Condorcet Voting Method

[Jedster]

In the eyes of the U.S. Supreme Court, the issue is so clearcut that they wouldn't even hear an appeal.

http://www.secstate.wa.gov/office/os...Bcp44oaQ%3D%3D

Oh well.

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Yeah, why don't we get rid of the playoffs and let 8 teams all play in the World Series. I'm sure we could figure out some special mathematical formula to figure out who the world champ is. [img]/images/graemlins/cool.gif[/img]

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Is this the problem? You don't understand the math, so you have to balk at the suggestion?

The math just makes the process more efficient.

What's really going on, is a series of playoffs... er, elections. So that the person that wins really is the one that most people would have voted for in a fair competition.

[El Barto]

Understanding the math isn't the problem. The game would be different if played with 8 teams, and elections would be messed up with 8 candidates.

Most people don't pay close attention to elections. Its hard enough to get them to pay attention to 2 candidates' positions. Your system would actually make the typical person less informed about each candidate.

Actually, most people would probably still pay attention to their ONE candidate. But, if you are concerned that voters aren't informed, then we should go back to how the Framers' intended the system to be.

[tylerdurden]

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parties have a constitutional right to choose their nominee

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God, you guys find constitutional rights to everything! Parties didn't even exist when the constitution was written. How did they suddenly get these special constitutional rights? [img]/images/graemlins/tongue.gif[/img]

Someone please show me where all these secretly hidden rights are written down. I'd like to find a few for myself. [img]/images/graemlins/grin.gif[/img]

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The most recent case of this actually involved both the Democratic and Republican parties in Washington state suing in order to have their "constitutional rights" protected. I agree, it's bull. But it is what it is. We used to have an open primary, now it is a closed primary because of them.

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People have a right to form associations and determine their own membership. Closed primaries are certainly permissible.

However, I do object to official state election commissions paying for and officiating such closed primaries.

[Jedster]

agreed. open primaries are much better.

[Autocratic]

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The "Condorcet Method" is any voting system that uses the Condorcet criteria in determining the winner. The Copeland system is an implementation of that, but it's not a very good one, in my opinion. Copeland assigns points to wins & losses, and then tallys those points to get a final number. It makes it easier for the less-informed to understand, but there are better ways that avoid picking the wrong winner.

Also, Condorcet & Copeland meet the Pareto condition. In your example (which is just like mine), "A" wins, and is not less preferred to any other candidate.

The worst part about Condorcet, is that you can get results where no candidate wins all the pair-wise "elections". Observe:

10: A>B>C
8: B>C>A
3: C>A>B

Here, A beats B, B beats C, and C beats A. There are ways to determine the winner, though... by dropping the person that is the "weakest" win (in this case, C beats A with 11 votes, so is dropped).

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The Pareto condition, in my experience, refers to first preferences, so my example is actually a counterexample, and the Copeland method does not satisfy the Pareto condition.

Also, the Copeland method does not assign points at all - I'm not sure where you got that. It individually compares voter preferences in one on one matches - the only system that the Condorcet winner can be derived from. The difference is that a Condorcet winner must win ALL of the pairwise comparisons, whereas the Copeland method has no such requirement.

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The Pareto condition, in my experience, refers to first preferences, so my example is actually a counterexample, and the Copeland method does not satisfy the Pareto condition.

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Pareto is a condition where every voter prefers candidate X to candidate Y:

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Pareto Optimality

A voting system is Pareto-optimal if when every voter prefers alternative x to alternative y, alternative y is not selected. This criterion is similar to the monotonicity criterion, but is more often satisfied by the voting systems that have been proposed. It is sometimes referred to as the unanimity criterion.

Both Pareto-optimality and monotonicity relate to the collective rationality of a group decision-making procedure. Clearly if one were to make a decision based entirely on one's own preferences, one would not select y if one preferred x. The rational individual would select an alternative other than y (x or an alternative preferred to x). Likewise if one had selected x and later received news that x was even better than originally thought or that y was even worse than originally thought, one would not switch the selection to y. The rational individual would stick with the selection of x. When many decision-makers must make a group decision, we can extend the rules we would follow for individual decision-making. Thus if every decision-maker prefers x to y then it would be irrational for the group as a whole to select y. Likewise, if the group selects x and one or more group members decide that x is even better than originally thought or y is even worse than originally thought, the group should not change its decision. Thus with Pareto-optimality and monotonicity, the notion of what is individually rational can be extended easily to what is collectively rational.

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The only method that I know fails Pareto is the "Approval" method. Borda, IRV, Condorcet (Copeland), all pass the Pareto condition.

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Also, the Copeland method does not assign points at all - I'm not sure where you got that.

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http://condorcet.org/emr/methods.shtml :
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Name: Copeland

Definition:

Each alternative's Copeland score is calculated by subtracting the number of alternatives that pairwise beat it from the number that it beats. The alternatives with the highest Copeland score win.

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http://theorem.ca/~mvcorks/code/voting_methods.html :
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The last system uses the Condorcet style of pairwise comparison. It was proposed by A. H. Copeland in 1950.

Copeland:
Hold pairwise votes between every pair of alternatives. Assign 1 points to an alternative for winning, and
-1 for losing. The winner is the alternative with the highest score.

This Condorcet-style system disregards the intensity of a voter’s preference between two alternatives (unlike, for example, the Borda count), and so leads to many ties.

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It individually compares voter preferences in one on one matches - the only system that the Condorcet winner can be derived from.

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A "Condorcet winner" is one that is not defeated any any pair-wise comparison. Yes, Copeland is a Condorcet method.

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The difference is that a Condorcet winner must win ALL of the pairwise comparisons, whereas the Copeland method has no such requirement.

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Well, a "Condorcet winner" must win all pair-wise comparisons. But Copeland deals with circular ambiguities by keeping a "score". Copeland will often result in ties and/or pick the wrong candidate. Other methods of resolving circular ambiguities are much better: Schulze, Smith, minimax, etc.