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Evaluation of MAM:<br><br>Forest--<br><br>I've been looking at various ways of doing Mutual Acquiescing Majorities (MAM). (I think that was the name that you used).<br><br>Initially I thought it worked, and that it had a better set of properties than any comparably simple method.<br><br>But then I realized that I couldn't make that method work.<br><br>Any success?<br><br>My definition of the MAM set:<br><br><br>A set of candidates whom every member of the same majority vote equal to or<br>over every candidate outside the set.<br><br>[end of MAM set definition]<br><br>That definition is the 1st paragraph of an MAM definition.<br><br>The 3rd paragraph is:<br><br>"If there are no MAM sets, then the winner is the most top-rated candidate.<br><br>I've tried several 2nd paragraphs for MAM, but none of them works:<br><br>1) "If there are 1 or more MAM sets, the winner is the most top-rated candidate who is in a MAM set."<br><br>Or<br><br>2) "For any MAM set, the winner must come from that set. The winner is the most top-rated candidate<br>consistent with that requirement."<br><br>In the ABE, #1 lets {A,B,C} be an MAM set, and the winner is C, even if the B voters rate A at<br>middle, or even at top.<br><br>#2 requires that the winner come from the intersection of {C,B} and {A,B}<br><br>But electing B is the one way to fail in the ABE.<br><br>So, as I said, I haven't been able to make MAM work.<br><br>Have you?<br><br>Summary of FBC/ABE methods:<br><br>I don't know there's a way of making MAM work. So, for the purposes of this posting, I'm going to<br>cautiously assume that such an MAM variation hasn't yet been found.<br><br>Then, there are six workable FBC/ABE methods described so far. In rough chronological order of their <br>proposing, they are:<br><br>MMPO<br>MDDTR<br>TTPDTR<br>MTAOC<br>MMT<br>MMMPO<br><br>Two of these were introduced by Forest, two were introduced by Chris, and two were introduced by me.<br><br>It seems to me that Forest proposed MMPO, some time ago. Chris suggested MDDTR when I asked if<br>there were a method that passes FBC and the ABE and Kevin's MMPO bad-example.<br><br>TTPDTR and MMMPO were recently proposed by Chris and Forest, respectively.<br><br>I proposed MTAOC and MMT.<br><br>Methods that let one faction unilaterally establish the win of a majority: MMPO, MDDTR, and probably MMMPO<br><br>Methods requiring mutuality: MTAOC, MMT.<br><br>I don't know which of those two classifications TTPDTR is in.<br><br>Here is an incomplete table of properties, for these six methods:<br><br>(I hope that format differences don't cause rollover in this table)<br><br>MAP means Mono-Add-Plump<br>KMBE means Kevin's MMPO bad-example<br>LNHe means Later-No-Help<br>U means that a majority can be established unilaterally<br><br>L means "less imporantly"<br><br>I emphasize that I don't consider the MAP & KMBE "failures" of MMPO & MDDTR to be important.<br>But the "L" means that a criticism is unlikely to be usable for convincing the public.<br><br>All of these methods meet FBC, pass in the ABE, and have some majority-rule protection.<br><br>.................MAP......KMBE.....LNHe.....U<br><br>MMPO........Yes.......No.........No........Yes<br>MDDTR.......No........Yes........No.......Yes<br>MMT..........No L.......Yes.......No L.....No<br>MTAOC......No L.......Yes.......No L......No<br>TTPDTR<br>MMMPO.....Yes?..............................Yes?<br><br>(I don't have the answers for MMMPO and TTPDTR). Maybe someone else can fill<br>the table in for those two methods).<br><br>Mike Ossipoff<br><br><br><br><br><br><br><br><br><br><br><br><br> </div></body>
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