[EM] Condorcet methods - should the cycle order always determine the result order?

[Toby Pereira]

Thank you Juho and Kevin for your replies. I agree with you both that the main point of a Condorcet method is to find a winner. Anything else is relatively unimportant. If, for example, we chose the Minimax method because we decided that it gave a better overall order, we might find cases where we'd disagree with the winner. So using something like Schulze or Ranked Pairs would still be better if we thought they were better at finding a winner regardless of what they said about the other candidates.

With Schulze, I thought its beatpath method was transitive. I wasn't thinking of removing the winner and recalculating. Maybe I'm wrong about that. But yes, River obviously only affirms the pairwise results that it needs to in order to get a winner, so certainly can't be said to produce an overall ranking in all cases.

But I was thinking that maybe a Condorcet method might be used to generate an ordering in a sporting competition, where you have head-to-head matches, and where you want to find more than just first place. I'm not sure many sports would want the added complication of Condorcet though.

Toby




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> From: Kevin Venzke <stepjak at yahoo.fr>
>To: em <election-methods at electorama.com> 
>Sent: Tuesday, 4 November 2014, 13:47
>Subject: Re: [EM] Condorcet methods - should the cycle order always	determine	the result order?
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>Hi Toby,
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>Especially with more than three candidates I think it is unclear how to define second or third place under Schulze. Are you removing the winner and recalculating?
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>River's "ranking" can fail to order two candidates, despite there being a pairwise winner between them.
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>I would say the only reason Ranked Pairs appears to indicate a ranking is that the only way we know how to find the RP winner is to construct this ranking. In other words, if you somehow find another method of calculating the RP winner, which doesn't involve constructing the full ranking, then it would be unclear to me that RP says anything about second or third place.
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>Kevin Venzke
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>________________________________
> De : Toby Pereira <tdp201b at yahoo.co.uk>
>À : "election-methods at electorama.com" <election-methods at electorama.com> 
>Envoyé le : Lundi 3 novembre 2014 19h00
>Objet : [EM] Condorcet methods - should the cycle order always determine	the result order?
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>In a lot of the more preferred Condorcet methods (e.g. I think all of Schulze, Ranked Pairs, River, Kemeny), if you have, for example, an A>B>C>A cycle, then if, say, A wins then B will automatically finish second and C third (if B wins, C will be second etc.). But you could have a similar number of A>B>C, B>C>A and C>A>B ballots but then also a lot of A>C>B ballots, meaning that in some sense C looks better than B. But as long as this doesn't break the cycle and A wins, then B will still finish second. I think the following example does it:
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>11: A>B>C
>10: B>C>A
>10: C>A>B
>8: A>C>B
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>A beats B 29:10
>C beats A 20:19
>B beats C 21:18
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>I'm not saying these methods are wrong for doing this, but there is an intuitive sense in which C is arguably a better choice than B. So is it:
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>1. There is a reasonable Condorcet method that would rank them A>C>B
>2. The intuition that C should finish ahead of B is poorly thought out.
>3. It is in a sense reasonable to think that C should finish ahead of B, but doing so would cause a method to fail certain criteria and end up worse as a result.
>4. Other?
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