Kevin, Forest, interested participants, My latest favourite FBC single-winner method:
"1)Voters submit 3-slot ratings ballot, default 'no rating' interpreted as bottom-rating. 2) Eliminate any candidate X who is above-bottom rated on fewer ballots than is some candidate Y on ballots that bottom-rate X. 3) On ballots that top-rate no candidates, promote middle-rated candidates to top- rating. 4) Elect the candidate that is (now) top-rated on the greatest number of ballots". For (at least) the time being, I call this "Strong Minimal Defense//FPP(Whole)". It meets a new criterion I suggest that I tentatively label "Strong Minimal Defense" which states: "If X has fewer votes (ranking/rating above bottom or equal-bottom) in total than Y has on ballots that have no votes for X, then X can't win". It implies both Minimal Defense and the Plurality Criterion. The method meets the FBC (and therefore the similar Sincere Favourite). If X wins, changing some ballots that top-rate X and not Y to top-rating both cannot cause X to be eliminated or for any candidate to be un-eliminated except Y. The changed ballots cannot diminish the absolute post-eliminations FPP(W) score of X and can boost the final score of only Y. The method compares favourably with the other 3-slot FBC methods. MDDA, MAMPO, MCA, ER-Bucklin (W) all fail the "Independence from Irrelevant Ballots" (IIB) criterion which states that if there is some losing candidate Y that only appears (voted above bottom or equal-bottom) on some ballots that ignore (vote equal-bottom) all other candidates (and Y is top rated/ranked on fewer ballots than any other candidate) then removing one/some/all of the Y-plumping ballots must not change the winner Adding or removing ballots that ignore all the viable candidates can change the winner just by changing the size of the majority threshold. If the election is contentious and the votes are not necessarily counted with the greatest accuracy and impartiality, it seems to me to be a great help if election monitors/scrutineers/observers can safely pay little attention to ballots that make no distinction among viable candidates. SMD//FPP(w) meets IIB. I think it meets Majority for Solid Coalitions (aka Mutual Majority) as well as any 3-slot method can, meaning that if more than half the voters rate a subset S of candidates above all others, then a member of S must win. In 3-candidate scenarios it generally gives Schulze(winning votes) like results. 49: A 24: B 27: C>B A eliminates C because C is above-bottom rated on a total of 27 ballots, while on ballots that bottom-rate (ignore) C A is above-bottom rated on 49 ballots. Likewise B eliminates A so B wins. 46: A>B 44: B>C 10: C C eliminates A, B wins. 46: A 44: B>C 10: C Now C eliminates A, A eliminates B. (Like Schulze the method fails Later-no-Harm) >40 A>B >35 A=B >25 B > > From the electowiki ICA page, giving B as the ICA winner(!?). In SMD//FPP(w) no candidate is eliminated, then A scores 75 versus B's 60. The method meets mono-raise and fails Clone-Winner. I invite comments and am open to suggestions for a more popular name, perhaps also for the "Strong Minimal Defense" criterion/set. Links re. MDDA, MAMPO, ICA for comparison : http://wiki.electorama.com/wiki/Majority_Defeat_Disqualification_Approval http://wiki.electorama.com/wiki/Majority_Approval%2C_Minimum_Pairwise_Opposition http://wiki.electorama.com/wiki/Improved_Condorcet_Approval http://nodesiege.tripod.com/elections/#methica Chris Benham I ---- Election-Methods mailing list - see http://electorama.com/em for list info
