Talk:Condorcet method

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[edit] Use of Condorcet voting Links

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)

[edit] Nanson's method

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 However, if I understand McLean's paper correctly, then 3 of these 4 uses are out of date.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 Therefore, it seems to me that all four examples for uses of Nanson's method are out of date.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 I've just corrected the out of date information in that article too.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)

[edit] Landau set

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 (talk • contribs) 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)

[edit] consistency and participation

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)

[edit] Request for a better introduction

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)

[edit] Potential for tactical voting

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)

[edit] Compromise incentive in Condorcet methods and IRV

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)

[edit] Confusion over the definition of the winner

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)