Talk:Condorcet method

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  1. November 2002 – March 2006

Reference for defeat strength[edit]

Currently there is no reference for the example used in the 'defeat strength' section. Does anyone have a reference for that example? (talk) 17:29, 21 April 2010 (UTC)

Use of Condorcet voting Links[edit]

I removed some links in the 'Use of Condorcet voting' section- my original though was that they were spam links, but after checking the history I realized that they were actually (non-notable) sites that used a Condorcet voting method. I'm leaving them removed for now, but if someone cares enough to put them back they should be able to. Paladinwannabe2 20:16, 10 October 2007 (UTC)

Nanson's method[edit]

Dear Iota, you have added 4 uses of Nanson's method. However, if I understand McLean's paper correctly, then 3 of these 4 uses are out of date. Markus Schulze 09:05, 21 March 2006 (UTC)

The website of the University of Adelaide says that its council is elected by proportional representation by the single transferable vote [1]. Therefore, it seems to me that all four examples for uses of Nanson's method are out of date. Markus Schulze 20:47, 21 March 2006 (UTC)

I have removed the examples for the use of Nanson's method. According to McLean's paper, the University of Melbourne abandoned Nanson's method in 1983. According to footnote no. 7 of his paper, also the Anglican diocese of Melbourne abandoned this method. According to the website of the University of Adelaide, its council is elected by proportional representation by the single transferable vote [2]. Markus Schulze 19:33, 22 March 2006 (UTC)

My bad. I was simply relying on the Nanson's method article. Tend to forget that Wikipedia can be unreliable sometimes. I've just corrected the out of date information in that article too. Iota 03:27, 23 March 2006 (UTC)

Landau set[edit]

I've created Landau set -- I thought I'd mention it here since this is the only article I've noticed that links there. Comments are welcome. CRGreathouse (talkcontribs) 06:23, 28 July 2006 (UTC)

I think the definition of the Landau set in this article is wrong. According to this post, instead of

the set of candidates, such that each member, for every other candidate (including those inside the set), either beats this candidate or beats a third candidate that itself beats the candidate that is unbeaten by the member.

the definition should be

the set of candidates, such that each member, for every other candidate (including those inside the set), either beats or ties this candidate, or beats or ties a third candidate that itself beats or ties the other candidate.

The definition in Landau set is also wrong; instead of

is the set of candidates x such that for every other candidate y, there is some candidate z (possibly the same as x, but distinct from y) such that y is not preferred to x and z is not preferred to y.

it should read

is the set of candidates x such that for every other candidate y, there is some candidate z (possibly the same as x, but distinct from y) such that z is not preferred to x and y is not preferred to z.

Smoerz 14:45, 3 October 2006 (UTC)

consistency and participation[edit]

Can anyone add an example to illustrate Condorcet fails these, and explain whether or not it is a valid concern? — ChristTrekker 21:25, 25 October 2006 (UTC)

It has been proven by Hervé Moulin ("Condorcet's Principle Implies the No Show Paradox", Journal of Economic Theory, vol. 45, no. 1 , pp. 53-64, 1988) that the participation criterion and the Condorcet criterion are incompatible. A summary of his proof is here. A short proof that the consistency criterion and the Condorcet criterion are incompatible is here. Markus Schulze 15:29, 26 October 2006 (UTC)
Thank you. Maybe I'll try to parse that through my noggin and write up something that the average reader could digest. — ChristTrekker 16:35, 26 October 2006 (UTC)
The Minmax seems to satisfy the Participation Criterion. And the Consistency Criterion doesn't seem to be important for a voting system. If 2 groups have different orders of preferences, then it's quite possible they can get different results when combined, and there's nothing wrong with that. It's not a flaw. Timofmars 22:19, 31 July 2007 (UTC)
Also the Minmax violates the participation criterion. As I said, it has been proven by Hervé Moulin that the participation criterion and the Condorcet criterion are incompatible. A summary of his proof is here. Please read Moulin's proof. His proof is very elegant; he shows how you can, when you have a concrete Condorcet method, create a situation where this method necessarily violates the participation criterion. Markus Schulze 11:53, 22 November 2007 (UTC)
As to the second part of the question, no, these two criteria are unimportant (like many other criteria). The participation criterion is designed to scare people into thinking Condorcet methods will reduce voter turnout, but there's no reason to believe that would happen or that outcomes would be worse. Surely other factors related to the voting method would have a much stronger effect, one way or the other, on voter turnout. No voter will have cause to whine "if only I'd stayed home" because ties are extremely rare in public elections, and if a group of voters have the information to realize their abstentions would give a more preferred outcome than their sincere votes, they also have the information to vote strategically and get that preferred outcome. The consistency criterion--such a great name for a criterion, since almost all of the standard criteria are about various forms of consistency--isn't a problem because minorities won't be given the power to partition the voters, which means the only concern is how society will respond when some wonk whines that consistency was violated. When the wonk advocates Borda, for instance, people will reply clones would be much worse. Given that IIA is violated by every method that reduces to majority rule when there are only two candidates (including Approval and Range Voting, when voters learn the obvious strategy) there will always be far worse things to worry about than occasional violations of participation or consistency. SEppley (talk) 23:49, 13 March 2012 (UTC)

Request for a better introduction[edit]

I find this a fascinating subject, but I fear that this article is just a little bit opaque for most people (myself included!) I think the article, as it stands, spends much too much time on minutiae, especially right at the beginning of the article. For example, right from the 2nd sentence starts it starts defining new terms (condorcet winner, condorcet criterion) which really aren't essential to understanding the basic concept.

It may be that it just requires a new paragraph at the start that sets out the following:

  • It's a voting system
  • It differs from other systems by ranking candidates, instead of just picking the favourite.
  • It solves, to some extent, the following problems with other commonly used systems (vote splits, strategic voting, etc)

Once that's done, a more in-depth exploration of the system with examples and all the theory and terminology would be appropriate, but not without giving an overview. Jaddle 02:13, 18 November 2006 (UTC)

OK, I took a shot at it. Shortened and tightened it, splitting some of it into two new sections. ⇔ ChristTrekker 19:16, 15 March 2007 (UTC)

Potential for tactical voting[edit]

This section seems to be unclear or worded incorrectly. It says:

"Like most voting methods, Condorcet methods are vulnerable to compromising. That is, voters can help avoid the election of a less-preferred candidate by insincerely raising the position of a more-preferred candidate on their ballot."

The idea of the Condorcet method is that people DO vote in order of preference. So it's assumed that people will "raise the position" of their preferred candidate over the ranking they give of a less-preferred candidate. That's not compromising or tactical voting. That's voting as it is intended by the Condorcet method.

Since to win in Condorcet voting, a candidate must beat every other candidate head to head, the only "tactical voting" I could see would be to rank a less-preferred candidate insincerely by ranking that candidate better than a more-preferred candidate in order for there to be no clear winner, should the most-preferred candidate fail to win overall.

For example, take Republican voters that want to elect a Republican. They could all agree to vote their preferences on the Republican candidates, but then for ranking Democrats, they all agree to rank the unlikely candidate Mike Gravel as their first Democratic choice, even if this candidate is their least preferred Democrat. Then, even if a popular Democrat like Clinton or Obama beats the Republican candidates, Mike Gravel could beat that Democrat in a head to head comparison, leading to there being no clear winner. The leading Democrat would beat the Republicans, the Republicans would beat Mike Gravel, and Mike Gravel would beat the leading Democrat. This would be tactical voting that wasn't intended by the method.

Though whether that would be effective in accomplishing anything would depend on how ties like that are resolved.Timofmars 21:54, 31 July 2007 (UTC)

Why is there a comparison to IRV in this section but not a comparison to other methods? This seems like an attempt to market Condorcet methods over IRV rather than an objective evaluation of Condorcet. Progressnerd (talk) 01:09, 5 April 2008 (UTC)

Plurality and runoffs are the only single-winner methods in political elections, and so for political use it's reasonable to offer a comparison from those. Tom Ruen (talk) 17:38, 7 April 2008 (UTC)

The discussion of "burying" seems to be somewhat limited. In a three candidate race, if the two leading candidates engage in insincere burying, then that could cause the election of the Condorcet loser. The tactical voting section only mentions the introduction of a Condorcet cycle, but not of the potential of electing a weaker candidate. Should such a discussion be added? Progressnerd (talk) 03:43, 20 June 2008 (UTC)

Agreed it is a worthy example. I can't get my head around tactical "cyclic voting" at all, but an easy scenario with a "weaker candidate", like Mr. Right, Mr. Left, and Mr. Smile. If right or left supporters rank anyone at all below first, it'll be Toothy. Smile is "weak" on plurality standards, but Condorcet supporters deny value for plurality weakness and say he ought to be elected on compromise appeal alone. Whether this "bury tactic" is strategic or sincere, is open to interpretation. Anyway, good to quote an example somewhere if you can find example. Not many real election books talk about Condorcet. Tom Ruen (talk) 05:15, 20 June 2008 (UTC)
Cute example with empty-headed Mr. Smile who deserves to lose, but what the example fails to see is that with a good Condorcet method, candidates who want to win will take median positions on issues. Voters will have better candidates to rank over Mr. Smile, and Mr. Smile won't win. To elaborate: Consider a candidate deciding what position to take on some issue (which could even be an issue that's not very important to the voters). If she takes a position for which a majority prefer some other position (think median), she creates an opportunity for other candidates to take the majority-preferred position on that issue and match her positions on the other issues, in which case a majority would tend to prefer the other candidates. The further from the median is her position, the larger the majority who prefer the candidate(s) who takes the median position. If the voting method pays attention to the majorities and their sizes, why would a candidate who wants to win risk taking a position far from the median? They would seek to minimize the chance that another candidate will be ranked higher by majority, or at least seek to minimize the sizes of those majorities when rock/paper/scissors is unavoidable. SEppley (talk) 22:57, 13 March 2012 (UTC)

Compromise incentive in Condorcet methods and IRV[edit]

I reverted the deletion of the statement that Condorcet methods are only vulnerable to compromising when a cycle is involved, and that IRV is vulnerable to compromising even without a cycle. It is easy to show both of these.

Take this scenario in IRV:

7 A>B
2 B
6 C>B

A wins, but the C voters can secure B's election by compromising in ranking B higher. Note that there is not a Condorcet cycle on these ballots.

Perhaps the Condorcet claim can be worded differently, but the point is that when there's a Condorcet winner, you can't get a better result by compromising unless you create a cycle by ranking the Condorcet winner beneath a candidate you like less. Why is this the only way? Because the alternative to creating a cycle is that you turn the "candidate you like less" into the Condorcet winner when you raise him (which obviously you don't have incentive to cause). No other candidate can become the Condorcet winner when you do this, because everybody else will still be losing pairwise to the original winner.

Incidentally, better Condorcet methods such as Schulze method also have the property that if more than half of the voters prefer A to B, and don't vote for B, then this majority doesn't have to compromise at all in order to ensure that B loses. (Think of B as the worse frontrunner, for instance.) KVenzke 01:59, 28 September 2007 (UTC)

Ranked Pairs also has that property (assuming the Maximize Affirmed Majorities variation, in which the sizes of opposing minorities are NOT subtracted from the sizes of majorities). Mike Ossipoff called that property the Strong Defensive Strategy Criterion, and I call it Minimal Defense in my webpages. You want to be careful about how the strategy is used, though: Suppose some of that majority who prefer A over B have A>B>C as their sincere order of preference (and the others have A>C>B or C>A>B, where B is already their bottom). If they omit B and vote A>C as KVenzke seems to suggest, it can create an opportunity for C to win: voters with C>A>B preferences have been given an incentive to vote C>B>A to elect C. I think the equilibrium that elects A is created if the voters with A>B>C or A>C>B preferences vote A>B=C. SEppley (talk) 22:17, 13 March 2012 (UTC)

Confusion over the definition of the winner[edit]

I am confused about the Condorcet criterion. That article says that the Condorcet winner is the candidate who wins all of her "one-on-one" contests with the other candidates. However, this article says (in the Summary section) that:

"The candidate with the greatest total wins is the one who is the most preferred, and hence the winner of the election."

In other words, a candidate just needs to have more one-on-one wins than any other, not win all of her head-to-head matchups. Which statement is right (or have I just misinterpreted the text)? Molinari (talk) 21:43, 19 November 2007 (UTC)

The statement in the Condorcet criterion article is correct. A candidate is only the Condorcet winner if they win all their pairwise contests. I have changed the wording in this article to reflect this. By the way, if no one wins all their one-on-one contests, then the one who has won the most is the winner by Copeland's method, an extension of the Condorcet method. Runner5k (talk) 23:13, 19 November 2007 (UTC)

Overstatement of the Potential for Ties a.k.a. Circular Ambiguities[edit]

In the introduction it says "There are then multiple, slightly differing methods for calculating the winner, due to the need to resolve circular ambiguities—including the Kemeny-Young method, Ranked Pairs, and the Schulze method." Mentioning this so early in the article is really overstating the potential for this to come into play.

The article about plurality voting doesn't mention ties at all, while 1/3 of this article is about resolving "circular ambiguities," a.k.a. ties. Do you know why the article on plurality voting doesn't mention ties? Because ties rarely happen in real elections, and when they do happen, they aren't resolved by tie-breaking algorithms but rather by lawers contesting ballot after ballot until the race is no longer close enough to a tie that the feel the need to continue.

To mention tie-breaking algorithms is simply to make Condorcet sound more difficult than it is. It's very simple. Everyone lists candidates in the order they prefer them. We then pretend we're having one-on-one elections between each pair of candidates and we decide how each voter would vote in these elections based on their ballots. When we're done it's rather obvious who the winner should be. There wasn't a tie. There rarely ever is. If there had been, we surely could have flipped a coin or drawn names from a hat. Simple, yes?

...but, no. Then someone comes along with a matrix which no normal person understands, seemingly for no reason other than a desire to overwhelm people with "here's how you'd do it if you were a computer," then several other people come along with various algorithms which, in the case of those very rare ties, try to read more out of the ballots than is actually there, seemingly because they cannot accept the fact that a tie is a tie, and before you know it, your average person thinks that Condorcet is the most complicated thing they've ever seen, that people everywhere are in disagreement about how exactly to implement it, and so, for all we know, maybe that much simpler instant runoff voting is the best way to do things.

...and then we get to "potential for tactical voting..." The answer is that there is none. It's these tie-breaking algorithms that have flaws, not Condorcet. ...but no, let's just pretend like Condorcet has no advantages whatsoever against other voting methods. When we find it has an advantage, let's tack something on to it to remove that advantage, then pretend like that something is an integral part of it.


One day I was thinking about voting methods and I came up with this wonderful way to conduct an election, and when I told someone about it, they pointed me to Condorcet voting. I read about it for an hour or two, and came back with "well, I'm not sure, but I think they're talking about the same thing I've thought of." Indeed, they were, but it was all stated in terms so complex that, even having the same idea in my head at that very moment, I still couldn't understand what they were talking about. That's when you know an explaination sucks.

It wasn't Wikipedia I was reading that day, but this article half-way in the same boat. Condorcet is a simple, clear, and obviously correct algorithm. There's no reason to make it sound so confusing and questionable.

Here are my suggestions:

Speak only of straight plain Condorcet at the beginning of the article, completely ignoring the possibility of ties. Describe the ballots and the counting in ways that average people who aren't computer programmers and who have probably never seen a matrix in their life can understand. Toss in some examples, like that awesome Tenessee example. It's excellent. It shows how to evaluate the ballots using the "this vs. that" method, it's an example that provides different outcomes vs. plurality and instant runoff. The only thing I can think to change is that I would mention that, while plurality would select Memphis as the winner because it received the most votes, the majority of voters listed Memphis as their last choice, which makes a serious statement about why Memphis should not be the winner of the election. It says something when an election method picks the same winner for "which city should be the capital" and "which city should not be the capital." Finally, if you must, include a small section at the end to discuss those "circular ambiguities" everyone is so facinated with, but be certain to mention that they are as rare as ties in any election and that, in addition to the many silly methods people have developed to resolve them, we could also just draw a name from a hat, thereby keeping things simple and avoiding the possibility of "tactile voting." I'd toss the actual descriptions of tie-breaking algorithms into subpages or seperate articles as it seems silly that so much of the article should be about details which so rarely come into play, and that's only if one chooses to allow them to come into play at all rather than doing something else entirely. -- The one and only Pj (talk) 04:29, 21 November 2008 (UTC)

It isn't quite clear to me whether you have understood the difference between a "tie" and a "circular ambiguity". Do you suggest that -- when A pairwise beats B, B pairwise beats C, and C pairwise beats A -- the winner should be chosen at random? Markus Schulze 13:19, 21 November 2008 (UTC)
What I don't understand, however, is why anyone would consider that situation to be different than a tie. We might have four ballots, cast "ABCD," "BCDA," "CDAB," and "DABC" thus ending with a four-way "circular ambiguity," or we might have three ballots, cast "ABC," "BCA," and "CAB" thus ending with a three-way "circuilar ambiguity," but for some reason when it comes down to two choices, and ballots cast "AB" and "BA," no one considers it a two-way "circular ambiguity."
I can only guess that the distinction people are making is that the last example will necessarily consist of symmetry in the ballots, and as such has no solution regardless of what algorithm you apply, whereas the three-way "circular ambiguity" doesn't necessarily exhibit symmetry in the ballots, and so a different algorithm may come up with a different answer.
I fail to see why a different method should be used to find a winner in the event of "circular ambiguities," aside from a political motivation to have a winner in every election. When the original Condorcet method results in one of these "circuilar ambiguities," it isn't as if it came to that conclusion because it was ignoring valuable information within the ballots. As such, there is less truth in any answer which declares a winner than there is in the answer that declares that no winner exists. So why pretend as if appending one of these tie-breaking algorithms creates a more ideal solution?
I keep putting "circular ambiguities" in quotation marks because there is nothing ambiguous about the result. When a "circuilar ambiguity" occurs, the answer is quite clear, it is simply that some people are unwilling to accept it. That isn't a valid reason to insist that a data processing algorithm is in need of amendment. -- The one and only Pj (talk) 06:57, 24 November 2008 (UTC)
The difference between a two-way tie and a circular ambiguity is that a two-way tie can always be broken by adding one more ballot within the system (say, the tie-breaking vote held by the chairperson). Resolving circular ambiguities requires stepping "outside the system" or overriding considerably more votes. These cycle-resolving rules can have significant effects on the outcome of elections, and therefore on the properties of the voting method, and they also occur more often than exact ties.
When you advocate flipping a coin, you're advocating replacing all Condorcet methods with Condorcet/Random Ballot or something similar. You are entitled to that opinion, but it is just as valid as someone who advocates replacing all Condorcet methods with, say, Ranked Pairs. So your argument is not particularly relevant to this article, because we're not going to rewrite it from your point of view. rspeer / ɹəədsɹ 07:50, 24 November 2008 (UTC)
It seems to me that the term "circular ambiguity" is too ambiguous. Maybe we should replace "circular ambiguity" with "situation without a Condorcet winner" to make clear that, in the article, we are not talking about perfect ties. Markus Schulze 12:06, 24 November 2008 (UTC)
...or, you might replace it with "circular tie" instead. That seems to be the preferred term. A Google search for Condorcet "circular tie" returns 512 results, while a Google search for Condorcet "circular ambiguity" returns only 25 results. I would simply call it a "tie" myself. "Condorcet tie" returns 184 results, but I'm not sure how much faith to put in Google's numbers when Condorcet turns up 1,090,000 and Condorcet -circular turns up 1,220,000.
Why do you not consider "circular ambiguities" to be ties? How else might a three-way tie present itself in one-on-one elections? Aside from the novelty of "A > B, B > C, C > A," what makes these "circular ambiguities" different from ties? -- The one and only Pj (talk) 09:08, 25 November 2008 (UTC)
Re: "You are entitled to that opinion, but it is just as valid as someone who advocates replacing all Condorcet methods with, say, Ranked Pairs."
I think you're missing my point. I'm not trying to say that everyone should choose my method of resolving ties over everyone else's. I certainly believe that, but that's not what I'm trying to say. What I'm trying to say is that these "circular ambiguities" are perfectly valid results, but they're being portrayed as defects of the Condorcet method, with the result being that Condorcet is presented as both less ideal and more complicated than it actually is.
As for your first paragraph... Not that I think it is relevant, but why can't a single ballot break a circular ambiguity? Can you provide an example? The only example I can think of is a ballot which fails to specify a preference between the relevant candidates, similar to attempting to break a plurality tie between A and B by casting a ballot for C. I also fail to see how any tie-resolving or "circular ambiguity"-resolving methods can have a significant effect on the outcome of an election which was a tie to begin with. I think it is rather obvious that they can have no more effect than any single ballot could have had, which is rather insignificant when there are thousands or millions of other ballots. -- The one and only Pj (talk) 09:08, 25 November 2008 (UTC)
Do you want to say that, in your opinion, the different Condorcet methods (e.g. Schulze, Ranked Pairs, Kemeny-Young, MinMax, Nanson, Baldwin, Copeland) don't differ significantly in their merits (e.g. Pareto, resolvability, independence of clones, monotonicity, reversal symmetry) so that we could simply choose the winner at random? Or do you question that circular ambiguities cannot be resolved by adding a single ballot?
In the first case, I have to repeat RSpeer's words: "You are entitled to that opinion, but it is just as valid as someone who advocates replacing all Condorcet methods with, say, Ranked Pairs." In the second case: This article contains several examples where the circular ambiguity cannot be resolved by adding a single ballot. Markus Schulze 16:59, 25 November 2008 (UTC)

Frivolous advocacy of IRV in article.[edit]

Quote: Since Condorcet voting guarantees to elect the centrist candidate, if there is any winner, extremist candidates would soon learn that they can't win by telling the truth if Condorcet is used. Condorcet elections may promote candidates using insincere campaigning to sound like the most centrist of the bunch. Voters would then learn the winner's true motives once they are elected.

In brief, "Candidates may lie to get elected." This does not add anything to the article, and I daresay that candidates may lie under any voting system to appeal to the most voters.

Nor will any voting system prevent such misrepresentation. In the case mentioned above, in a Condorcet election, an extremist would need to run to the center of the political spectrum rather than stay on the fringe. The argument seems to be saying that an otherwise honest fringe candidate would be tempted to lie in order to win the election. Is it really better to have someone saying nutty things from the fringe than the same person saying relatively sane things from the center? "IRV allows non-mainstream candidates to win without appealing to the center" doesn't seem to be a plus.

With Instant Runoff Voting, candidates have a larger incentive to campaign sincerely for the vote of like minded voters. Vote splitting is not the issue some claim it is, since votes will only be distributed to that nearby candidate, and the voters in that part of the spectrum are best able to judge, and are the only ones hurt if they judge wrong.

See above. A dishonest candidate will go to where the most votes are, and it would seem that a candidate with some history of being in the center would have an advantage over someone who recently saw the virtue of being a centrist. And votes will be distributed to the nearest candidate still in the race after previous rounds, not necessarily the next preferred candidate if that candidate has already been dropped.

Cleanup Tags Added[edit]

The first sections of this article were HORRIBLY written! Look at this first line of the definition:

"A Condorcet method is a voting system that will always elect the Condorcet winner; this is the candidate whom voters prefer to each other candidate, when compared to them one at a time."

Rule #1 of writing a definition: NEVER use a word to define itself! For someone who doesn't know what "Condorcet" is in reference to, this definition is completely meaningless and confusing. On top of that, the wording itself is needlessly convoluted and verbose.

The introduction suffers these same problems as well, as do numerous other parts of the article. I originally just put a section cleanup tag in the definition section, but after trying to decipher this article in its entirety and after reading previous comments in talk regarding this same issue ("Request for a better introduction"), I no longer feel that is sufficient.

The definition at the very start of the article is even worse: "A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is, which always selects the Condorcet winner, the candidate who would beat each of the other candidates in a run-off election, if such a candidate exists."

In other words.... "Huh?!"

Therefore, I'm taking the drastic step of applying a total rewrite tag for the entire article. This thing should be about a third, *maybe* half the size it is now. And the wording needs to be scrapped and done from scratch.

On top of all that, many critical sections (most notably, the summary and definition) have absolutely NO CITATIONS whatsoever! So I'm gonna add a tag for that as well. Hopefully somebody with a lot of time on their hands will step up and re-do this nightmarish mess of an article. (talk) 07:34, 26 January 2010 (UTC)

Okay, I waded in today and rewrote the introduction and summary. I also deleted a paragraph in the summary that looked POV-ish, about electing a compromise candidate that's least disliked by a majority. Maybe something of that sort does belong in the summary, but the paragraph that was there was vague and misleading. Clearly much more rewriting is needed in other sections, and I think a lot of jargon can and should be eliminated. For example, a "pairwise defeat" is simply a majority who ranked another candidate higher, and the "strength" of a defeat is simply the size of the majority. SEppley (talk) 21:48, 13 March 2012 (UTC)

The requirement of single-peakedness[edit]

I believe that this section needs to be either deleted or revised. It states that the Condorcet criterion implies single-peaked preferences, but argues this on an example where there is no Condorcet winner. It also treats the pair-wise comparisons sequentially whereas Condorcet methods should view all these comparisons simultaneously. Kolacinski (talk) 15:03, 9 July 2010 (UTC)

I favor removing this section. If it is retained, at a minimum it needs to explain what single-peakedness means. Currently its meaning is completely unclear. This section is within the Schulze method section, so it probably does not relate to all Condorcet methods. VoteFair (talk) 16:17, 9 July 2010 (UTC)

To get single peaked preferences, you assume that all political positions can be modeled along a line, left to right. Each voter has a particular "Bliss Point" and his or her preferences are determined by the candidates' distances from this point. It's a restriction of Arrow's Universality condition.Kolacinski (talk) 18:40, 9 July 2010 (UTC)

Thank you for the explanation. What remains unclear (to me, at least) is why the article states: "The Condorcet criteria requires preferences to be single-peaked." What does single-peakedness have to do with the Condorcet criteria?
More broadly, single peakedness seems to be related to all types of voting methods (and especially Range voting), so it should be explained elsewhere, either in its own article or within the Arrow's impossibility article (or some other article that applies to all voting methods). Then it can be referenced here (if it does apply). VoteFair (talk) 15:14, 10 July 2010 (UTC)

The Condorcet criterion doesn't require single peaked preferences. On the other side, when the preferences are single-peaked, then there is always a Condorcet winner. Markus Schulze 16:52, 10 July 2010 (UTC)

There are several inaccuracies above. (1) Voters' preferences can be single-peaked even if the number of issue dimensions is greater than one. (2) If there are two or more dimensions, single-peaked preferences do not imply a Condorcet winner point exists; see McKelvey's majority chaos theorem. (3) The Condorcet criterion does not assume voters' preferences are single-peaked; there may be a Condorcet winner even when voters' preferences are not single-peaked and there may be a Condorcet winner even when the alternatives do not lie on a single dimension, and the criterion says it should be elected (regardless of whether the voters' preferences are single-peaked or whether the alternatives are on a single dimension). Regarding the definition of single-peaked: A voter's preferences are single-peaked if the voter has a favorite point and the voter prefers point x over point y whenever x is between y and her favorite point. (In one dimension, the meaning of 'between' is clear. In two or more dimensions, if there is a way to define betweenness so that all voters' preferences are single-peaked, then the voters' preferences are single-peaked.) Note that single-peakedness implies more than a single peak; the voter's preferences are also not flat anywhere. (In other words, the voter isn't indifferent between any two points that are both on the same side of his/her favorite point.) SEppley (talk) 11:55, 13 March 2012 (UTC)

Multiple-winner Condorcet?[edit]

Why can't Condorcet be used for multiple-winner elections? I think that would be useful to address in this article, and I'm personally very curious. —Darxus (talk) 05:13, 14 September 2010 (UTC)

The example given shows how the candidates can be ranked. Why not just take the top candidates from a Condorcet election, however many are required? —Darxus (talk) 05:31, 14 September 2010 (UTC)
Several Condorcet methods, like the Schulze method or ranked pairs, produce a complete ranking of all candidates. So if you are interested in a majority-at-large method, you can use one of these methods to calculate a complete ranking of all candidates and then take the top candidates. If you are interested in some kind of proportional representation, you can use the Schulze STV method or CPO-STV. Markus Schulze 17:48, 14 September 2010 (UTC)
Reply to Darxus: Multiple-winner elections normally require two or more representatives who do not all represent the same majority of voters, so the Condorcet method does not directly apply to such cases. VoteFair representation ranking also provides multiple-winner semi-proportional results, and it uses Condorcet winners (when they exist) after first applying other adjustments -- to ensure that the same voters who choose the most popular candidate do not also choose the winner of the second seat (and further seats). In other words, multiple-winner elections involve much more than just looking at who is second-most popular, and that's why it's not addressed in this article. VoteFair (talk) 01:19, 15 September 2010 (UTC)
I agree with Darxus that multiwinner Condorcet methods should be described in the article; they are a logical alternative to proportional representation voting methods. I disagree with VoteFair's comment; it's not uncommon to allow the same majority to elect all of the representatives (if there is a majority who are so inclined), and it makes sense to do so if the voting method is a good one (which identifies all the majorities, doesn't get fooled by clones, etc.). Accountable representation is about the legislature collectively producing policies that are similar to what the people themselves would produce if the people could vote directly on policies (using a good voting method, and if they had time to deliberate). So, a voting method that tends to elect similar candidates who all advocate the policies the people themselves would collectively choose would seem to be an excellent way to get accountable representation. (It would also settle more issues and reduce polarization.) If instead the representatives are elected proportionally, it's unclear how the representatives will choose to compromise on issues where their position isn't favored by a majority of the representatives, since each wins office based on his/her most preferred positions (on a few issues), not on how s/he will compromise when compromise is necessary... and not at all on how s/he will vote on issues that are of less importance to his/her supporters. In my opinion, accountability on more issues is the most important criterion for evaluating voting methods (but I haven't found a way to rigorously define it, unfortunately). A key point to remember is that the voting method affects the positions taken by candidates who want to win, yet most comparisons of voting methods wrongly assume candidates' positions, and hence voters' preferences, are independent of the voting method. SEppley (talk) 19:00, 13 March 2012 (UTC)

Dimensionality of Political Space[edit]

"Where this kind of spectrum exists and voters prefer candidates who are closest to their own position on the spectrum there is a Condorcet winner (Black's Single-Peakedness Theorem). Real political spectra, however, are at least two dimensional, with some political scientists advocating three dimensional models."

This is at odds with modern empirical political science. It's actually possible to estimate the latent dimension of ideological space by applying IRT to roll-call matrices and opinion polls. While there are some political systems that seem to be two-dimensional, that's because of regionalism (Canada and Quebec separatism, Civil Rights in the US during the 60's, etc). As of now, the vast majority of political systems that have been analysed, including the US's right now, seem to be overwhelmingly one dimensional (Roughly 94% of roll-call votes in the US congress, for example, can be predicted with a one-dimensional model). The only body I'm aware of that has a dimension greater than two is the general assembly.

This is at odds with a lot of commentary you see about social and economic issues forming their own spectrum. But empirically, people's views on social and economic matters are almost perfectly correlated when it comes to deciding actual political issues in the US.

The other thing worth mentioning is that non-condorcet outcomes, while theoretically being possible in higher-dimensional systems, are *extremely rare* as the number of voters approaches infinity. — Preceding unsigned comment added by Dynotec (talkcontribs) 06:08, 22 September 2011 (UTC)

The claim that analysis of Congress members' voting implies the public is one-dimensional looks dubious. Congress is elected using a voting system (plurality rule) that forces the voting public to choose between two large coalitions (parties) in order to avoid the spoiler effect, and each party has incentives to enforce discipline for one of two platforms on the issues. For example, if voter 1 cares mainly about banning abortion and voter 2 cares mainly about slashing taxes, both appear to support both positions when they are forced to vote for the candidate who advocates both positions, but the two voters don't necessarily support both positions. Also, many issues, though important, are not of the most importance to many voters, which allows the representatives to be unaccountable to the public on those issues (e.g., bank regulations); they can represent the preferences of wealthy special interest minorities. The claim that there will almost always be a Condorcet winner as the number of voters goes to infinity seems totally unsupported; Plott's Theorem (which is about the conditions under which McKelvey's Chaos Theorem holds) implies the opposite: the chance that some point is a Condorcet winner falls to zero as the number of voters increases. SEppley (talk) 11:08, 13 March 2012 (UTC)

Weakened the unsupported claim about calculation speed of Kemeny-Young[edit]

The section about Kemeny-Young makes an unreferenced claim about executing "in seconds" when there are 40 candidates. Discussion in the Talk page of the main K-Y article indicates this claim has not been established. I inserted the word some (some cases) in the claim to make it more closely match the weaker claim made in the main K-Y article. SEppley (talk) 10:38, 13 March 2012 (UTC)


Can someone add the pronunciation? I am guessing it is con-door-say, but I have never heard it in conversation, and have no background in French. — Preceding unsigned comment added by (talk) 14:16, 5 October 2012 (UTC)

The article on Marquis de Condorcet contains a pronunciation. Markus Schulze 17:46, 5 October 2012 (UTC)

Ballot Image Necessary?[edit]

Is the image of the ballot with John Citizen and Mary Doe useful? The article already contains an example from a wikimedia election as well as numerous in article tables depicting ballots. The John Citizen ballot is cartoonish in my opinion and does little except take up space. DouglasCalvert (talk) 04:08, 19 February 2014 (UTC)

Summary incorrect[edit]

The sentence "The concise rule that defines a Condorcet method can be stated in a single sentence: "If more voters mark their ballots that they prefer Candidate A over Candidate B for office than the number of voters who mark their ballots to the contrary, then Candidate B is not elected."" sounds incorrect to me. It suggests that a Condorcet method must elect no candidate in the case of a condorcet cyle and I think that's incorrect. clahey (talk) 19:10, 2 February 2017 (UTC)