Dear Diana, suppose "d[X,Y]" is the number of voters who strictly prefer candidate X to candidate Y.
Condorcet: Suppose that there is a candidate A with d[A,B] > d[B,A] for every other candidate B. Then "Condorcet" says that this candidate A must be elected. Smith: The "Smith set" is the smallest non-empty set of candidates with d[A,B] > d[B,A] for every candidate A of this set and for every candidate B outside this set. "Smith" says that the winner must be a candidate of the Smith set. Participation: "Participation" says that adding a set of identical ballots on which candidate A is strictly preferred to candidate B must not change the winner from candidate A to candidate B. mono-add-top: "mono-add-top" says that adding a set of identical ballots on which candidate A is strictly preferred to every other candidate must not change the winner from candidate A to another candidate. mono-delete-bottom: "mono-delete-bottom" says that adding a set of identical ballots on which every other candidate is strictly preferred to candidate B must not change the winner from another candidate to candidate B. Participation implies mono-add-top and mono-delete-bottom. Condorcet and participation are incompatible. Condorcet, mono-add-top, and mono-delete-bottom are compatible. For example: The MinMax method satisfies Condorcet, mono-add-top, and mono-delete-bottom. It is not known whether Smith and mono-add-top are compatible. It is not known whether Smith and mono-delete-bottom are compatible. Participation is met e.g. by First-Past-The-Post (FPP), Borda, Approval, and Woodall's "Descending Acquiescing Coalitions" method: http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf Here are examples that my beatpath method and Tideman's ranked pairs method violate mono-add-top and mono-delete-bottom: http://groups.yahoo.com/group/election-methods-list/message/12014 http://groups.yahoo.com/group/election-methods-list/message/12051 Markus Schulze ---- Election-methods mailing list - see http://electorama.com/em for list info
