...for methods that don't meet CD: 1. Weak CD: Smith//MMPO & Smith//NEO meet it. In the CD premise, replace "The B voters don't vote A over anyone" with "The B voters vote A & C equal bottom." 2. Conditional votes: I described this at EM years ago: A voter can designate as conditional any vote, or 2nd or equal-1st place ranking. If you top-vote A, and conditionally vote for B, and if some B>A voters conditionally vote for A, then: Then, for whichever faction's conditional + unconditional vote total for the other faction's candidate is greater: Devalue their conditional votes just enough so that both factions are giving eachother's candidates the same # of votes (or 2nd place or equal-1st ranking). If the conditional percentage of their votes isn't sufficient to achieve that, then devalue them to zero. ..in order to achieve it as nearly as possible. Variation: Instead of devaluing the conditional votes so as to make the shared votes equal, make them an equal fraction of the giving faction's size. ...or allow the option for either. Michael Ossipoff