Deluxe MDDA or DMMDA for short: 0. Votes are preference-rank-orderigs of the candidates, AND each vote also includes an "approval threshhold" where all candidates ranked at or above it are "approved" by that voter. Rankings can include both > and = relationships, e.g. A>B=C>D=E>F=G.
1. A candidate is "disqualified" if another candidate is ranked over him/her by a majority of the voters. (Unless that rule would disqualify all the candidates, in which case no one is disqualified.) 2. The winner is the most-approved un-disqualified candidate. [end of DMDDA definition] Here is the definition of a related voting method devided by Warren D Smith, (actually originally due to a misunderstanding of DMMDA, but I'll take it:) call it WMDDA: 1. A candidate is "disqualified" if not in the "Smith set" (The "Smith set" is the candidates S such that each candidate in S is pairwise winner over each candidate not in S. Different Smith - not me.) 2. The winner is the most-approved un-disqualified candidate. [end of WMDDA definition] I claim both DMMDA and WMDDA obey SFC, SDSC, and FBC. PROOFS of above 3 DMDDA claims (by Venzke) with WMDDA add-on proofs by WD Smith: * satisfies SDSC because if a majority prefer X to Y, and don't approve Y, then Y will have a majority-strength defeat. If not all candidates have such defeats, then Y can't win. If all candidates have such defeats, then Y still can't win, because X has greater approval than Y. WDS adds note: WMMDA also satisfies SDSC because of the same proof with this addition: Y is either not in the SMith set (in which case Y cannot win) or is, in which case X and Y ill be in the same Condorcet cycle. In that latter case Y cannot win because X has greater approval than Y. * satisfies SFC because if no majority prefers anyone to X, then X will not be disqualified. If X has a majority-strength win over Y, then Y will be disqualified, so that Y can't win. WDS adds note: WMMDA also satisfies SFC because of the same proof. * satisfies FBC because if X wins, and a faction has ranked Y insincerely low, then if this faction raises X and Y to the first position, the winner will then be either X or Y. This is because X and Y can only lose defeats in this way, and other candidates can only gain them. Also, X and Y's approval can only increase. NOTE: this FBC proof only works if the "ranking" is allowed to include EQUALITIES not just ">" relations, e.g. A>B=C=D>E=F>G=H. WDS adds note: WMMDA also satisfies FBC because of the same proof. wds ---- election-methods mailing list - see http://electorama.com/em for list info
