Hi, Markus S wrote about Paul Crowley's proposed voting method: > your Condorcet/RP variant sounds like Steve Eppley's > "minimize thwarted majorities" (MTM) method.
I think of the name MTM as an old name for MAM, which stands for "maximize affirmed majorities." To my ear, "maximize affirmed majorities" has a more positive sound than "minimize thwarted majorities." (I'm open to suggestions for a better name, although so much has already been written about MAM that changing the name again will be problematic.) I don't recall which tiebreaking technique I defined for it back in those days, years ago. I may have posted more than one tiebreaker as the method evolved, and may even have left tiebreaking undefined initially. If he thinks it matters, hopefully Markus will tell us which MTM tiebreaker he has in mind. The tiebreaking in Paul's method sounds different than MAM's. But I'd appreciate seeing examples to clarify each case Paul wrote about. I got the impression his tiebreaker is not independent of clones, but I'm not confident I understand what he intended. I'd appreciate if Paul would elaborate on why he thinks its tiebreaking is "fairer" and "cleaner" than MAM's. Are there any criteria we can use to more clearly define "fairer" and/or "cleaner?" What I want from a tiebreaker is for it to be as simple as possible, but without sacrificing any criteria that people consider important. Even though my principal concern is with public elections, where it's unlikely any pairing will be a tie and unlikely two majorities will be the same size, I think it's important that the tiebreaker behave well in small group voting. That's because I expect the public will be reluctant to accept a voting method for public elections that hasn't been thoroughly tested by many organizations. (A couple of months ago in the discussion of the Kemeny-Young method, I didn't find the time to mention this connection between public elections and small group voting. K-Y's failure of clone independence is likely to cause problems if K-Y is used by small groups voting on propositions and amendments, since clone amendments cannot refuse to be nominated, and the participants typically won't know at nomination time whether or not there will be any pairwise ties or same-size majorities. Clone nominations might also be a simple way to make K-Y fail the minimal defense criterion, but I haven't looked at this.) There's also the issue of execution time. There's no inherent upper bound on the number of alternatives in an election (particularly when voting on propositions). I don't want to have to defend a voting method from attacks by "hired gun" academics who argue that its worst case execution time blows up as the number of alternatives increases. Election reform is tough enough already; there's no reason to unnecessarily give ammo to the enemy, who'll be able to afford much more media time. I spent months trying to develop a quick algorithm to implement MTM before finally finding one. Then I recognized that algorithm was equivalent to Tideman's top-down algorithm that had been posted in the EM list a year earlier--except using "winning votes" instead of margins, and the open issue of tiebreaking. So then I got ahold of Tideman's 1987 paper and Zavist-Tideman's 1989 paper. I misinterpreted Zavist's tiebreaker when I copied it for MAM, but that turned out to be good luck since my version provides monotonicity but Zavist's does not. (I don't mean to imply I think monotonicity is important. To me monotonicity is just another unimportant "consistency" criterion. I only care about monotonicity because people have been known to criticize methods that aren't monotonic.) It's common for small groups to use voting methods that violate neutrality and anonymity. The basic Robert's Rules method, a pairwise single-elimination method, resolves the top cycle (if there is one) based on the order in which amendments are proposed, thus violating neutrality. Ties are typically broken by appealing to the chairperson or the agenda order, thus violating anonymity or neutrality. So, if a group wants to eliminate randomness by trading away anonymity or neutrality, they can do so by favoring the alternatives nominated earlier--status quo treated as first--and/or a seniority order of the voters. (But I haven't checked whether using the nomination order satisfies a criterion weaker than clone independence: independence from all clones except the earliest. Although weaker, its satisfaction would seem to be sufficient.) If he hasn't already done so, Paul might want to look at the section entitled "MAM2, a voting rule equivalent to MAM" in the following webpage: www.alumni.caltech.edu/~seppley/MAM%20formal%20definition.htm Here's an excerpt from that section: MAM2 finds the social orderings which "maximize affirmed majorities" and elects an alternative which tops such an ordering. This is similar to the Kemeny-Young "maximum likelihood estimation" voting rule, except MAM2 uses a leximax comparison of the possible social orderings while Kemeny-Young scores each of the possible social orderings by adding the sizes of the majorities it agrees with. MAM2 is completely equivalent to MAM due to the way it handles tiebreaking. --Steve ---- Election-methods mailing list - see http://electorama.com/em for list info