On Tue, 07 Jan 2003 18:29:02 +0200 Markus Schulze wrote:
Just looking at the above words:Dear Eric, you wrote (7 Jan 2003):The algorithm implemented is Beatpath Winner, now mentioned on the site.I have suggested that the strength of a pairwise defeat should be measured primarily by the number of winning votes and secondarily by the margin. An implementation can be found here: http://www.topica.com/lists/RankedPairs/read/message.html?mid=1601349191&sort=d&start=34 When there is no unique beat path winner then random ballot should be used to choose from the potential winners. I recommend that the beat path method should not be restarted with the potential winners since this could lead to a violation of monotonicity. Markus Schulze
We agreed a few months ago that there was need for an agreed method for resolving Condorcet cycles - if that discussion ever got completed, I missed it.
I find random ballots acceptable for resolving true ties, assuming the authority conducting the election agrees. I do not find them acceptable as an excuse for not doing what is possible with Condorcet vote counts.
IF beatpath winner describes an acceptable method - so be it - else I hope we look for or construct an acceptable method.
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Eric offered a test case yesterday, and annoyed me by using a method that reported a tie - and which did not please him either.
Steve Barney mentioned "Kemeny's method" yesterday, but did not provide enough defense to convince me that it belongs here.
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Opinion as to advanced math:
NOT acceptable in what the average voter needs to understand.
Limited amounts in what we tell the average voter about resolving Condorcet cycles - even here there must be limits to complexity, but we are resolving near ties and that can be necessarily complex.
No limits in what is used within the research community, though even here authors need to successfully communicate with readers.
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