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Voting theory articles

For discussion of which methods and should be included in the mainstream of the voting theory articles, see Talk:Voting system/Included methods and criteria

— Preceding unsigned comment added by Hermitage (talk • contribs) 00:51, 27 July 2005‎ (UTC)

Voting system related pages WikiProject

A WikiProject is being developed at Wikipedia:WikiProject Voting Systems for further work on this and other voting system related pages.

— Preceding unsigned comment added by RobLa (talk • contribs) 00:54, 16 February 2003 (UTC)

Yay/Nay System

I'm looking for information on the Yay/Nay Voting System, but Wikipedia does not appear to have anything on this. Can I request someone write this up? —Preceding unsigned comment added by 82.37.37.44 (talk) 18:56, 10 May 2010 (UTC)

Do you mean approval voting or disapproval voting? Markus Schulze 22:54, 10 May 2010 (UTC)

IRV runtime (was: Added "summability" column)

Since both summability and "polynomial time" are fundamentally a question of big-O notation, the values are commensurable, even if they represent different steps of the process. Also, both refer to the counting process and not to the results. I'd love to find a way to word it so that we could collapse two columns (with one "red" each) into one column (with two "red" values). Homunq (talk) 20:36, 12 February 2010 (UTC)

Wait a minute. If IRV has non-polynomial data, how can it be polynomial time?

I think it's not polynomial time. Proof sketch: Consider the case of N candidates, in which all N! possible complete votes have been made by at least one voter. Each counting round is an order N operation on the remaining candidates (because the eliminated candidate's votes must be redistributed to each remaining candidate - that's at least one addition), and there are at worst N-1 counting rounds. Overall, that is order N!. I'm going to be bold and redo the given cell as a red "disputed", and I'd encourage anyone who can find (or make) a decent source on this question to make it "No". Homunq (talk) 15:30, 15 February 2010 (UTC)

Of course, that's a worst-case behavior. I'd be open to leaving it as a light-pink "no" with a footnote about how it's a worst case but the method is polynomial time in typical real-life cases. Homunq (talk) 15:37, 15 February 2010 (UTC)

Dear User:MarkusSchulze, your edit here, while good in other ways, changed IRV to be polynomial runtime. This is not in fact the worst-case runtime for the method, though it's not typically a problem practically. You are welcome to propose a different wording for the criterion such that IRV passes, but as it stands, this is wrong. I'm changing it. As always, if you differ, please comment here. I am aware that if you consider my view on this cell to be original research, as I consider yours to be (as well as false), we will have to blank out the cell for lack of consensus. Homunq (talk) 17:45, 27 May 2010 (UTC)

What nonsense. IRV takes up to (n-1) rounds of counting, each round counting m ballots. That's O(m*n) time! Comparatively Condorcet would be n*(n-1)/2 rounds of counting, O(n^2*m) time. The really STUPID thing here, is Condorcet is MORE comprehensive, and thus has a higher complexity of counting, while calling it O(n!) time could suggest IRV is more comprehensive, which isn't true at all! Tom Ruen (talk) 19:35, 27 May 2010 (UTC)

Apparently this confusion is caused by the desired summability stuff, which is an attempt to summarize data, BUT that is "space complexity" (And a theoretically one at that, since real elections will just transmit entire ballot data) but has nothing to do at all with "time complexity". Tom Ruen (talk) 19:40, 27 May 2010 (UTC)

The criteria as it stands states: "Can the winner be calculated in a runtime that is polynomial in the number of candidates and in the number of voters?". As Tomruen indicates, that's the wrong measure for IRV, which is nonpolynomial in number of candidates but only linear in number of ballots. Replacing "and" with "or linear" in the criteria lets IRV pass, and is an acceptable change to me. I'll do it. Homunq (talk) 20:03, 27 May 2010 (UTC) ps. Condorcet is not O(n^2 * m) but O(n^2 + m), which is an entirely different story.

Condorcet time complexity IS O(n^2*m). There are (n-1)*n/2 rounds of counting, and each round processes m ballots. If m doubles, the time doubles! Tom Ruen (talk) 21:47, 27 May 2010 (UTC)

In each IRV round, not more than m ballots have to be re-counted. There are (n-1) rounds in worst case. So the worst-case runtime of IRV is O(m*n). Markus Schulze 21:12, 27 May 2010 (UTC)

Sorry, you're right. I was trying to separate out the terms for M and N which gives O(n! + m). Mine is often optimal, because it's lower if m > n!, which is common. But yours is polynomial and so passes the criterion as before. I apologize. Homunq (talk) 21:47, 27 May 2010 (UTC)

Proxy voting

Not sure this belongs in the article, but isn't another voting system the use of proxies? In fact, Proxy voting is out there, but wasn't referenced (it is now.) Shouldn't there be a section on proxies in this article? More generally, don't proxies fix the fundamental flaws that have led to instant-runoffs and other variations (specifically for legislative elections in which there are subsequent votes)? I.e., that every candidate who runs for election "wins" and then gets a vote in the legislature weighted by the number votes he/she received. Then all points of view would be represented appropriately. I'm not trying to start an argument over this approach's merits, but shouldn't it be in the article?

— Preceding unsigned comment added by Lfstevens (talk • contribs) 01:30, 4 May 2010‎ (UTC)

Bucklin criteria

I added Bucklin to the table, mistakenly editing as an anon. User:MarkusSchulze then made a number of changes. He is right and I was wrong about the Condorcet Loser criterion. However, with equal rankings allowed, Bucklin clearly and simply complies with clone independence and IIA.

He also marked Bucklin as O(N**2), even though with a fixed number of ranks, it can be O(N). I understand that technically anything in a lower order is also in a higher order, so Schulze voting is technically also O(N!!!!!), but the point of O notation is to choose the lowest order possible.

Also, he put colors into the later no harm column, despite the text: "If, in any election, a voter gives an additional ranking, vote or positive rating to a less preferred candidate, can that additional ranking, vote or rating cause a more preferred candidate to lose? (This column in the table below is not colored, as some theorists dispute whether this property, which encourages fuller voting but prevents the system from choosing compromise candidates, is desirable.)"

All of this was done without comment, either in the edit note or here. Please, if you're changing substantive material, make at least a brief comment as to why. Homunq (talk) 19:22, 15 May 2010 (UTC)

Dear Homunq, your edits were not justified. Even the Wikipedia article on Bucklin voting says: "It fails the Condorcet criterion, independence of clones criterion, later-no-harm, participation, consistency, reversal symmetry, the Condorcet loser criterion and the independence of irrelevant alternatives criterion." Markus Schulze 19:44, 15 May 2010 (UTC)

We're not talking about other articles here. Wikipedia is not a reliable source. The fact is that with equality allowed and limited rankings, it passes IIA and clone independence. Since each candidate is separately ranked, the cutoff for winning in any round is absolute, and the cutoff for winning at the end is simply the highest total, both of these results are trivial.

Would you prefer to discuss this here, or over at the Bucklin article? I think that here is better, it has a wider potential audience. But if you want to do it there, that's fine with me too.

Also, what's your response on LNH? Homunq (talk) 20:04, 15 May 2010 (UTC)

Thank you for your response, User:MarkusSchulze. In the future, if there's an edit dispute, it is polite to make the argument on talk as well as in edit comments. Even better would be to resolve the matter on talk before going to the page.

You say: 'Removed weasel words: "Some theorists dispute whether this property is desirable."'. I have redone the statement without weasel words, as supported by the cited source. Homunq (talk) 10:42, 16 May 2010 (UTC)

User:MarkusSchulze, you just violated WP:3RR. I said I wouldn't consider it a violation if you responded here - but you didn't. I'm not going to report you, but consider this a warning. Politeness goes a long way.

As to substance, you say: "(Removed weasel words: "Michael Dummett and others dispute whether this property is desirable." For every criterion, there are people who don't consider this criterion desirable.)" You are wrong on two counts. First, "Michael Dummet and others" is no longer a matter of weasel words; your contention now is apparently that this is WP:UNDUE, not WP:WEASEL. Second, there is a difference between considering a criterion relatively unimportant compared to a conflicting criterion (which is, as you say, common), and considering it positively undesirable in itself (which is, I contend, only the case for LNH among the criteria given).

Please also respond regarding the Bucklin criteria. As I've pointed out on Talk:Bucklin voting, Arrow's theorem does not apply to most versions of Bucklin. Homunq (talk) 11:14, 16 May 2010 (UTC)

This discussion is boring. Every few days someone proposes a new method and claims that this method satisfies all important criteria and that the well-known theorems don't apply to this method. Homunq's claims are either original research or obviously false. Whatever they are, they don't belong to Wikipedia. Wikipedia is not a forum to check the correctness of original ideas. Markus Schulze 01:25, 17 May 2010 (UTC)

The truth is that much of the material on this page lacks citations. Nevertheless, it maintains consensus because it is true, and various parties which certainly have bones of contention still accept mathematical truth. And the mathematical truth is that Arrow's theorem simply does not apply to most versions of Bucklin. (It actually doesn't mathematically apply to any system which does not require full, equality-free ranking; but, unlike equality-allowed Bucklin, most of them nevertheless don't satisfy both MC and IIA).

If you insist on citation for the Bucklin row, that is your right. I certainly won't try to make a WP:POINT by being similarly insistent for the other rows or the rest of the article. However, I cannot permit you to value your own "original research" over mine. The relevant cells must then simply say "no reliable sources".

I hope that Bucklin will not be subject to standards of citation which other systems are not attaining. For instance, Markus, as I write this, your latest edits to the page, made AFTER your above accusation of OR against me, were to remove a pair of footnotes and thus strengthen the assertion (without sources) that Plurality and Runoff meet LNH. Since this is true and improves the page (good job, BTW), I'm not going to revert that or call it OR, even though you included no RS citations and I honestly doubt you have any.

I hope that the relevant cells (bucklin for IIA and clone independence) can say "depends on variant", with a footnote that explains that equality-allowed bucklin does satisfy these criteria, and perhaps some qualifier about the criteria being defined originally with only preferential systems in mind. I hope that we can avoid unsightly "no reliable sources" cells. MarkusSchulze, the ball is in your court. Please engage with the facts first, we can get the citations right later. Homunq (talk) 20:09, 17 May 2010 (UTC)

By the way: I would accept extending any quibbling footnote to the Bucklin/Majority criterion cell. If the MC is based on underlying preferences and not on the ballots, =Bucklin fails it. However, the top-line answer must still be that Bucklin passes the criterion; any quibbles go in a footnote.Homunq (talk) 20:47, 17 May 2010 (UTC)

Markus Schulze continues the edit war with [index.php?title=Voting_system&action=historysubmit&diff=362842652&oldid=362837811 this edit], saying "Dear Homunq, your claim, that it is unknown whether Bucklin voting satisfies independence of irrelevant alternatives, is ridiculous. See: Arrow's impossibility theorem." He is wrong for four separate reasons.

1. On the substance of the matter. Arrow's theorem shows that no voting system can meet universality, majority criterion, and IIA. Bucklin voting with equalities allowed (called =Bucklin from now on) obeys this theorem. It is not universal in the sense of Arrow, as the same preferences could lead to different votes. It also may not meet the majority criterion, depending on how that criterion is defined (there are several definitions which are equivalent for preferential systems but not for absolute ranking systems like =Bucklin. =Bucklin does, however, unequivocally meet IIA, under any definition.
2. On the substance of the edit. My version he reverted did not claim that "it is unknown whether Bucklin voting satisfies independence of irrelevant alternatives"; it simply stated the fact that we do not have any reliable sources that speak to the question. If he has such a source, I invite him to cite it.
3. About wikipedia content policy. On unsourced, disputed questions, the truth does not matter. Until there's at least a consensus on the truth (see above), the article must simply refuse to answer the question. That is exactly what my version did.
4. About wikipedia editing policy. This edit constitutes edit WP:WARring, which is strongly discouraged. Given that I recently reported him for violating WP:3RR, the one bright line in edit warring, he should have been particularly careful.

When I reported his 3RR violation, I asked for the minimum sanction necessary to bring him to participate in talk. That is still my position. If he continues his current behaviour, however, I will have to consider supporting having him banned from the article. That would be a pity. Mr. Schulze, please, please, step back from the edge, and let's treat each other like reasonable adults. Homunq (talk) 17:49, 18 May 2010 (UTC)

Copied from the 3RR report: "Dear Homunq, your claim, that it was unknown whether Bucklin voting satisfies independence of irrelevant alternatives, is obviously false. See: Arrow's impossibility theorem. Your edits are a clear violation of WP:WEASEL, WP:OR, WP:SOAP, and WP:NONSENSE. Markus Schulze 19:36, 18 May 2010 (UTC)"

Dear User:MarkusSchulze, I suggest you review Arrow's impossibility theorem. It proves 5 criteria incompatible: Non-dictatorship, Unrestricted domain, Independence of irrelevant alternatives (IIA), Monotonicity, and Non-imposition. Bucklin voting with equal ranking (=Bucklin) allowed satisfies 1, 3, 4, and 5, but violates 2 (unrestricted domain, as defined by Arrow). Thus it is fully compatible with the theorem. I've said this several times now, and you have yet to respond except by continuing to point to Arrow's theorem. If I didn't know better, I'd suggest you don't understand Arrow's theorem; since I do know better, I'm sure it's just an oversight, but it still does you no credit to insist without responding cogently.

Moreover, as I say above, though I personally do claim that =Bucklin satisfies both MC and IIA, your most recent article edit reverted a version of the article which made no such claim, but which simply reported the fact that there are no pertinent references associated with the article. If you're impervious to reason, then either one of us finds a citation, or the article returns to the version you reverted. End of story. Now stop edit warring, or you're going to get blocked. Homunq (talk) 20:04, 18 May 2010 (UTC)

Dear Homunq, what you label "Bucklin voting" is not Bucklin voting but Majority Choice Approval. It is clear that a Wikipedia article on Bucklin voting must be on Bucklin voting.

Furthermore, it is well known that Bucklin voting is not clone-proof. Example: Situation 1: 20:A>B>C, 17:B>C>A, 13:C>A>B. The Bucklin winner is B. Situation 2: A is cloned. 20:D>A>B>C, 17:B>C>A>D, 13:C>A>D>B. Now the Bucklin winner is A. Markus Schulze 16:42, 19 May 2010 (UTC)

So, you finally come to understand that it's a difference of definition. But you're wrong, and your tautologies don't help matters. Majority choice approval is a form of Bucklin. In at least one US municipality (I'll check which), "Bucklin voting" (so-called at the time) allowed equal rankings.

Furthermore, your "furthermore" is just saying the same thing in different words. You can say it 5 times and you'll still be wrong. Homunq (talk) 22:16, 19 May 2010 (UTC)

Not everything that is allowed in a mailing list is also allowed at Wikipedia. For example: Original research is strictly prohibited at Wikipedia. Biased articles are strictly prohibited at Wikipedia. By the way: The majority choice approval article has been deleted because it was original research. Markus Schulze 22:54, 19 May 2010 (UTC)

Right now, you are the one promoting your own original research in this article. If there are no sources on what gets called Bucklin or on whether it passes clone or IIA, then the relevant cells must be left blank. Homunq (talk) 23:01, 19 May 2010 (UTC)

Try to get majority choice approval adopted or published somewhere and then write a Wikipedia article about it. Markus Schulze 23:19, 19 May 2010 (UTC)

This is not about MCA, this is about Bucklin. Which has been used in major US cities, and so is clearly a more notable inclusion in the table than Schulze voting.

Where are your sources which say Bucklin does not meet clone independence and IIA? Until you find them, you are pushing original research. Homunq (talk) 23:22, 19 May 2010 (UTC)

NOTE: This discussion has now moved to Talk:Bucklin voting.

Dear Homunq, the reason, why I don't want to discuss with you at Talk:Voting system or at Talk:Bucklin voting or anywhere else at Wikipedia, is that, according to my understanding of Wikipedia, the talk pages have a very limited purpose. What you are doing at Talk:Bucklin voting is far beyond the purpose of a talk page. Markus Schulze 01:49, 24 May 2010 (UTC)

Short, sarcastic answer: The definition of Bucklin voting to be used in the article is not an appropriate topic for Talk:Bucklin voting?

Longer answer: Thank you, that is a response. However, like all your other responses so far, it doesn't address the three issues separately, and thus forces everybody else to try to read between the lines. Apparently, you are saying that the criteria compliance of Bucklin voting is not an appropriate topic for discussion, because without sources, it constitutes original research. That answers the latter two of the three questions I posed. However, it does not answer the first question. And unless the answer to the first question is that equal-rankings variants are NOT Bucklin methods by wikipedia standards, then your position would appear to be in direct conflict with the edits you are willing to repeatedly violate Wikipedia rules to promulgate. That is: if any answer to these questions is original research, then your own answer (that Bucklin does not meet ICC and IIAC) is clearly original research, by simple syllogism, and this page should simply state that (by leaving the appropriate cells blank.)

So, once again, please answer the three questions separately. You can simply copy-and-paste the above to answer the latter two questions. As for the first question: The Bucklin implementation in Duluth allowed equalities in third rank. Do you think that equal-rankings-at-all-levels-allowed Bucklin a) has a WP:DUE weight of 0 in the Bucklin article; b) is not a form of Bucklin voting; c) should be included in the Bucklin article, if there are primary sources (ie, the Duluth statute); or d) should be included in the Bucklin article, only if there are secondary sources which specifically discuss this variation and call it Bucklin? Homunq (talk) 17:53, 24 May 2010 (UTC)

Dear Markus Schulze, how would you feel about the following footnote on Bucklin voting in the table: "The compliances shown are for Bucklin Voting without equal rankings allowed. There are no reliable sources for compliances of variants of Bucklin voting with equal or skipped rankings allowed. This is akin to the difference between Plurality and Approval voting."? If you feel it is original research, please give us some idea of why you're being much more insistent about this rule here than in the numerous other uncited assertions on this page? If the reason is that you believe that, unlike those assertions, this one is somehow false... well then, the truth or falsity may be inadmissible on the page itself, but you cannot refuse to discuss it on talk, because it is in this case very relevant to your objection, which is relevant to page content. (For the nth time, I'm not asking you to post a million back and forth repetitive arguments, just to explain yourself fully once. In the long run, you would save everyone time.) Homunq (talk) 00:50, 26 May 2010 (UTC)

It would appear that Markus Schulze is taking two contradictory positions. The first is that uncited views on the criteria compliance of Bucklin voting are original research. Though I feel that such a view would be blatant selective enforcement of a strict view of WP:OR, it's certainly within his right to say so, and, if this were all he were saying, there would really be little point in any talk page discussion. It's policy, so he wins; we blank out the relevant cells, and the debate is over. The second, contradictory position is that Bucklin does not meet IIAC and ICC. To support this view requires, at a minimum, either references or talk page discussion and consensus, and possibly both if there are problems with the references. He has provided neither.

Since he keeps coming back to Arrow's impossibility theorem, I believe that his views on that theorem are central to this debate. Of course I agree with him that a mathematical theorem is logically bulletproof, and debating the results is senseless. I also agree with him that applying theorem results in an uncontroversial way is WP:CALC and needs no source, even if the average editor might lack the capacity to confirm the results, as long as consensus upholds it. However, this is not a question of the actual theorem, but of the practical interpretation. He apparently believes that Arrow's theorem proves that no real-world voting system can satisfy the Majority criterion and the Independence of irrelevant alternatives criterion. That is, he believes that anything which does not have unlimited domain, in the sense Arrow used - that is, is not a mapping from any set of voter preferences to a result - is not a voting system. I believe that this is simply, flatly false; that any "non-preferential" system where a given preference ordering can lead to more than one ballot, including Approval, Range, Bucklin, and arguably others, lacks unlimited domain. Of these, only Approval and Bucklin might meet both the other criteria mentioned (ICC and IIAC), and even that depends critically on how the definitions of those criteria are extended to cover these systems.

Perhaps he's right. Certainly, I believe that Kenneth Arrow did not foresee that systems without universal domain could be practical; so Schulze would not lack for citations to back up his point of view. Perhaps I am; my point of view is a more recent advance, but I could come up with some citations too. Perhaps we're both right, and it is a matter of interpretation. In any case, as long as the disagreement holds, Schulze's application of Arrow's theorem to this article is no longer WP:CALC, but WP:SYNTH. He is welcome to try to resolve the dispute on Talk, or within his rights to believe that Wikipedia is not the forum for doing so; but he is not within his rights to insist that therefore he wins.

Either discuss here, or we must blank out the relevant cells. Homunq (talk) 15:13, 26 May 2010 (UTC)

LNH colors dispute (subsection)

I believe that the the following text is justified in the article: "(This column in the table below is not colored, as Michael Dummett and others dispute whether this property, which encourages fuller voting but prevents the system from choosing compromise candidates, is desirable.)". Clearly, that also involves the colors of the relevant column. This is based on the following text in the given citation: "As we saw in Election 4, under STV the later preferences on a ballot are not even considered until the fates of all candidates of earlier preference have been decided. Thus a voter can be certain that adding extra preferences to his or her preference listing can neither help nor harm any candidate already listed. Supporters of STV usually regard this as a very important property, although it has to be said that not everyone agrees; the property has been described (by Michael Dummett, in a letter to Robert Newland) as "quite unreasonable", and (by an anonymous referee) as "unpalatable". There are really two properties here, which we can state as follows. -Later-no-help. Adding a later preference to a ballot should not help any candidate already listed. -Later-no-harm. Adding a later preference to a ballot should not harm any candidate already listed."

This compromise - including the column without colors, and the given text - are, as far as I can recall, my own suggestions. I believe it is the right solution, though I'd also accept removing the column from the table entirely.

User:MarkusSchulze apparently disagrees, as evidenced by his three recent reverts to this text. The edit comment to the last revert was: "Removed weasel words: "Michael Dummett and others dispute whether this property is desirable." For every criterion, there are people who don't consider this criterion desirable." In support of his position, it is true that there is considerable debate about the relative merits of voting systems criteria in general. On the other hand, I believe that the LNH criterion is particularly disputed; in the given citation, which proposes the standard terminology still used for dozens of criteria, it (along with the related Later-no-help and the unsupported House-monotonicity) is one of the few criteria whose desirability is placed in doubt.

It is difficult to resolve this matter when he reverts the page while resisting repeated invitations to join the discussion here. (His comment above is a reply to a different dispute arising from the same series of edits.) Nevertheless, I believe that this issue should be decided on its merits, not on the basis of the behavior of the editors involved. Homunq (talk) 13:26, 16 May 2010 (UTC)

Later-no-harm is a fundamentally important criteria for anyone who believes that it matters how voters will use a system in real-life elections. It's a primary reason for backing instant runoff voting, as obvious from the chart which otherwise would make it odd for anyone to support IRV. Seems to me that taking it out would would be a political position. RRichie (talk) 20:48, 16 May 2010 (UTC)

Dear Homunq, I am not an IRV supporter. However, Wikipedia articles must be written in a neutral manner; this implies that the table must refer to the most frequently mentioned election methods and to the most frequently mentioned criteria. Markus Schulze 21:53, 16 May 2010 (UTC)

Response to Your Third Opinion Request

Hello. This is a response to your recent request for a third opinion. The opinion offered here is not one that has any authority greater or more special than any participant's opinion here; it should not be considered a tiebreaker and does not count towards creating a sense of consensus; its purpose is merely to offer a fresh opinion from someone new to the situation.

Opinion. It is difficult to establish a clear opinion on this matter when there is so little documentation of the other side of the dispute aside from edit summaries; MarkusSchulze, purely from a self-interest standpoint, even aside from Wikipedia's desired consensus-building, this may be a good reason why joining in an article's talk page might be a good idea. As it stands, looking over the problem, as an outsider, there seems to be not much to go off of here on either side. Both sides seem so "guilty" (poor choice of words) of "weasel words" that I don't really have a belief as to who's right and who's wrong here, as it just manifests to an outsider as a battle of opinions backed up solely by "weasel words". (a) The suggested wording of "this column is not colored [...] as some dispute whether this property [...] is desirable" is based on a weasel word, but, then again, (b) the article's table coloring itself is based on a "weasel word" phrasing of "many voting theorists". (c) The second half of MarkusSchulze's reverting edit summary -- the one that states that the Dummett citation is weasel-wordy -- is ironically itself weasel-wordy, in that it says "Removed weasel words: 'Michael Dummett and others dispute whether this property is desirable.' For every criterion, there are people who don't consider this criterion desirable." (d) Homunq was correct in pointing out that once a source is cited, it isn't a question of weasel-words, it's a question of the credibility of the reference; the fact that Markus' reversion edit summary stayed the same is of particularly important note. Other than that, I'd note that while the subject matter itself is a bit too riddled with weasel words on both sides to be properly viewed by an outsider, with regards to the conduct of the disagreement itself, homunq lands firmly on the "right" side of the matter, in that throughout the disagreement he restrained himself from edit-warring and tried to work out the matter on the talk page. I encourage you, Markus, to work out a disagreement on a talk page, especially when you run across an editor who is level-headed enough to not immediately go into butting-heads mode. I'm just a fellow editor so this is hardly any sort of "reprimand", but keeping a clean record of conduct is useful to your own self-interest when others are brought in either at this point or later in the process, and one cannot merely force one's opinion onto an article via continual reverts. Anyway, that's my 2¢.

Next up. If there are any questions you have that are specific to this particular opinion, I am happy to answer them; please alert me to the need for further follow-up by clicking here to leave me a note on my talk page, as I may not have this page on my watchlist. I will then post the requested follow-up here on this page. (This is done this way to avoid ex parte discussions.)

However, as the third-opinion process is not a mediation process, if you find the opinion below is insufficient to resolve the situation, you should proceed to a request for comment, wikiquette alert, noticeboard post, WikiProject post, or other dispute resolution process for further assistance. WCityMike 22:44, 16 May 2010 (UTC)

Dispute resolution: Talk ⇨ Editor assistance ⇨ Third opinion ⇨ Request for comment ⇨ Wikiquette ⇨ Mediation (informal) ⇨ Mediation (formal) ⇨ Arbitration

Dear WCityMike, when the later-no-harm criterion is removed, then there is no criterion anymore that is satisfied by IRV and violated by Ranked Pairs or Schulze. But there are several criteria that are satisfied by Ranked Pairs and Schulze and violated by IRV. A naive reader will necessarily get to the conclusion that only ignorant people promote IRV. Markus Schulze 01:14, 17 May 2010 (UTC)

First off, it was never my intention to remove the LNH column entirely; I simply stated that as a possible compromise which I'd consider inferior but acceptable. Since there's nobody here supporting that, forget it. So the debate is whether to have a white or a colored LNH column.

So. The third opinion, as I read it, takes no position on the substance, but supports me on the form of debate. I'd also like to note that MarkusSchulze is still in violation of 3RR; despite the fact I politely asked, on his user page, for him to revert the offending edit, he has now continued to participate in the debate without doing so.

Thus, I am going to revert the offending edit. If MarkusSchulze reapplies it, I will report him for the 3RR violation. However, I still welcome his point of view here on the talk page, and any unrelated edits from him. I also welcome others (for instance, RRichie) to be bold with related consensus-seeking edits to the page, as long as they're accompanied with productive discussion here on talk.

Finally, one minor comment on the third opinion: in my view, this is not a question of the credibility of the reference (which is unquestioned), but of its notability. Thus, if they want to dispute my contention that LNH is of particularly debatable desirability, compared to the other criteria listed, Schulze or Richie should look for other unbiased (that is, Richie, no citing FairVote) sources which present similar reservations about other criteria included here. Homunq (talk) 19:52, 17 May 2010 (UTC)

I don't entirely follow this full discussion, but the LNH criteria is the foundation of the legal case that overruled the use of Bucklin in Duluth Minnesota political elections in the early 1900's, so I'd consider it a vital inclusion. Tom Ruen (talk) 01:49, 18 May 2010 (UTC)

All this discussion of the Minnesota case is original research, so inadmissible on the article page. But I've read the decision, and I believe that you're wrong. The Minnesota case was based on a naive "one person one vote" logic - in my opinion invalid - under which even LNH-compliant methods such as IRV would count as unconstitutional. Again, let's not get caught in this argument... I'd love to see an article on that case, and over there we could look for sources on the page and, on the talk page, have discursive arguments citing chapter and verse of the decision to support our OR theories. Homunq (talk) 15:31, 18 May 2010 (UTC)

Since Markus Schulze continues to edit war on this issue, I have reported him for his earlier 3RR violation. As I said in the report, I hope that any sanctions he receives are the minimum necessary to make him seek consensus here on talk instead of edit-warring on the article. (As to his last edit summary ("removed original research"), he actually made 2 changes. On the question of the LNH colors (discussed in this section here on talk), the issue of debate is the notability of a cited source, and there's no question of WP:OR. On the question of Bucklin criteria compliance (discussed in the previous section here on talk), he has a point; my version was lacking citation. However, his version is also lacking citation; and furthermore, his version is both more unequivocal, and unequivocally false. I could also point out that most of the table, including his most recent contributions, is uncited, but I don't want to make a WP:POINT; the rest of the table is definitely an asset to the article, and while more citations should be a goal, it should not be crippled in the meantime. Homunq (talk) 16:28, 18 May 2010 (UTC)

Homunq: I know you hang out in the Internet with people who think FairVote is some evil, manipulative force and that only FairVote might suggest that later-no-harm is a concern, but once you get out more in the real world of working for reform on the ground, all the lovely mathematical theory about finding the compromise candidate, etc, melts away. Imagine approval voting in the Hawaii congressional race right now, for example, with two Democrats who don't like each other splitting the vote, and likely to help elect a Republican who only can earn a plurality. With IRV, it's simple for Democratic voters - you rank your favorite first and probably hold your nose and rank the other Democrat second. With approval, however, backers of those Democrats would be torn -- do I vote for both Democrats, potentially causing the defeat of my favorite choice, or do I bullet vote for just my favorite and in turn risk electing my greater evil, the Republican? You also would see lots of insider whisper campaigns among proponents of one candidate or anotehr to say "don't tell anyone, but yes, just bullet vote for our candidate". This kind of stuff would play out all the time with systems that violate later-no-harm (especially in such a direct way as approval --less so with Condorcet systems, which have their own political baggage of potentially allowing a no-name candidate to defeat better-known rivals simply by being so wishy-washy/unknown that no one ranks that candidate last).

Okay, that's just introductory verbiage, but perhaps worth considering as you critique FairVote for its advocacy of the one single winner (in a single election) system that avoids the later-no-harm problem. Turning to the Smallwood case, I think you're wrong,and citing the Landskroener/Solgard article (which is linked from the later-no-harm Wikipedia article, so not too hard to find -- see http://www2.mnbar.org/benchandbar/2002/oct02/voting.htm) addressing Smallwood would be appropriate grounding for suggesting later-no-harm is legitimate. I assume there's some also theoretical writing that addresses it too, but if there isn't, it to me just shows the real limits of such theoretical writing-- great on the math board, lousy in real political life where the science of human psychology matters too.

Here's a direct quote from the Smallwood opinion, as cited in the Landskroeer article: "The preferential system [Bucklin voting] directly diminishes the right of an elector to give an effective vote for the candidate of his choice. If he votes for him once, his power to help him is exhausted. If he votes for other candidates he may harm his choice, but cannot help him." Pretty clear to me, and explains in a nutshell why so many voters didn't rank anyone second in Bucklin elections where I've seen results.

I know this is a bit testy and you're following proper procedure, but it can be exasperating to argue with people (not you, but others you know well) who are so certain they are right, but NEVER seem to engage with the real reform work of trying to convince policymakers of the value of reform, and instead just plunge into reform opportunities at the last moment to oppose IRV. Certainly doing so would help demonstrate why later-no-harm is a substantive criterion RRichie (talk) 10:56, 19 May 2010 (UTC)

RRichie, I think we should have this discussion on the LNH talk page, which should speak to the debate. Meanwhile, your citation has convinced me; I still feel that Schulze's edit war on the colors was out of line, but pending the discussion on the LNH page, I'd be happy to consider the colors as valid and to take them as being your, not MarkusSchulze's, edit.

I still maintain my prior position on the Bucklin cells, though. The correct answer is that =Bucklin meets IIA and Clone Independence; and, if Schulze wants to be a stickler for verifiability and hold those cells to a higher standard than the rest of the page, the verifiable answer is that there are no sources. Homunq (talk) 16:14, 19 May 2010 (UTC)

ps RRichie, can you strike out the "you and" in "if you and others did so"? As you know, I've phonebanked for FairVote itself, and you certainly don't know all my activity (much in Guatemala and Chiapas). Homunq (talk) 16:20, 19 May 2010 (UTC)

Thanks on LNH. Also, I made that text change, although just replaced text, as wasn't sure how strikeout works. RRichie (talk) 04:25, 20 May 2010 (UTC)

"Proportional Voting Rights" or "Adjusted Voting Rights" or "Proportional Voting Power"(?)

I have seen a voting system suggested by a couple of people (one a friend of mine, and one who wrote a letter to New Scientst) and I cannot find it amongst the ones listed in Electoral methods box.

I do not even know if it belongs in this article, or series of articles, and I do not know if it has a well-known name.

This is how it arose in New Scentist, and a brief description: New Scientist did a feature on voting in their 1 May 2010 issue, and there was a letter in the 22 May 2010 issue, page 28, that said "... The number of votes a particular MP could wield would be calculated by taking all the votes for their party, from every constituency, and sharing them evenly between all its MPs. ...". The effect would be that the "voting power" of a party would be proportional to the number of votes the party had received.

Does anyone know any more about it... does it have a well-known name? With a name I could probably find the rest of the info myself, such as references, its notability, and articles in Wikipedia. FrankSier (talk) 12:12, 22 May 2010 (UTC)

Asset voting is an idea somewhat similar to that, where each representative has different voting power. Yours sounds like a half-step in that direction, because the voting power is smoothed out within each party, just not between them. Hope that helps. Homunq (talk) 18:45, 26 May 2010 (UTC)

How is Approval Voting with an Arbitrary Cutoff not Independent of Clones?

If this has already been a subject of debate, I apologize, but I fail to see how it is not independent, especially when, within the Independence of Clones Criterion, it states that approval votes meets this requirement--noting that approval voting would naturally have a cutoff. For instance, keeping in mind that these percentages would overlap thanks to approval's ability to vote for multiple candidates, if two-thirds of the population like 2 Libertarian candidates, one-third of the population prefers the 4 DEM candidates and half of the population prefers the 8 GOP candidates, the winner would be one of the Libertarian candidates, wouldn't it? Thanks for reading. —Preceding unsigned comment added by 12.129.87.3 (talk) 18:47, 14 September 2010 (UTC)

Write-in criterion

I would like to suggest a new criterion that seems fairly essential for democratic elections: ability to write-in a candidate. This is satisfied by: Approval, Bucklin, IRV, Plurality, Range, Runoff. It is not satisfied by any condorcet voting system or Borda count. Khashishi (talk) 20:57, 2 November 2010 (UTC)

The Condorcet Kemeny method does allow write-in candidates. As explained in [this book], for any ballot on which a write-in candidate's name does not appear, all the write-in candidates (whose names appear on other ballots) are ranked below the preference level of all the listed candidates. Of course any write-in name that has absolutely no chance of winning (e.g. "Mickey Mouse") would not appear in the tally table (which lists the pairwise counts). I believe the same approach would also work for other Condorcet methods. [Message continues below ...] (VoteFair , 19:19, 6 November 2010 (UTC)

Perhaps it's possible in theory, but the tabulation becomes totally unwieldy with a few dozen write-ins. Also, to automatically rank a write-in candidate below all others in a ballot without the write-in is unacceptably unfair. It's far more unfair than the situation in plurality voting. At least, the voter must make positive action to choose another candidate over the write-in candidate. A blank ballot doesn't automatically select a balloted candidate over all write-ins. Because of this, I do not consider the criterion satisfied. Unless you can come up with a more fair way of incorporating write-ins.Khashishi (talk) 08:15, 31 January 2011 (UTC)

Your comments are related to several different issues. First, the current popularity of write-in candidates reflects the unfairness of plurality voting. Specifically, in many/most elections in most "democratic" countries, it is common for a majority of voters to not want any of the listed candidates. In that case a majority of voters may prefer someone else who is not listed on the ballot. However, if fair election methods were used, the listed candidates (or most of them) would be truly popular, and if the nomination process is also fair, then any candidate who has any chance of getting elected would already be listed on the ballot. In other words, the popularity of write-in candidates applies to plurality voting, but becomes much less relevant when fairer election methods are adopted.

Second, when a voter chooses – on a single-mark (plurality) ballot – not to mark any candidate as preferred, current rules interpret that as the voter not expressing a preference in that race. This action is not counted as a "none of the above" preference, which you seem to imply. (If you think this is unfair, that's an issue related to plurality voting, not Condorcet and other alternate methods.)

Third, if you and I were voters in the same election, you would not want my write-in candidate to be ranked higher than all (or any of) the choices listed on your ballot. If it's important for you to know whether or not my write-in candidate is someone you strongly dislike, then we are getting sidetracked into politics and distracted from the topic here, which is election methods. For true fairness, a voter who only ranks the listed candidates must not have their preferences ignored in favor of another candidate they didn't even know was a possible candidate. (If lots of people believe that this write-in candidate should have been known to other voters, then we are back to the first issue.)

Fourth, as for "tabulation [becoming] totally unwieldy", that's not a fairness issue, it's a counting issue that applies when there are lots of ballots. And, it applies to all election methods, including plurality.

Please continue to advocate for greater fairness in elections, but consider that write-in candidates -- which I agree are very important in plurality elections -- become less important to the extent that election methods become fairer. VoteFair (talk) 19:27, 1 February 2011 (UTC)

As far as I know, only the Borda count method cannot handle write-in candidates. VoteFair (talk) 19:19, 6 November 2010 (UTC)

The suggested method for dealing with write-ins in Condorcet methods (rank them below all non-write-ins on ballots which don't mention them) is not what I would want, if I were a non-write-in voter. I would want them ranked equal-last, not below-last. In this case, Condorcet systems which allow equal ranking would work with write-ins, but those which don't wouldn't. However, this counts as WP:OR; without sources, I don't see how we could allow such a criterion on this page. Homunq (talk) 16:27, 4 February 2011 (UTC)

Thoughts on a new sub-section: ordinality

Arend Lijphart, a leading academic in the field of electoral systems, writes about two key dimensions to describe electoral systems: proportionality and ordinality. The former is dealt with well by the current article, but the latter isn't. Ordinality is the ability to express preferences in various ways: it includes, but is not limited to, preferential voting systems (Alternative Vote, Single Transferable Vote etc.). It can also be applied to systems like apparentment (linked party lists in PR), two-ballot systems or even the use of primaries. Systems can be proportional and ordinal (STV), proportional but not ordinal (closed list system), not proportional but ordinal (AV), or not proportional or ordinal (FPTP). How would people feel about a sub-section or new article on this topic? Bondegezou (talk) 14:22, 30 November 2010 (UTC)

I agree that the article needs improvement relating to this issue, but rather than introducing a new term -- "ordinality" -- I suggest adding more clarity to the separation of ballot type -- such as single-mark ballots, approval ballots, ordinal/"preferential" ballots, and rating/score ballots -- and the way in which ballots are counted. For example, Condorcet methods and IRV use the same kind of ballot -- academically called "preferential ballots" but more descriptively called "1-2-3 ballots" -- but the methods count the ballots differently, and often yield different results regarding who wins. VoteFair (talk) 16:11, 30 November 2010 (UTC)

Criteria

Would it be useful to have a table of which (single) criteria imply other criteria, and which are incompatible? Here's a quick sketch of what it would look like. There's a sort of anti-symmetry to the matrix, but I'm not sure if leaving the lower triangular entries in or out is better.

	Condorcet	Majority	IIA	Consistent
Condorcet		Implied	Incompatible	Incompatible
Majority	Implied by		Independent	Independent
IIA	Incompatible	Independent		Independent
Consistent	Incompatible	Independent	Independent

Even your example has problems. It claims that majority and IIA are independent, an assertion which I, who support rated systems, (as well as my sources) would agree with, but which many would claim is at odds with Arrow's theorem. To avoid such pie fights, let's not. Homunq (talk) 15:32, 28 June 2011 (UTC)

Push back to featured?

The article as it now stands has no more "fact"/"citation needed" tags. I realize that this is a far cry from it having no unsupported facts, but I think it's possible to dream that we could get this back up to featured status. Is anyone else interested in making such a push? Homunq (talk) 15:29, 28 June 2011 (UTC)

Majority judgment and later-no-harm

Houmng: Please explain how this system allows you to indicate support for a second choice without that expression of support potentially causing the defeat of your first choice. RRichie (talk) 15:38, 1 July 2011 (UTC)

As the table states, MJ satisfies later-no-help, and does not satisfy later-no-harm. There are two criteria at the head of that column, and MJ is the only one of the systems listed which satisfies one and not the other, so it is the only one with a "Yes/No". As for the ordering of the two, putting later-no-help first saves a few precious pixels, allowing the table to fit without ugly hyphenation on smaller screens.

Note that there are also two criteria (MC and MMC) in the first column now; that the consistency/participation column is also covering two criteria; and that the IIA column effectively also includes ISDA. So it makes sense to put the two LNH criteria together too.

If you can think of any way to make this graphically clearer, wp:be bold. -Homunq (talk) 18:02, 1 July 2011 (UTC)

ps. I believe I've told you before that it's hoMUnQ, not hoUMnG. No big deal, just for future reference. Homunq (talk) 18:04, 1 July 2011 (UTC)

I put an explanation of "Yes/No" underneath the table, with the explanation of "NA". Homunq (talk) 18:34, 1 July 2011 (UTC)

Make them separate criteria -- if you can pass one and fail another, then they shouldn't be a single column. RRichie (talk) 12:27, 2 July 2011 (UTC)

That would be good, but it simply doesn't fit. As it stands, even with abbreviations like "Cond. loser", the table barely fits without wrapping on a screen with 1280px, and even with all the ugly soft hyphens I've added, barely wraps down to fit in a 1024px window. Adding two columns (for MMC and later no help) or three (for Participation too) just wouldn't fit.Homunq (talk) 20:33, 2 July 2011 (UTC)

Approval "allows equal rankings"?

Earlier, the table had a qualified "No" for approval in the "allows equal rankings" column. This was confusing, as equal rankings are the only thing approval allows; so, unlike all the other "no"s in that column, this meant that instead of allowing it "forces", not "prohibits".

I split the column into two: allows equal rankings, and "later prefs" (allows later preferences). In this framework, a system like plurality would be no for both; a system like IRV or Borda would allow later preferences but not equal rankings; a system like Schulze would allow both... and yes, a system like approval would allow equal rankings but not later prefs. That is, Approval's failure which was previously in the "equal rankings" column is still there, but it has been moved to the "later prefs" column.

Markus Schulze changed the approval/equal rankings cell to a flat (unqualified, unfootnoted) "No", with an edit comment about how approval doesn't allow equal rankings, it forces them.

I am going to revert Schulze's edit, and then change "allows equal rankings" to "equal rankings can exist". The point is that the failure he is trying to highlight, the inability to use more than one ranking, is already covered elsewhere in the table.

Markus, you have a history of violating 3RR on this page, so please, discuss this matter here rather than edit warring.

Homunq (talk) 22:43, 6 July 2011 (UTC)

Approval voting doesn't allow voters to cast equal rankings; it forces them to do so. Criteria usually describe desirable properties; but it isn't desirable to force voters to cast equal rankings. So the only usefull formulation would be to use this criterion: "allows equal and unequal rankings". Here, approval voting clearly fails this criterion. Markus Schulze 06:30, 7 July 2011 (UTC)

Are you saying that Approval does not give voters more expressive choice than Plurality? If you're not saying that, what would you call the thing that Approval allows and Plurality does not? If you can think of a better wording for the column head, we should use it. Homunq (talk) 12:50, 7 July 2011 (UTC)

Suppose C is the number of candidates. If plurality voting is being used, then there are C possible voting patterns. If approval voting is being used, then there are (2^C)-2 possible voting patterns. If instant-runoff voting is being used, then there are C! possible voting patterns [when we ignore truncation]. If the used preferential voting method also allows equal rankings, then there are A000670-1 possible voting patterns. Markus Schulze 14:04, 7 July 2011 (UTC)

So are you suggesting that those two columns be replaced by an "expressive possibilities" column, with those numbers? That would be OK with me. The downside of that is that it would break my proposed solution to the Approval/LNH issue (see previous section here). Without an "allows later prefs" column, we can't use colspan to hide the fact that Approval/LNH technically deserves an "NA" or "Yes" but practically deserves a "No".

My point here is that there is a desirable property that Approval and Schulze have, and which Plurality and Borda do not. There is a different desirable property that Borda and Schulze have, that Approval and Plurality do not. I've called these properties "allows equal rankings" and "later prefs", but I'd be open to any solution which expresses this information clearly, using any column names, and either one or two columns. "Expressive possibilities" would be one such solution. If you can put the correct equations in, I will handle the colors and sort keys. (Schulze would be green, Borda light green, approval light red, and plurality red).Homunq (talk) 16:04, 7 July 2011 (UTC)

Split Later-no-help and Later-no-harm into two columns

I feel that we should split the LNH column of criteria the table into two. A number of the voting systems on that table, like Approval, Range, and other ranked systems, meet the later-no-help criterion, but fail the later-no-harm criterion. It only makes sense to split them apart. Nick2253 (talk) 21:59, 14 September 2011 (UTC)