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

[Juho Laatu]

On 04 Nov 2014, at 17:38, Toby Pereira <tdp201b at yahoo.co.uk> wrote:

> 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.

I'm coming back to this topic. It is easier to comment it now, after some discussion about the clones.

In minmax(margins) the explanation would be that the candidate who could win all others with the smallest improvements to his skills should win. We assume here that if he lost 3-7 to someone, he would need 5 points worth of extra skills or strength to win this match. We also (not completely accurately) assume that the same skills would earn him as many points also in all the other matches. There may however be some problems in this approach. If the nature of the matches is somewhat random (sometimes you win by luck, and a lot, but on average the best one still wins the more often than loses), then it may be that the measure of "worst result of each candidate" is also somewhat radom since it is based on the reasult of one match only (that could have gone badly wrong due to some bad luck and random variation).

In sports it is quite common to count the number of losses to other competitors. This brings us back to the clone problem. Sports are however different from politics. We could claim that clones are not a problem in many sports. Let's assume that there are three competitors that win each others in way that forms a loop. Then we add one more competitior that is an identical twin of one of the three competitiors. He will win one of the others, and lose to one, and will be exactly equal to his twin brother, just like we expected. Now one of the competitors has lost to two competitors. Maybe it is ok to say that he does not deserve to win. If you cant beat the twins, you are in trouble, and that's fair. He should focus on winning those candidates that are numerous (2) next year.

My point thus is that the winning criteria might be similar or different from what we are used to in politics. I believe we can make use of Condorcet methods in sports sine the "beats all othrers" criterion is vey natural also in many sports. But as the two examples above demonstrate, the rules can be different from politics. Different sports may also have very different needs (e.g. because of the random nature vs. non-random nature on individual matches).

Juho




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