Re: [EM] Advocacy of Kemeny's method

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-------- Original Message -------- Subject:     Re: [EM] Advocacy of Kemeny's method Date:     Thu, 16 Sep 2004 21:05:52 -0700 From:     Steve Eppley <[EMAIL PROTECTED]> Reply-To:     [EMAIL PROTECTED] To:     [EMAIL PROTECTED] References:     <[EMAIL PROTECTED]> I'm not sure what Mike means by some of those terms. (Extended Condorcet?  Cycle "removal"?  Voting manipulation "resistance"?)  I wonder if he can tell me if MAM, described at www.alumni.caltech.edu/~seppley, meets those criteria.  MAM does satisfy the above criteria that I do understand: It chooses within the top cycle, hence is Condorcet-consistent, and it socially orders all the candidates. (Like Kemeny, MAM's ordering satisfies local independence of irrelevant alternatives, and, unlike Kemeny, MAM satisfies a stronger criterion, immunity from majority complaints.)  Also, MAM can be tallied in a time that's a small polynomial function of the number of voters and the number of candidates. Michel Truchon gives the following description of XCC (the Extended Condorcet Criterion): The usual Condorcet Criterion says that if an alternative is ranked ahead of all other alternatives by an absolute majority of voters, it should be declared the winner. The following partial extension of this criterion to other ranks is proposed: If an alternative is consistently ranked ahead of another alternative by an absolute majority of voters, it should be ahead in the final ranking. The term "consistently" refers to the absence of cycles in the majority relation involving these two alternatives. He goes into a bit more detail in his paper Figure Skating And The Theory Of Social Choice at http://citeseer.ist.psu.edu/cache/papers/cs/11707/http:zSzzSzwww.ecn.ulaval.cazSzw3zSzrecherchezSzcahierszSz1998zSz9814.pdf/truchon98figure.pdf Cycle removal just means that when you have a circular tie with regular Condorcet voting -- Candidate A is preferred to B, Candidate B is preferred to C, and Candidate C is preferred to A -- the Kemeny order will unwind the cycle and put the candidates in a specific order without the need for a tie-breaker method. Tie-breakers are fine, I just find is more aesthetically pleasing this way. By "voting manipulation resistance," I mean it is difficult for a voter to come up with a way to improve his outcome over voting sincerely. Partly this is because it's a NP-hard problem to solve and requires complete knowledge of voting preferences, partly because it disregards orders it considers outlandish compared to majority preferences (the people who actually do prefer Nader>Bush>Kerry lose out, but hey...). Of course, like any non-dictatorial method it's still theoretically possible to manipulate. I've heard of MAM, even read a bit about it, and it appears to be a fairly attractive system --especially  the ease of calculation compared to Kemeny. I haven't read it in depth enough to compare it to Kemeny-Young, though (and to be honest, a lot of the math involved in Kemeny is beyond me to begin with), but I'll check it out some more this weekend and see if I can get a better feel for it. I'll check out the rest of the email in a bit -- I'm doing this between tech calls, and they frown on me if I do this too much :) Mike

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