Consider Enhanced DMC as defined in this message from Forest Simmons, dated July 12, 2011:
http://old.nabble.com/-EM--Enhanced-DMC-td32048790.html I prefer the name Strong Preference Approval Round Robin (SPARR), following from the idea that this is a form of Condorcet (Instant Round Robin) that looks for the highest-approved candidate who is most strongly preferred, in some sense. Here's my restatement of the algorithm: Find P, the set of all candidates who are not defeated pairwise by any other higher-approved candidates. Number the p candidates in this set in order of approval from lowest, X_1, to highest, X_p. If there is only one candidate in P, the SPARR winner is that candidate, X_1. Otherwise, initialize the Strong set U to P. Remove P-member-covered candidates from U: For i from 1 to p-1, For j from i+1 to p, If all of X_j's defeats are defeated by X_i, remove X_j from U. When finished, the Strong set U contains only those members of P who are uncovered by other members of P. The Strong set U always has at least one member, the DMC winner (X_1), because by definition X_1 can never be defeated pairwise by other members of P. The highest approved member of U is the SPARR winner. ***** End of algorithm Motivation: The motivation for the SPARR method is, as Forest stated 6 months ago, that the winner should come from the set P of candidates who are not defeated by higher-approved candidates, which includes the Approval winner, but should not necessarily be the least-approved member of P just because that candidate defeats all other P-set members pairwise. If the Approval winner X were chosen, another P-set candidate Y could have grounds to object if Y covers X. "Hey, I defeat you pairwise, and everyone else you beat too! I'm a stronger candidate than you are." Therefore we consider as 'strong' members of P only those candidates who are not covered by other members of P. The highest-approved strong candidate is the SPARR winner. ***** End of motivation Questions: What happens if the SPARR winner X is covered by another candidate Y *outside* the P set? And not only that, but the *only* reason Y is not in P is that Y is pairwise-defeated by another non-P-member with higher approval. So Forest's statements about Y being defeated by Z in P would not apply. Here's an example of that situation: A Smith set of 6 candidates, lettered in descending order of approval as A through F, with the P set = {A,B,C}. Fifteen defeats: A > D, B > A, B > F B uncovered by C, => B is SPARR winner C > A, C > B, C > D C covers A, eliminating A from strong set D > B, D > E E > A, E > B, E > C, E > F E covers B, defeated only by non-P-member D F > A, F > C, F > D B's beatpath to E goes through F B is the highest approved uncovered P-member and is the SPARR winner. I don't think this could be considered a version of Ranked Pairs, because even if you affirm all the High-low defeats first, you still can't eliminate the E > B defeat by first affirming B > F > D > B, because D has higher approval than F. Could there be a beatpath strength formulation that applies to SPARR? Ted -- araucaria dot araucana at gmail dot com ---- Election-Methods mailing list - see http://electorama.com/em for list info