Condorcet Voting Method

In another thread, I mentioned the Condorcet method of voting. Has anyone ever looked into this? From what I've read, this seems to be the best preferential voting system out there. I know IRV is more popular, but Condorcet seems to have fewer problems and be more "fair".

Here's an example of how the Condorcet system would work:

Three candidates, (A,B,C), and 100 voters. Instead of just picking their "first choice" (like we do currently), we ask them to rank their choices. Here are the results:

30:A>B>C
10:A>C>B
05:B>A>C
20:B>C>A
10:C>A>B
25:C>B>A

(ie: 30 people like A first, B second, and C last)

Then, you set up pair-wise "virtual elections" to see which candidate would be undefeated when paired against the other candidates. In this case, the results would be:

If A & B run, there is a 50/50 tie.
If B & C run, B wins with 55% of the vote.
If A & C run, C wins with 55% of the vote.

So, B beats C, C beats A, and A ties with B (note, I could have actually made it so that A beats B but with less [than 55] votes, 51 for instance).

B is the only candidate that is undefeated. When paired with each of the other candidates, B never loses. In this case, B would win using the Condorcet system, but A would have won using our current system.

I like it. What do you all think?

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I like it. What do you all think?



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Your opinion, fellow voter, just doesn't matter when it comes to Washington figuring out how to run elections. Or finance them.

Any system which, in the opinion of the hoi polloi (me and you), might bring about sensible change in who gets in and who goes home (from DC), simply will not even get into a committee. Much less reach a vote. Sorry. It's just the way it works.

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[slickpoppa]

In our two party system I don't think this would make much of a difference.

[Autocratic]

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In our two party system I don't think this would make much of a difference.

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That's not true, it would actually force several third parties into the spotlight if they were allowed on ballots.

Also, the Condorcet winner is not a voting method - the method is the Copeland method, the Condorcet winner is a candidate who wins all of its match ups under the Copeland method, and the Condorcet criterion for voting. I didn't look at your links so perhaps that was covered.

The major problem with the Copeland method is that it violates the Pareto condition, which states that if everyone prefers candidate X to Y, Y cannot win. Observe:

3 candidates, A, B, and C. Here is a chart of numbered preferences for several groups of people:

9 voters vote: ABC (A is the first choice, C the third).
10 voters vote: BAC
11 voters vote: CAB

Now, counting just first place votes (meaning by plurality), C wins, with 11 first place votes. Here is when you test the Condorcet criterion:

A vs B: A wins with 20 voters to 10 preferring it.
A vs C: A wins with 19 votes to 11.
B vs C: B wins with 19 to 11.

Here, A is the winner with the Copeland method, not C. Though it's accepted that no voting system is perfect.

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).

[El Barto]

The purpose of voting is to elect a winning candidate. Anything that detracts from that is not a good thing.

All these ranking type plans do is encourage people to engage in fantasies and single issue candidacies.

A simple past the post system is the best. It forces people to form a broad coalition with people they do not agree with even 80% of the time. Both of the two major parties are good examples of such broad coalitions.

We aren't voting to indulge ourselves, we are voting to pick a winner. We should discourage third parties and who cares if someone does not win a majority?

We can get a new person in office for the next election, we are not electing a person for life. Rotating between the parties is more effective than trying to pick the absolute "perfect" candidate each time. The very idea of condorcet voting is based on a flawed assumption about what an election is all about.

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The purpose of voting is to elect a winning candidate. Anything that detracts from that is not a good thing.

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I think the purpose of voting is to voice your opinion/preference in the candidates, and have the winner be the one that satisfies most people's preferences. Any system that prohibits people from voicing thier true candidate preference, is not a good thing.

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We should discourage third parties

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I totally agree. If they thought that 150 years ago we wouldn't have the Republican Party.

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[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.