Kristofer Munsterhjelm wrote: > If Schulze and Kemeny produces the same result so often, why not just > switch to Schulze and gain clone independence and polynomial runtime? > Independence of clones seems more important than Kemeny's unique > Reinforcement criterion anyway.
The Condorcet-Kemeny method has significant advantages over the Condorcet-Schulze method, but some of those advantages have not yet been recognized. Some of the advantages involve not-yet named criteria. For example, reversal symmetry just requires that the winner not be the winner if all the ballot preferences are reversed, and both Condorcet-Kemeny and Condorcet-Schulze meet that criteria. A not-yet named criteria beyond that, which I would call "full reversal symmetry," would require a complete symmetrical reversal of popularity ranking if all the ballot preferences are symmetrically reversed, and Condorcet-Kemeny meets that criteria, but Condorcet-Schulze does not. (I'm not saying this new criteria is significant, I'm just pointing out that unnamed criteria do exist, and this is an example.) As long as we just focus on which criteria are met, and which are failed (by each method), we are only skimming the surface. A deeper way to quantify fairness criteria would be to count the percentage of (all possible) cases in which a criteria is met. (Subtracting that percentage from 100% gives the failure rate.) That will yield more meaningful measurements of fairness criteria, far beyond the current yes/no, meet/fail checklists. At that point some overlooked advantages of the Condorcet-Kemeny method will emerge. (I point out in my reply to Markus Schulze why the calculation runtime is not an issue.) > If the answer is, as you hint later, that Kemeny somehow produces better > outcomes than Schulze in the cases they do differ, how would you > quantify better? ... See above. > ... Perhaps there's a better method still than Kemeny, say > a method that is at least as good on average and satisfies clone > independence (or perhaps IPDA, etc). Further improvements are certainly possible. I've created an algorithm at NegotiationTool.com that handles situations that go beyond the kind of voting discussed here. For example, it can handle the election of Cabinet ministers, which involves far more complexity than even proportional election methods. One of those complexities is that an MP (member of parliament) can be nominated for multiple cabinet positions, yet can fill only one (typically chosen as the most-favored position). It also ensures proportional representation throughout the cabinet, taking into account that the Prime Minister is part of the cabinet. For that matter, the selection of Prime Minister is part of the results. (Of course the process is interactive, just as for current deliberations.) And the algorithm handles rules about party-based quotas. All of those complexities go far beyond what we are talking about here. > On 5/4/2010 9:01 PM, Richard Fobes wrote: >> The Condorcet-Schulze method and the Condorcet-Tideman method use a >> similar elimination approach, where one looks for the biggest pairwise >> numbers and the other looks for the biggest margins of victory. > (Kristofer Munsterhjelm wrote:) > Not necessarily. The beatpath approach (count number of stronger > beatpaths between all pairs of candidates - the winner is the one with > no stronger beatpath to him than away from him) doesn't involve > elimination. I used the word elimination in a different sense than eliminating candidates. My intent was to convey the idea that the Condorcet-Schulze method looks at pairwise counts to identify which paths to eliminate (because those paths are weaker), whereas the Condorcet-Kemeny method looks at Kemeny scores for (non-representative) sequences to eliminate. Richard Fobes ---- Election-Methods mailing list - see http://electorama.com/em for list info
