems of very very low quality. Dubious methods, original research, even more dubious axioms. I feel like currently it might be better to just delete it and then start to restructure stuff a bit. @Closed Limelike Curves@Wotwotwoot Jannikp97 (talk) 19:22, 5 April 2024 (UTC)

I think that's a good idea! Closed Limelike Curves (talk) 20:48, 5 April 2024 (UTC)

I think the "Compliance of non-majoritarian party-agnostic multi-winner methods" could be salvaged by removing self-published properties and methods. As for the other tables, I think they can just be deleted. The "Compliance of party-based multi-winner methods" section is just a mess and the majoritarian table more or less just repeats the properties of the corresponding single-winner methods. Wotwotwoot (talk) 20:54, 5 April 2024 (UTC)

Cleaning up the single-winner criterion section

I've been cleaning up the tables and reducing the redundant information into just the one template table shared with other articles. Let me know if I should put back in a second table containing the information I left out of the template table. The preceding list of criteria probably needs to be cleaned up, since the reader can just go to the page on that criterion if they want to learn about it. It's already basically just a list of definitions, which makes for a very difficult read. Jasavina (talk) 03:42, 23 May 2024 (UTC)

I'm going to clean up that section for readability. I'm going to try and preserve as much information as possible, which includes adding back in some of the information I took out of the table and putting it in a second table. Any suggestions welcome but my plan is to put the list of definitions into yet another table. It's hard to keep them distinct listed as-is. Jasavina (talk) 17:14, 26 May 2024 (UTC)

I've got almost all of the changes staged on my user sandbox page. If you (the reader) could please take a look for any errors and let me know that would be very helpful. Of particular concern are the big-O notation columns in the last table along with the Dodgson row, for which I could only find limited information. Cheers. Jasavina (talk) 14:04, 14 June 2024 (UTC)

Thank you greatly for the effort. I'm apologize if my notes are too numerous, scattered in topic, or mixing of content/structure and objective/subjective feedback. I'm going to try to go in sandbox page order.

-I think the organization of criterion in multiple tables is appropriate, more concise, and more readable.

-It's very eyebrow-raising that we maintain different ranked and rated majority criterions purely for the sake of Approval. All of our other criterion are based on whether a scenario of underlying voter preferences result in a given outcome (such as a majority of voters most supporting a candidate electing that candidate), while the rated majority criterion flips this and only evaluates such scenarios as can be determined by the ballots produced. In other words, it supposes that preferences are determined by ballots rather than the other way around. By this logic, Plurality passes Condorcet Winner, because it indeed elects any Condorcet winner that is self-evident from its own ballots!

-I would suggest Majority Loser being its own row in the definitions table, only because it is its own column in the table.

-It's "Condorcet criterion" in the definitions table, and "Condorcet winner (criterion)" in the column header. Ideally they match.

-LIIA is in a different order in the definitions table than the columns; I prefer the column order.

-LIIA is so specific that I don't think it merits its own column. An argument could be made for it to be collapsed into an IIA cell footnote for Ranked Pairs and Kemeny-Young.

-I've always found "phenomena" to be a weird word to describe the impact of clones, implying a some exotic event more subject to observation than reason. As a straightforward mathematical interaction, I would use "interaction" or "dynamic."

-The Resolvability definition should probably be more firm in stating "all cases except exact ties by ballot count" or similar.

-The Summability line about higher-order functions making it "harder to catch fraud by election administrators" is uncited speculative junk. It might also be prudent to specify "easier hand-counting."

-The brief Ballot Format section is a little editorialized.

Now, the table:

-I really dislike having a split, two-part table.

-As suggested above, I would consider merging LIIA/IIA columns. Ranked Pairs and Kemeny-Young can be "No" with a footnote.

-Cardinal methods being listed as "Yes" for IIA is misleading, even with the footnote. The default assumption should be that cardinal ballots are normalized, and most related content (including some criteria on this very table) reflects this. Either these methods should be bifurcated into normalized and non-normalized row entries (such as "Approval" and "Approval (IIA)") that are listed as fulfilling their respective different criteria, the entire row should reflect the normalized version, or affected boxes should be a "yellow option" like "Depends."

-I'm not sure reversal symmetry merits inclusion on the table. Pretty much every scenario that violates it is non-pathological, whereas all other listed criteria are presented as desirable properties. This is more of a mathematical curiosity, of which there are countless we could entertain. It's also highly nuanced for more complex cardinal methods.

-I have mixed feelings about the polytime column. I don't think it is terribly relevant, and this is strictly worst-case. All Condorcet methods have a O(N^2) typical case computation time.

-The "Semi" Resolvable entries are nonsense.

-It's unclear why Sortition fails Resolvability but Random Ballot passes. It feels like the semantics of the definition are being applied unevenly or too literally. Perhaps the Resolvability definition should reflect that a method cannot fail such that it need to defer to another method, such as randomness. A method that *is* randomness should certainly be said to "resolve" when it delivers its definition.

-Summable is also weird. All methods are inherently summable in the min of the listed value and the voter count, so there's a cap on things that is not clearly implied. (In most cases, the relevant context here is precinct-level, precinct size.) Additionally, certain methods like Tideman Alternative have lower (O(N^2)) expected case summability than worst-case. Chocolate Pi a la Mode (talk) 21:33, 15 June 2024 (UTC)

Thank you VERY much for your detailed feedback. I agree with most of your helpful feedback and will be taking some time to go through it and make changes where I can. My stamina-related disability may stretch the timeline a little bit.

As an explainer, the new formatting I plan on putting in is mostly just tho same information that was in the section before I started to clean it up. My educational background in this area is solidly casual, so I try not to make too many judgment calls about the information itself. That's actually where tho second table comes from. It's the information I had to take out to simplify tho original pair of tables. (The first is a template shared between multiple pages.) However, I feel that the information in that second table is mostly pointless, so with your welcome disapproval I'm going to leave it out.

To make my reply easier to reference back to yours:

-I think the organization of criterion in multiple tables is appropriate, more concise, and more readable.

I'm happy we agree

-It's very eyebrow-raising that we maintain [...]

Valid criticism of the current definitions and I'll see how easy it'll be to merge them,

-I would suggest Majority Loser being its own row in the definitions table, only because it is its own column in the table.

Good point, will do.

-It's "Condorcet criterion" in the definitions table, and "Condorcet winner (criterion)" in the column header. Ideally they match.

Will fix

-LIIA is in a different order in the definitions table than the columns; I prefer the column order.

-LIIA is so specific that I don't think it merits its own column. An argument could be made for it to be collapsed into an IIA cell footnote for Ranked Pairs and Kemeny-Young.

I agree. I had them separated to match the original template table, but the footnote solution is better.

-I've always found "phenomena" to be a weird word to describe the impact of clones, implying a some exotic event more subject to observation than reason. As a straightforward mathematical interaction, I would use "interaction" or "dynamic."

I might go with "situations"

-The Resolvability definition should probably be more firm in stating "all cases except exact ties by ballot count" or similar.

I'll use that wording

-The Summability line about higher-order functions making it "harder to catch fraud by election administrators" is uncited speculative junk. It might also be prudent to specify "easier hand-counting."

Agreed

-The brief Ballot Format section is a little editorialized.

I'll completely rewrite that with a neutral tone.

-I really dislike having a split, two-part table.

I think none of the information in the second table is meaningful enough to be included, I was trying to minimize the amount of information I changed, but I vote we just leave it out.

-Cardinal methods being listed as "Yes" for IIA is misleading, even with the footnote. The default assumption [...]

This one goes over my head, but if you want to give me the exact changes you want I can implement them. Or you can fix the live template at any time, since it's the same source.

The rest of your comments are addressed to the second table, which I really propose we just leave out. It was an attempt to restore information that was on the main page before I started cleaning it up, but I don't think it should be included.

Again, massive thank you for going through the changes and I'll get to work cleaning it up and push it to the main page when it's ready. Jasavina (talk) 22:35, 20 June 2024 (UTC)

You asked for feedback. The ballot type is a very important comparison, yet it has disappeared. I find it useful to sort the table based on that ballot type. And it's extremely useful for someone newly learning about the differences between the methods. Personally I would put it at the left side. Otherwise I like the cleanup! VoteFair (talk) 17:57, 18 June 2024 (UTC)

I can add that back in, no problem! Jasavina (talk) 22:36, 20 June 2024 (UTC)