Markus Schulze wrote: > > Richard Fobes wrote (2 May 2010): > >> Once again Markus Schulze is trying to discredit >> the Condorcet-Kemeny method. > > If I really wanted to discredit this method, then > I would mention ...
Thank you for giving me the opportunity to put these issues into perspective. > ... that this method violates independence of clones. A violation of the independence-of-clones criteria would require both of these conditions to occur in the same election: * There is circular ambiguity, which means there is no Condorcet winner. * Two (or more) of the candidates are recognizable as clones of one another. Each of these is uncommon (but not rare), but to have both in the same election would be rare. Yes, the Condorcet-Kemeny method fails to meet the independence-of-clones criteria, whereas the Condorcet-Schulze method meets this criteria. This is a small difference. For perspective, most of the currently recognized fairness criteria apply to both the Condorcet-Kemeny and Condorcet-Schulze methods. In other words, they meet and fail most of the same criteria. > ... that this method has a prohibitive runtime so > that it is illusory that VoteFair representation > ranking could ever be used e.g. to fill 7 seats > out of 30 candidates. The computer-calculation runtime for getting Condorcet-Kemeny results is long (factorial according to the number of candidates) if (!) all the Kemeny scores are calculated. However, not all the scores need to be calculated just to find the sequence with the largest Kemeny score. The wording we agreed on in Wikipedia, with the involvement of a neutral election-method expert, is that calculating the results for 40 candidates only takes a few seconds if well-known mathematical techniques are used. That's not a prohibitive runtime. My VoteFair ranking software calculates the results even faster, using an algorithm that I have not yet revealed. I'm still looking for a forum in which to share the algorithm. (Unlike you, I do not have academic connections that make it easy to publish papers in academic publications.) Yes, it takes the VoteFair ranking software a few seconds longer to calculate Condorcet-Kemeny results compared to software that calculates Condorcet-Schulze results. But even if the calculation time were a few minutes (for a particularly convoluted case), such a wait is not a deterrent for use in real elections. When the number of candidates reaches 30, the bigger challenge is for voters to meaningfully rank that many choices. That's why I recommend using approval (yes/no) voting to narrow the candidates to a reasonable number for ranking. The Condorcet-Schulze method has this same issue of a ballot with 30 candidates being difficult to meaningfully rank. > ... that, although this method has been proposed > more than 30 years ago, it has never been used by > a larger organization. The Condorcet-Kemeny method is impractical to calculate without a computer, and the Kemeny method was proposed before computers became widely available, so it's lack of use prior to a decade ago is not significant. The Condorcet-Schulze method was the first (of these two methods) to be implemented in software, and the Condorcet criteria is so important that it is natural for early adopters to choose what's available. But the first Condorcet method to be adopted in this new digital era is not necessarily the best. The benefits of the Kemeny method -- including the fact that it is a Condorcet method -- are becoming known only slowly. The popularity of "your" Condorcet-Schulze method reflects the popularity of Condorcet methods, not necessarily the popularity of the Schulze-versus-Kemeny choice. Most of the people and organizations that use the Condorcet-Schulze method would not notice any difference in the results if the Condorcet-Kemeny method were used instead. Surely you have noticed that I have not made changes to "your" "Schulze method" page in Wikipedia, whereas you have repeatedly attempted to remove every mention of the word "VoteFair" from the "Kemeny-Young method" page, and to remove the link that reveals that there is a place where Condorcet-Kemeny calculations are available (for free). If I were more aggressive about promoting the Condorcet-Kemeny method, or if you were less active about trying to suppress it, it would be more popular. It takes time for wise people to make wise decisions. And fairness is very important to me. I'll continue to be patient as I wait for more people to recognize the advantages of the Condorcet-Kemeny method (which is a topic I'll explain in another post, in reply to a fan of "your" method). By the way, I don't keep track of all the groups that use VoteFair ranking. They find out about it online somewhere, they use it to elect their organization's officers, and I never hear about it. Occasionally I peek at the file contents to see how my free VoteFair ranking service is being used, make sure it's not being abused, verify there is no evidence of bugs, and so on. That's when I get a glimpse of where it's used. When someone wants to use it for more than 6 choices (the default limit), then I get a call or email and I set up a special Voting ID number, but otherwise it quietly gets used, without lots of fanfare. In the case of the San Francisco Bay Area Curling club, a member called and asked for help, including a request to handle extra choices; otherwise I wouldn't have known about the club using VoteFair ranking. When I peek at data, I see that many organizations do not include their name in the title, and when their name appears I have to keep it anonymous, unless they contact me and agree to write a testimonial with their name. Everyone who has used VoteFair ranking has liked it, and as far as I know, no one has stopped using it. The fact that it is not yet used in as many organizations as the Condorcet-Schulze method reflects that it has not been promoted as heavily. Only us election-method experts know about the under-the-hood differences between the Condorcet-Schulze and Condorcet-Kemeny methods. To most people the two most-popular Condorcet methods (C-K and C-S) would appear to be clones. In fact, that's one reason I haven't felt a need to promote the Condorcet-Kemeny over the Condorcet-Schulze method. But now the Czech Green party wants a fair proportional method, and that's where VoteFair representation ranking offers a dramatic advantage. > ... that many of the claims in your book are > ridiculous; for example, your claim that > this method was strategyproof and satisfied > independence of irrelevant alternatives. Your Condorcet-Schulze method also fails the "independence of irrelevant alternatives," so let's make it clear that your comment about independence-of-irrelevant-alternatives criteria is not a criticism of the Condorcet-Kemeny method. Your criticism is about my book. Well, my book is about real elections, and this effect for this method is seldom a significant issue in real elections. If my book were intended for an academic audience, then of course it would be appropriate to talk about special edge cases in which adding a non-winning candidate can cause the first-most popular candidate to drop down in popularity ranking. (For the record, the book does not refer to the independence of irrelevant alternatives criteria, so where did you get the idea that it claims to satisfy that criteria?) Regarding "strategyproof," the book talks about real elections, not edge cases where one, or a relatively few, ballots can cause the results to change. The portion about the Condorcet-Kemeny method (called VoteFair popularity ranking in the book) refers to single-winner elections, not filling multiple seats. In single-winner real elections, the only strategies to which the Condorcet-Kemeny method is vulnerable involve shifting the results into a case of circular ambiguity, where there is no Condorcet winner, or exploiting a naturally occurring circular ambiguity. In such a case of circular ambiguity, any strategy that changes the results would be risky, and could easily backfire. Also, it would require comprehensive and accurate knowledge of how other voters will vote, and that knowledge is not available in real elections. In real voting situations where VoteFair ranking is used, the only strategic vulnerability I have observed is burying, where a large portion (especially when a majority) of the voters give an insincerely low ranking of an otherwise-popular competitor. This causes the contestant to get a lower-than-expected ranking in the results. But that's what any voting method should do. It reflects what large numbers of voters, and especially a majority of voters, express. But I have not seen burying affect who "wins" (who is ranked most popular). If someone makes the mistake of choosing the second-most popular candidate to fill a second seat, then that would produce an unfair outcome -- because that would be an improper use of the method (not because the method is unfair). In situations where a second seat is being filled -- such as the presidential and vice-presidential council seats in the Czech Green party -- a different method is needed. If VoteFair representation ranking is used to fill the second seat, there is no strategy (that I know of) that could change who wins either the first or second seat -- without also likely changing (for the worse) who wins the other seat. I wrote "Ending The Hidden Unfairness In U.S. Elections" for a general audience, not for an academic audience. I figure that Wikipedia and many other publications already address academic issues, such as edge cases changing the results. In my opinion, edge-case issues (and similar academic arguments) are insignificant compared to the big political influences such as campaign contributions, advertising and marketing techniques, election-process unfairnesses (which are common in certain U.S. states such as Florida, Louisiana, Texas, New Jersey, and Illinois), and politicians lying, selling influence, not answering questions, not taking clear positions, and more. (The first two chapters of the book explain lots of political realities that have nothing to do with vote-counting, but which have far more influence on election results.) As an example of the gap between reality and academic analysis, two politicians who are actually "clones" in terms of political position would not be recognizable as clones in a real race because they would claim to be quite different, which means that an academic analysis to test the results for "independence of clones" would not be meaningful. In closing ... Let's recognize that Peter Zbornik is providing an opportunity to get fairer voting methods out of the academic, analysis-paralysis state, and into real elections, so let's get real: For the Czech Green party council elections, I have already recommended VoteFair representation ranking (which uses the Condorcet-Kemeny method at its core). I will add that if the underlying Condorcet-Kemeny method were replaced by the Condorcet-Schulze method, that would provide nearly the same results. More importantly, both of those choices are significantly better than two-seat STV and approval voting. And all those methods are better than IRV, three-seat STV, four-and-more-seat STV, Range voting, and other assorted methods. (Yes, I've left out Schulze-STV. It's a new method and I don't yet understand it. (I've tried.) If I did understand it, and it looked like it would do what it claims to do, then I would have indicated where it fits in this list of methods, which I've prioritized by fairness.) (To Range-voting fans: Decades from now voters may use range ballots to provide richer preference information, but we don't yet have counting methods that handle those ballots in ways that resist approval-like strategic voting.) The main point I'm trying to make is that the Condorcet-Kemeny and Condorcet-Schulze methods are much more similar than different. Richard Fobes ---- Election-Methods mailing list - see http://electorama.com/em for list info