Talk:Voting system

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)

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

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.

Archived discussion: /archive1 /archive2

Later no harm criteria?

This seems like an important criterion. Why is it not included in the chart and discussion? - 71.163.241.185

Later-no-harm criterion Indeed! My guess is LNH is uninteresting because only IRV/STV (and single seat plurality) support it. Tom Ruen (talk) 02:14, 23 September 2009 (UTC)

I didn't realize that. An inconvenient truth to some, I guess, but perhaps one Wikipedia shouldn't obscure? So people know what later-no-harm is, it's written up on the site: its key point is: "The later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less preferred candidate cannot cause a more preferred candidate to lose." That seems important. -71.163.241.185

For many election methods, it is disputed whether this method satisfies the later-no-harm criterion:

• It is disputed for Coombs' method and for anti-plurality voting, because it isn't clear how these methods are defined for incomplete individual rankings.
• It is disputed for plurality voting, supplementary voting, and Sri Lankan contingent voting, because it is disputed whether the later-no-harm criterion can be applied to election methods that restrict the number of cast preferences.
• It is disputed for the Borda count and the MinMax method, because some implementations of these methods satisfy the later-no-harm criterion while other implementations don't.

Markus Schulze 01:17, 24 September 2009 (UTC)

Even so, it seems like it should be addressed rather than just avoid the topic. It's an important criterion and seems misleading to not include it. -71.163.241.185

I don't see how any interpretation could allow Borda count passing. Tom Ruen (talk) 05:14, 24 September 2009 (UTC)

Suppose C is the number of candidates. Then usually, a candidate gets C-1 points for each first preference, C-2 points for each second preference, C-3 points for each third preference, etc.. This definition for the Borda count violates the later-no-harm criterion.

However, this implementation of the Borda count satisfies the later-no-harm criterion: Suppose R is the number of candidates who are ranked by this voter. Then the candidate with the first preference gets R points, the candidate with the second preference gets R-1 points, the candidate with the third preference gets R-2 points, etc.. Markus Schulze 10:41, 24 September 2009 (UTC)

I don't get it. Let's suppose I rank three candidates. R is "3." My first choice gets three points. My second choice gets two points. Let's suppose my second choice defeats my first choice by one point. Didn't my ranking that second choice cause my first choice to lose by one point? If I instead had ranked only my first choice, then those candidates would have tied and my first choice could have won in a tiebreaker. ... Also my broader point is that Later-No-Harm belongs in the list. Its absence comes across like a political decision, not one reflecting the policy choices that a government or organization makes in choosing a system.71.163.241.185 (talk) 12:18, 24 September 2009 (UTC)

When you rank 3 candidates, then the candidate with your first preference gets 3 points, the candidate with your second preference gets 2 points, and the candidate with your third preference gets one point. When you bullet vote for only one candidate, then this candidate gets only one point. So a candidate cannot be harmed by casting an additional preference. Markus Schulze 14:19, 24 September 2009 (UTC)

Wow, that's an insane way to satisfy a criterion, but I suppose that implementation creates a counter incentive against partial rankings, and a HUGE advantage to voters who like many candidates! Tom Ruen (talk) 20:39, 24 September 2009 (UTC)

I see your point, Marcus, but agree with Tom. This would never fly. The criterion belongs in the list, comparing the systems as they basically are without bizarre, unlikely variations. 71.163.241.185 (talk) 03:57, 25 September 2009 (UTC)

The argument to include later-no-harm is persuasive. Those like Markus Schulze with a potential self-interest in not including it because it favors a system they may oppose, should be working harder to demonstrate their fairness by including it, with whatever footnoted caveats seem appropriate. If they know how to manage this chart, they should adjust the chart to include it —Preceding unsigned comment added by 12.130.118.1 (talk) 15:02, 3 January 2010 (UTC)

I would accept including later-no-harm, but without colors. There is considerable fundamental philosophical disagreement with whether later-no-harm, in itself, constitutes a desirable property. (ie, you could equally well call the reverse property the "compromise" property and tout it as a positive aspect.) 187.143.7.74 (talk) 19:18, 12 February 2010 (UTC)

I have added Later-no-harm to the chart, drawing as best I could on existing consensus. That consensus is based on the present discussion and the content of other, relevant Wikipedia articles, all of which I linked when I could. Jack (talk) 22:21, 15 February 2010 (UTC)

Good job. I reordered the columns. Note: By my reckoning, Minimax meets both Condorcet and LNH. I've heard that's impossible, but I think that people who say that are actually not thinking of the Condorcet criterion but the "Smith criterion" that requires a winner in the Smith set. I could be wrong here. Homunq (talk) 22:47, 15 February 2010 (UTC)

Note: above comment based on misinterpreting LNH. Homunq (talk) 12:44, 23 May 2010 (UTC)

It seems very odd to mark Plurality as compliant with Later No Harm when there is no option to specify a later preference? Surely it should be marked not applicable? —Preceding unsigned comment added by 78.105.167.241 (talk) 21:40, 12 March 2011 (UTC)

Would someone who claims it's important that Later No Harm be satisfied explain why it's important? In other words, explain the harm caused to society when it's violated, or show that violations will be exploited to produce winners that are worse or less accountable to the voters as a whole. If the justification is merely that some voters will sometimes have cause to regret they didn't misrepresent their preferences, it must be pointed out that satisfaction of LNH will not prevent voters from sometimes having cause to regret not misrepresenting preferences. For example, Instant Runoff satisfies LNH but voters would still have cause to regret when their failure to rank a compromise on top allows their least preferred alternative to win. I think it's fair to include LNH in the article, but only because so many other unimportant criteria are included. For more thoughts on the relative importance (or unimportance) of criteria, see the section below. SEppley (talk) 00:07, 12 March 2012 (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)

Yet another proposed column: "Equal rankings"

• Allows equal rankings—Allows a voter to rank any two candidates equally at any position on the ballot. This can reduce the prevalence of spoiled ballots due to overvotes, and can give a less-dishonest alternative to some voting strategies.

Borda, IRV, Plurality, and Runoff would be red "No"; Minimax and Kemeny-Young would be white "Depends on variant used"; and all others would be green "Yes".

(The "less-dishonest alternative to some strategies" point is NPOV, not how I'd put it personally. Personally, I'd add some words to point out that dishonest strategies by more than one voter group can give pathological results desired by none, and so if there are semi-honest alternatives, that risk is significantly reduced.) Homunq (talk) 16:00, 15 February 2010 (UTC)

Kemeny-Young would be "yes"; it always allows "equal rankings". (BTW, the Kemeny-Young method does not have any variants that affect the input (votes) or output (results); the only variants are in how quickly the result is reached.) VoteFair (talk) 19:11, 15 February 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?

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/LNH

RRichie, you put a "No" instead of an "NA" for Approval in the LNH column. In approval, the only rating which is "later" than approved is unapproved. Marking another candidate unapproved of course can't harm an approved candidate, so, technically, the system passes the criterion, mathematically defined. Of course, I understand your argument that, if we were to look inside the voters head to see the preferences there, the system would not pass with regard to those preferences. Still, "No" is mathematically inaccurate. So, I think "NA" is more in the spirit of the criterion; but if you insist on having a value there, "Yes" is the only one that fits. (Note that the page previously included a definition of LNH which made approval fail. However, that definition was WP:OR; I replaced it with the definition from the source it already cited.) Homunq (talk) 18:52, 1 July 2011 (UTC)

Note that even by the uncited mindreading definition ("same-but-I-wish-it-was-later no harm"?) which RRichie apparently advocates, Approval passes later-no-help, just not later-no-harm. But I'm willing to leave an "NA" in the cell as a whole, rather than the "Yes/NA" which it would deserve.Homunq (talk) 19:31, 1 July 2011 (UTC)

I very much disagree. You are suggesting because a system doesn't allow a voter to indicate strength of preference except "0" or "1" that we can then assume voters have no sense of preference. But that is patently absurd. Consider a situation (a common one in minor variations) where you really like Candidate A, feel neutral about a second Candidate B and really dislike Candidate C. You are saying quite indefensibly that if I decide to approve of the first two candidates in order to try to defeat candidate C that my expression of support for Candidate B. For one academic discussion of such a situation, see Burr's Dilemma, discussed here: http://en.wikipedia.org/wiki/Burr_dilemma

It is not controversial to say approval voting fails to meet this criterion. Certainly it is central to the case against it in any real world debate -- and something any policymaker would understand immediately.RRichie (talk) 12:27, 2 July 2011 (UTC)

I've edited the page with a proposed resolution to this issue. Here's a copy:

	Major­ity/ MMC	Mono­tone	Consist­ency/ Particip­ation	Condorcet	Cond. loser	IIA	Cloneproof	Reversal symmetry	Polytime	Summ­able	Allows equal rankings	Later prefs	Later-no-help/ Later-no-harm
Approval	3Ambig­uous	1Yes	2Yes	4No	5No	3Ambig­uous	3Ambig.­	1Yes	1Yes	1O(N)	1Yes	No
Borda count	5No	1Yes	1Yes	5No	1Yes	5No	5No (teaming)	1Yes	1Yes	1O(N)	5No	1Yes	5No
IRV (AV)	1Yes	5No	5No	5No	1Yes	5No	1Yes	5No	1Yes	5O(N!)­	5No	Yes	1Yes
Kemeny-Young	1Yes	1Yes	5No	1Yes	1Yes	4No (but ISDA)	5No (teaming)	1Yes	5No	2O(N2)­	1Yes	1Yes	5No
Majority Judgment	1Yes	1Yes	4No	4No	4No	2Yes	1Yes	2Yes	1Yes	1O(N)­	1Yes	1Yes	3Yes/No
Minimax	2Yes/No	1Yes	5No	2Yes	5No	5No	5No (spoilers)	5No	1Yes	2O(N2)	3Some variants	1Yes	4No
Plurality	2Yes/No	1Yes	1Yes	5No	5No	5No	5No (spoilers)	5No	1Yes	1O(N)	5No	No
Range voting	5No	1Yes	2Yes	4No	5No	2Yes	3Ambig.­	1Yes	1Yes	1O(N)	1Yes	1Yes	5No
Ranked pairs	1Yes	1Yes	5No	1Yes	1Yes	4No (but ISDA)	1Yes	1Yes	1Yes	2O(N2)	1Yes	1Yes	5No
Runoff voting	2Yes/No	5No	5No	5No	1Yes	5No	5No (spoilers)	5No	1Yes	2O(N)­	5No	4No	2Yes
Schulze	1Yes	1Yes	5No	1Yes	1Yes	4No (but ISDA)	1Yes	1Yes	1Yes	2O(N2)	1Yes	1Yes	5No

Is this acceptable to you in its treatment of approval and LNH? Homunq (talk) 20:33, 2 July 2011 (UTC)

I definitely appreciate your effort here, but you're assuming that a voter has a simple "yes on equal level" to all" and "no to everyone else", and that kind of view of candidates in a multi-candidate racies is going to be the exception, not the rule. Unlikely plurality voting, approval voting gives you every opportunity to indicate a preference for a second choice who is much preferred to a last choice, but because it violates later-no-harm, you may well not do so and instead bullet vote for your first choice. So I think it's fundamentally misleading about the system to suggest it's in the same category as plurality voting. RRichie (talk) 22:28, 3 July 2011 (UTC)

Umm... I don't know what you want. The table as I've edited it makes a distinction between the mathematical definition of the criterion (what you've called my "assumption") and the practical meaning (basically, the thing you're arguing for). It gives priority to the practical meaning; the color of the relevant cell is red. It's only if you read the footnote that you get the quibbling about how the system technically passes the criterion.

I think that in your professional advocacy, you've grown accustomed to using the term "LNH" to refer to a practical argument, not a mathematical one. And I sympathize; I think I'm bending over backward to accommodate this. But in a section about mathematically-defined criteria, we can't completely abandon the mathematical definition given by the referenced source.

If you're willing to settle for the page as it is now, great. If not, please say or demonstrate specifically what you'd like to do to change it. I'm not Obama, I can't negotiate with myself forever.

Homunq (talk) 00:10, 4 July 2011 (UTC)

What I want is a return to the simple fact that approval voting violates the later-no-harm criterion in no uncertain terms. Note that Wikipedia's article states: "The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less preferred candidate cannot cause a more preferred candidate to lose. You say the color is red, but you don't seem to leave the box blank, right?. I don't think you'e "bending backwards" to contradict common sense and Wikipedia's own article on later-no-harm. It's not "professional advocacy" that results in this understanding -- it's the simple fact that with approval voting you cannot give a positive rating to a less preferred candidate without counting against the chances of your more preferred candidate. RRichie (talk) 03:13, 5 July 2011 (UTC)

You're citing the definition from another wikipedia page, but Wikipedia is not a reliable source. The mathematical definition does not refer to an "additional" preference, but a "later" preference, as the source currently cited here in this article shows. And indeed, with the name "Later no harm", I can't really see how you could argue otherwise. Homunq (talk) 09:41, 5 July 2011 (UTC)

Amazing logic. To you the fact that with approval voting you can't indicate support for a second choice without it counting against your first choice means that anyone who doesn't indicate a second choice for that reason doesn't in fact have a second choice. I think the true test of meeting this criterion is what the sytems means when you DO have a disinct first, second and third choice. Please tell me how approval voting in such a situation allows you to indicate that fact. Furthermore, you should read the original source (the 1994 article cited for the defintion). This is what it says: "Later-no-harm. Adding a later preference to a ballot should not harm any candidate already listed." Can you please tell me how approval voting satisfies that criterion? RRichie (talk) 14:57, 5 July 2011 (UTC)

The key word there is "later".

Mathematical criteria do not deal with people and their preferences, they deal with sets, functions, and relations. I am sympathetic to your argument; sympathetic enough that I agree, I'd like to find a way for that cell to be red, as it is in my compromise proposal. If I were claiming what you say I am claiming, I would not be saying that. What I am saying is that we should find a way to reconcile the practical meaning of the criterion - on which you are correct - with the mathematical meaning it is given by the cited source - with which your only engagement is to recouch it in practical terms and then misattribute that as "my" position.

What is so wrong with the compromise I'm offering? 99% of people will never read the footnote, will just see a red square and infer that approval does not meet LNH. Those who do read the footnote will see that there's a technical debate, but that it is generally acknowledged that approval does not provide the practical guarantees that LNH is intended to ensure. In crafting that proposed compromise, I intended to convey nothing else; and I would welcome your edits intended to clarify this. But the simple fact is, that mathematically defined, a "later" preference means not the same preference level on the ballot, and so approval, technically speaking, passes that criterion; unless you can cite another definition (and yes, I'm sorry, but I will reserve the right to be picky about letting you cite FairVote promotional material on this matter, if I feel in good faith that such material is biased, and more importantly if it does not clearly lay out or refer to a precise mathematical definition), all your argumentation here constitutes original research. Homunq (talk) 17:46, 5 July 2011 (UTC)

How is the 1994 article that is the basis for the definition of the later-no-harm criterion original research? What does it have to do with "FairVote promotional material"? We're talking about a specific property of approval voting. It does not allow you to add a later preference to a ballot without that harming a candidate already listed." I guess this is the problem with Wikipedia -- no referees who can say "yes, the sky is blue" I'm done with this debate here, but I believe this (as well as the incredibly muddy presentation of approval voting in the main article on the subject) is a disservice to those seeking to understand the pro's and con's of different voting methods.RRichie (talk) 03:08, 7 July 2011 (UTC)

The 1994 article is not original research. It has nothing to do with FairVote. What it says is: "Adding a later preference to a ballot should not harm any candidate already listed." Approval does not allow adding a later preference; it only allows adding equal preferences. Therefore, it passes the criterion on a technicality. The current state of the page reflects that; a reader who does not care about technicalities will get the (practically right but not technically correct) impression that approval fails this criterion (and also Later-no-help, defined in a similar way).

I'm sorry you feel that this debate represents a failure of Wikipedia. Wikipedia certainly has failures, but I am convinced that in this case, a neutral referee would support me. ("In a context which requires precision, sometimes you must say that the sky usually appears blue, rather than saying that the sky is blue.") But please do not be discouraged. In the main approval voting article, we have a lot more space than one table row to explain things, and I'm sure you could help us do better; I'd invite you to make edits there. Homunq (talk) 13:33, 7 July 2011 (UTC)

You write "Approval does not allow adding a later preference; it only allows adding equal preferences." This is nonsense. The fact that the approval voting method is so unnuanced that it doesn't allow a voter to indicate strength of preference does not mean that voters in fact do not have strength of preference. So if I like A, am neutral on B and hate C, I cannot vote for B without it counting against A. This is crystal clear, yet you pull out a trick of saying "well, if a voter decides to vote for B, then that voter is saying that B is not a 'later preference.'" Again, simply nonsense.... I suppose by this definition you would say that range voting, which also violates is a system where indicating support for a second choice can cause a first choice to lose, violates LNH because of the voter's greater ability to indicate strength of preference. So in other words, a relative virtue for range voting becomes a vice.

I do not believe truly neutral referees could not support your position. They only could do do by accepting your solipsism that because a voter cannot indicate strength of preference, that voter in fact has no strength of preference.... What I would think would be a truly clear way to evaluate a system on this criterion is to establish a scenario (one that would exist in nearly all multi-candidates races in ther eal world) where voters have a range of preferences and see which systems allow voters to voter their interest - e.g, support their favorite to the maximum degree and oppose their least favorite to the maximum degree. Approval voting cannot do this, as you know, yet you not allow this limitation to be expressed. .. I truly hope you can see your position is indefensible and you need to allow this limitation to be indicated despite your advocacy for the method.RRichie (talk) 12:04, 9 July 2011 (UTC)

As I have said a number of times, I agree with you that, from a practical standpoint, approval's passing of LNH is nonsense. But it's a mathematical fact. Mathematical facts are often practical nonsense.

You propose a non-mathematical way to evaluate this criterion. I like your proposal, which could even be re-couched in a mathematically rigorous way (though it would be several times more complex than the mathematical formulation I've been relying on throughout this argument, and it would essentially amount to making a special case for approval so that it didn't pass). But unless you can find a source for your version of the criterion, we just can't use it.

Your bottom line is: "I truly hope you can see your position is indefensible and you need to allow this limitation to be indicated despite your advocacy for the method." As far as I can see, I am allowing this limitation to be indicated; the cell is red (as is the "later prefs" cell, which shows the "relative virtue for range voting" of which you speak). In fact, I thank you for bringing this issue up; I think the page is better this way than it was with "NA" as I had it before. So why are we still arguing? Homunq (talk) 12:43, 11 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)

Multiple-winner methods and consituencies

Do representatives in Multiple-winner election systems represent a constituency? How could they? They are not elected by a specific constituency. I mean, if some jurisdiction voted 100% for a party, say California voted 100% for the Democratic party for the Senate (using a multiple-winner method), how could a Republican be appointed to California's Senate seat and be considered to represent that constituency, ie. represent California? Int21h (talk) 23:41, 27 December 2011 (UTC)

The U.S. Constitution requires that U.S. Senate seats be filled in different years, which make those seats incompatible with multiple-winner methods -- which require filling the multiple seats using the same set of ballots.

Yes, a single representative cannot represent both Republican and Democratic voters. Double-size districts with a good multiple-winner method (I suggest VoteFair representation ranking) would elect one Republican and one Democrat. I think that would be fairer, but some people claim that larger districts make the representatives less "local" -- because they represent twice the area. VoteFair (talk) 19:42, 29 December 2011 (UTC)

While that is good information related to the subject of the hypothetical I advanced, it is unrelated to my underlying question regarding constituency representation in multiple-winner election systems. (This is why I am so loathe to give hypotheticals, because an answer may be related to the hypothetical but unrelated to the underlying question.) Int21h (talk) 14:20, 5 January 2012 (UTC)

If the voters give 100% support for only Democratic-party candidates, then a Republican cannot get elected. If you mean that the voters give 80% support for Democratic-party candidates, and a Republican candidate somehow gets elected to the second U.S. Senate seat, then of course the Republican Senator over-represents the 20% "constituency", and the Democratic Senator under-represents the 80% "constituency". If you are you asking a different question, please clarify. VoteFair (talk) 17:51, 6 January 2012 (UTC)

Yes, they can: California voters, in my hyopthetical, are not "the" voters, but only "some" (about 12%) of them. So no, I mean 100% of California voters (composing 12% of the national voters) voting Democratic, yet being represented in the US Senate by a Republican in national elections. Both my question and hypothetical probably imply a proportional or semi-proportional multiple-winner system, but I am not sure about this, hence I did not mention them. ("Jurisdiction" may have been misleading, but in the US the various states hold national elections, under state law, not the federal government, hence their are multiple voting jurisdictions. But "California's Senate seat", singular, should have implied I was referring to the US Senate as no state senate has only 1 seat, and therefore national elections.) Int21h (talk) 09:58, 7 January 2012 (UTC)

California (and each state) elects two U.S. Senators. (I'm the author of Ending The Hidden Unfairness In U.S. Elections, so I'm quite familiar with U.S. elections.) Under current conditions it is possible that California could elect one Democratic Senator and one Republican Senator, even with a strong Democratic bias. If a proportional (PR-like) election method were used to fill U.S. Senate seats, then some more U.S. Senate seats would have to be created, and one of those additional seats could be filled by a Republican who represents the (hypothetically?) few Republicans in California and also represents unrepresented Republicans in other states. If you are asking about a multiple-winner election method like STV (single transferable vote) -- which is not fully proportional -- then the results depend on how many seats are being filled, because anything beyond filling a first and second seat easily produces results that are unpredictable and unrepresentative. (Using a multiple-winner method to elect a single winner simply becomes a single-winner election.) VoteFair (talk) 17:26, 8 January 2012 (UTC)

Color of the table for criteria pass/fail

There is a table in which the different voting systems each have their own row, and the different critera by which they are evaluated each has its own column. In this table, each cell is filled with a No or Yes, or in some cases a a more nuanced statement. The cells are color-coded, and that is the problem. The colors are so bleached so that it is hard to see the different between a very light red (No) and a very light green (Yes). I suggest that the colors are changed to stronger versions of those colors - I envision something like the red and green colors on the Italian flag.213.21.66.189 (talk) 15:49, 26 January 2012 (UTC)

I made all the colors twice as strong. 200.49.162.42 (talk) 02:07, 31 January 2012 (UTC)

Consistency/Participation of Random Ballot Y Done

The criteria table states that "Random Ballot" fulfills the consistency and participation criterion, whereas "Random Winner" does not. Can anyone explain these two(/four) entries? I think the following is correct:

- "Random Ballot", Consistency: NO. If the voters are separated in two groups and in both groups a random-chosen ballot determines the same winner A, it doesn't mean that a random-chosen ballot of the combined voter groups will also determine A as winner. So, Random ballot doesn't fulfill consistency.

- "Random Winner", Participation: NA (or YES). Since the participation criterion explicitly needs the addition of ballots to produce a violation, "Random winner" can't ever violate this criterion. Since the criterion depends on ballots, but "Random Winner" doesn't know any ballots, it should be marked as not applicable.

Arno Nymus 134.102.209.204 (talk) 17:46, 8 March 2012 (UTC)

I think you're right. For RW/Participation, I'd go with NA. Be bold, make an edit you find reasonable. I don't think anyone really paid much attention to those cells before, and so I wouldn't look for too much logic behind what's in them now.

BTW, I agree with your edits removing the hedging from the Range/Approval/Participation/Consistency cells. I wouldn't be suprised if MarkusSchulze doesn't, though; as you can see from the talk page above, he's a stickler for which criteria are incompatible. In other words, if these systems pass Condorcet under Nash, then they fail Participation/Consistency under the same assumptions. Yes, that means people using logic like: "If voter x realizes that I prefer candidate A over B, she'll vote for C; so perhaps it's better that I just don't vote at all, and hope x realizes that", which I find implausible. But it's Markus's right to be a stickler if he wants to. Homunq (talk) 13:50, 9 March 2012 (UTC)

So, I changed it as discussed. Thx for your feedback. --Arno Nymus 77.23.79.151 (talk) 00:43, 10 March 2012 (UTC)

Y Done -- Arno Nymus (talk) 17:53, 15 March 2012 (UTC)

Criteria Table: Ballot types column Y Done

I think, it would be reasonable to add a ballot type column to the criteria table, that describes what information the ballots used for the method possess.

For example Approval voting ballots contain approvals, i.e. a set of candidates that are approved by the voter;

IRV ballots are rankings, i.e. a endorelation which is transitive, anti-symmetric and every two not compared candidates are ranked "last" (that means for all candidates A,B,C (¬A>B and ¬B>A) implies (¬A>C and ¬B>C) )

Schulze ballots are simple orderings, i.e. endorelations. That means, Schulze method can easily handle rankings, but it does not need rankings. It outclasses IRV, since it also could handle if a voter only says "A>B and C>D, but I don't want to say whether I prefer A or C".

However, "rankings" and "orderings" are mostly referred identically as "preferential ballots".

Any objections against such a column? --Arno Nymus 77.23.79.151 (talk) 15:26, 10 March 2012 (UTC)

Adding the column is an excellent idea! I agree it's wise to clarify ballot-marking limitations/restrictions/ambiguities. Note that Wikipedia defines "ranking" in a way that allows equal ranking, which is regarded as a spoiled ballot in IRV. Wikipedia redirects "ordering" to the "order" article, which lists different kinds of ordering. So, the names used in the ballot-type column may need to be cleared up first. VoteFair (talk) 19:16, 10 March 2012 (UTC)

I looked around a little bit and came to the following results:

- ballots with only one candidate (plurality) are called "categorical" ballots [1]

- ballots for IRV/Borda can be called "strict rankings" [e.g. Tideman]

- ballots for Schulze etc. can just be seen as a set of "comparisons" (or in one term as an "endorelation", although it is a mathematical term). But looking "in the rush" didn't bring me any indication that anyone has researched using something other than "rankings" (strict or not strict) for these methods, although I read in some paper these days that forbidding preference cycles on a ballot because they are irrational would be a bad idea, since voters should not be banned from voting only for being irrational. That means that the idea of using non-ranking relations at least exists. Also, the construction of Ranked pairs and Schulze makes it totally obvious that they could handle a non-ranked set of comparisons without any change or problem.

I would just add a short description of each ballot type (categorical, approvals, (strict) rankings, comparisons, scores) before the table. Or in footnotes if this is preferred. -- Arno Nymus 77.23.79.151 (talk) 21:32, 10 March 2012 (UTC)

This is the explanation of the ballot types:

Ballot type: The voter have to state his choice in form of...

• ... a categorical choice of one candidate (e.g. "A is my favorite candidate.")
• ... approvals, i.e. a set of candidates the voter approves (e.g. "I approve candidates A, B and E.")
• ... a (strict) ranking, i.e. an list of candidates strictly ordered by the preferences of the voter (e.g. "A > B > E > D > H" or "I prefer A to B, B to E, E to D and D to H.")
• ... a set of comparisons (e.g. "A > B and E > H and H = C" or "I prefer A to B, E to H, and I think, H is equally capable as C, but I don't want to distinguish between A and E or A and H."). This is a generalized form of a ranking, so every voting system that can handle comparisons, also can be used if the ballots are rankings.
• ... scores, i.e. the voter gives cardinal values within in a certain range (e.g. 0-100) to each candidate (e.g. "A gets score 100, E gets 0, H 47, B 12 and D also 12") --Arno Nymus 77.23.79.151 (talk) 22:31, 10 March 2012 (UTC)

I suggest using "non-strict ranking" instead of "set of comparisons" because the comparison approach is never used on election ballots. (The fact that Condorcet methods can be used for search engines and other pairwise-comparison applications is irrelevant to elections.) Also I suggest using "plurality" or "single mark" instead of "categorical" because approval ballots are also "categorical", i.e. each candidate can be categorized as "approved" or "disapproved". Note that these suggestions are based on the need to choose appropriate words in the comparison table where the text-based descriptions won't fit, which means, for example, the column would be labelled "ballot type" (or "ballot") and the word "score" (not "scores") would be used for range voting. VoteFair (talk) 20:06, 11 March 2012 (UTC)

Now, I added the column to the table and the description into the descriptions of criteria above the table. So, you can see how it looks like. Additional feedback is welcome.

As you proposed, I changed "categorical" to "single mark".

Respective the "comparisons" I think, it looks quite good in the column, it is not significantly longer than "single mark", so I tend to leave it this way.

Respective "score"/"scores". I chose the plural "scores" since the voter gives one "score" to each candidate. But, if you think that this is incorrect, we can change it.

Thx for your feedback. --Arno Nymus77.23.79.151 (talk) 20:45, 11 March 2012 (UTC)

Y Done --Arno Nymus (talk) 23:26, 16 March 2012 (UTC)

Article lacks information about the relative importance of criteria.

The article presents quite a few criteria for comparing voting methods, but no info about which criteria are more important. It says only that there is disagreement about which criteria should be used. I think the article could be greatly improved by adding arguments why some criteria are more important than others.

My own point of view is that many of the standard criteria are relatively unimportant. For example, the so-called consistency criterion says that if 2 collections of votes produce the same winner, then the combined collection must produce that winner. Is it important? Since the rules can easily prevent a minority from partitioning the voters, minorities can't exploit scenarios where the voting method violates consistency, so that criterion seems quite unimportant compared to a criterion such as independence of clone alternatives. Tiny minorities can easily exploit scenarios where the voting method violates independence of clones, and they wouldn't even need knowledge of voters' preferences to successfully manipulate the outcome.

Also, a criterion that may be the most important of all isn't listed in the article. The work of many social choice theorists assumes the positions that candidates take on issues do not depend on the voting method; in other words, voters' preferences on candidates are wrongly assumed constant when comparing voting methods. In reality, candidates who want to win tend to take positions they believe will help them win, so positions do depend on the voting method. Some examples: The overly simplistic model in the Median Voter Theorem--two candidates, single issue with positions on a one-dimensional spectrum, single-peaked voter preferences--leads to a game-theoretic strategy where both candidates take the voters' median position. In a somewhat more realistic model, the two candidates know that additional candidates may enter the race, and this knowledge leads to a strategy where both avoid the median since if either takes the median it would create a winning opportunity for a third candidate; instead, one takes a position to the left and the other takes a position to the right. Another example is the system of partisan primary elections in the United States, which induces candidates to take positions that appeal to a segment of the voters (called the "base" of the party) who are not a representative sample of the general electorate, and who tend to defeat candidates who take median positions. Another example is the Borda voting method, where any platform of positions can be made to win regardless of the voters' preferences by nominating enough clones. With these examples in mind, the criterion I think is most important is that candidates who want to win should be induced to take positions that are accountable to the voters, even on issues that are not very important to the voters. (By accountable, I mean something along these lines: a position p on some issue is strongly accountable to the voters if no other position q on that issue is preferred over p by a majority, and a position p on some issue is reasonably accountable to the voters if, for all positions q on that issue that are preferred over p by majority, there exists a position r on that issue that is preferred over q by a majority at least as large.) Voting methods that perform well on this criterion would tend to settle issues on which the voters' preferences are settled, promote policy stability, reduce polarization, and reduce opportunities for wealthy special interest minorities to lobby/bribe their way to policies on "lesser" issues that large majorities would oppose. SEppley (talk) 23:22, 11 March 2012 (UTC)

The problem is that the importance of criteria is highly subjective. For example, IRV advocates highly appreciate the later-no-harm-criterion, whereas other people say that satisfying LNH only means to ignore important information. Also, there are different views about whether the only important thing about criteria is if their violation can be exploited for tactical voting (e.g. by adding candidates to steal votes; IIA, FBC) or if their violations also reveal unfair or unconstitutional flaws (e.g. that a vote is counted against the explicit will of the voter; Monotonicity, Participation). So both, IoC and Consistency are important - although, or maybe just because, they reveal qualitatively different problems of a voting system.

And last, but not least, there are objective differences of the importance of the criteria in relation to the ballots used. Best example is the "Mutual majority criterion". Both, Plurality and Range voting do not satisfy it. Plurality do not satisfy it because the voters do not have any chance to express on their ballots the information that is needed to fulfill MMC, thus Plurality itself does not have any chance to identify the winner, MMC considers best. So, for plurality the violation of MMC is a disadvantage. Instead of that, for Range voting it is the total opposite. Range Voting gives the voter not only the possibility to express the information the MMC uses to propose a winner, but even more information. And since Range voting uses this additional information in his process of assigning the winner (whilst the MMC does not), it sometimes leads to a better choice than the MMC and so "fails" it. So, Range voting "fails" the MMC since it has superior information, whilst Plurality fails it because it has inferior information. However, for voting system that have exactly the information the MMC uses, i.e. preferential-voting systems, it is a reasonable criterion.

Arno Nymus, 77.23.79.151 (talk) 22:18, 12 March 2012 (UTC)

Edit: I replaced "Majority criterion" by "Mutual majority criterion" in the last paragraph --Arno Nymus 77.23.79.151 (talk) 23:37, 12 March 2012 (UTC)

Granted the relative importance is subject to debate. One of my points is that the reader needs to see the arguments used in that debate in order to be able to judge which criteria are most important, and in which contexts the arguments apply. SEppley (talk) 17:19, 13 March 2012 (UTC)

I would like to have some pro- and contra-arguments on the according wikilinked criterion sites, but not in between of the short definitions. The later one would only limit the overview capabilities the table is made for. -- Arno Nymus (talk) 18:02, 15 March 2012 (UTC)

I agree that criteria-specific articles, not this article, should be where advantages (pros) and disadvantages (cons) should be explained. Note that trying to consolidate those advantages and disadvantages into a single scale of importance is impossible -- in a way that meets Wikipedia's requirement that such an importance ranking be appropriately referenced. VoteFair (talk) 18:08, 16 March 2012 (UTC)