Here's an equivalent but simpler description of the FBC/ABE compliant method that I have been calling (since Mike's pointer about MaxMin vs. MinMax) MaxMin(EqualRankPairwiseRule): Let M be a matrix whose entry in row i and column j is the number of ballots on which candidate i is rated or ranked strictly above candidate j plus half the number of ballots on which candidates i and j are ranked or rated equal bottom (i.e. neither one is ranked or rated ahead of any other candidate on the ballot). Find the maximum value in each column of M. Find the column j whose maximum value is minimal. Elect candidate j. In other words, elect the MinMax(ModifiedPairwiseOpposition) candidate, where the modified pairwwise opposition of candidate x against candidate y includes half the number of ballots on which neither x nor y is ranked or rated above any other candidate. In other words, it is the same as MMPO after symmetrical completion of the order among the equal bottom candidates on each ballot (but not among other equally ranked or rated candidates). Note that this method is a modification of MMPO that retains the FBC compliance as well as the mono- add-equal-top compliance. In addition it finesses the Approval Bad Example (defection problem) and does not elect the weak middle candidate of Kevin's Bad MMPO example. Note that mono-add-equal-top is stronger than mono-add-top, which in turn is stronger than mono-add- plump. Shall we abbreviate MinMax(ModifiedPairwiseOpposition) with MMMPO? It still needs a fancier name for public consumption. > From: [email protected] > To: [email protected] > Subject: [EM] Chris: Forest's FBC/ABC method (MIKE OSSIPOFF) > Message-ID: > Content-Type: text/plain; charset=us-ascii > > Mike is right; it should be called MaxMin instead of MinMax. > > > From: MIKE OSSIPOFF > > To: > > Subject: [EM] Chris: Forest's FBC/ABC method > > Message-ID: > > Content-Type: text/plain; charset="iso-8859-1" > > > > > > Chris-- > > > > I'll describe Forest's proposal briefly: > > > > It's minmax margins (but it's defined as maxmin, with respect > to > > x>y - y>x), > > looking at all pairwise comparisons, rather than just at defeats. > > > > But, instead of just x>y - y>x, it's x top or >y - y>x. > > > > As I said in my other posting, it seems to have the same properties > > as MMT. In other words, FBC, LNHa, 3P, and the (unnecessary) > > Mono-Add-Plump > > and the (unnecessary) avoidance of electing C in Kevin's MMPO > > "bad"-example. > > > > Though Mono-Add-Plump and complying in Kevin's example are > > unnecessary,they avoid misguided or dishonest criticism by > > opponents of a reform proposal. > > > > As I've said, maybe it's better to ask for a little less than > > MMPO and MDDTR, > > in order to avoid the distraction that such criticisms could > > cause, during an > > enactment campaign. --especially given that the opponents are > > likely to have > > a lot more media money than the proponents. > > > > Mike Ossipoff > ---- Election-Methods mailing list - see http://electorama.com/em for list info
