Hi Forest,
>________________________________ > De : Forest Simmons <fsimm...@pcc.edu> >À : EM <election-methods@lists.electorama.com> >Envoyé le : Dimanche 6 octobre 2013 17h21 >Objet : [EM] Try this method on your favorite election scenario > >Ballots are ranked or rated. If ranked, then equal ranking and truncation are >allowed. > >Let IA stand for Implicit Approval, which for any candidate X is the number of >ballots on which X is ranked or rated above bottom, i.e. neither truncated nor >rated at zero. > >Let MPO stand for maximum pairwise opposition, which (for candidate X) is the >maximum (as Y varies over the other candidates) of the number of ballots on >which a strict preference of Y over X is indicated. > >The winner of this method (IA/MPO) is the candidate with the highest ratio of >IA to MPO. > >Example > >45 A>B >35 B>C >20 C > >For A IA is 45 and MPO is 55, so IA/MPO is 45/55 or 9/11. >For B IA is 80 and MPO is 45, so IA/MPO is 80/45 or 16/9. >For C IA is 55 and MPO is 80, so IA/MPO is 55/80 or 11/16. > >The IA/MPO winner is B. > >If, instead, the A faction votes 45 A, then the ratios become ... > >For A (the same) 9/11. >For B IA is 35 and MPO is still 45, so the ratio is 7/9. >For C IA is still 55 and MPO is 45, so the ratio is 11/9. > >This time C wins. IA/MPO seems like a pretty good method. It seems to be guaranteed that at least one candidate will have a score >= 100%. That's elegant. With that assumption it seems easy to demonstrate that the method satisfies Plurality and SDSC/Minimal Defense. My guess is that it must satisfy FBC since the component scores each do, and the only "processing" is taking the ratio. I suspect that we have lost SFC compared to MMPO ("Strategy-Free": roughly, if A has a majority over B and there is no majority over A, B can't win), but it might be hard to contrive a failure scenario. If it's right that IA/MPO satisfies FBC, MD, and Plurality, it's not in a crowded space... Though MAMPO satisfies those as well as SFC, it's probably less sensitive to the rankings. (MDDA has SFC but can fail Plurality.) I should get my simulations running again. I seem to recall being disappointed with the performance of MDDA and MAMPO. Kevin Venzke ---- Election-Methods mailing list - see http://electorama.com/em for list info