Dear David, you wrote (25 Feb 2005): > I know Mike Ossipoff advocates WV as opposed to WM for > the completion of methods such as Ranked Pairs, Schulze, > etc. Was he actually the first person to come up with > the idea as the sentence above seems to imply?
As far as I remember correctly, two different approaches have been discussed at this mailing list. First approach: Mike Ossipoff suggested that when a given voter strictly prefers candidate A to candidate B then this voter "approves" candidate A and "rejects" candidate B. In the archives of this mailing list, Mike calls a candidate B "majority rejected" or "majority beaten" when there is a candidate A such that a majority of the voters strictly prefers candidate A to candidate B. Mike always said that "majority rejected" candidates shouldn't be elected. In my opinion, this approach is very problematic because it isn't clear how it can be generalized to other election methods than MinMax. As far as I know, Mike still uses this approach. See e.g.: http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/013047.html Second approach: The second approach says that when some voters cast only a partial ranking (because of strategic considerations or other reasons) then the effect of this behaviour should be as small as possible. For example, in 1997 I proposed the following criterion ("majority beatpath criterion"): "X >> Y" means that a majority of the voters strictly prefers candidate X to candidate Y. A "majority beatpath" from candidate X to candidate Y is an ordered set of candidates Z(1),...,Z(n) with the following properties: 1. Z(1) is identical to X. 2. Z(n) is identical to Y. 3. Z(i) >> Z(i+1) for all i = 1,...,(n-1). If there is a majority beatpath from candidate A to candidate B and no majority beatpath from candidate B to candidate A, then candidate B must be elected with zero probability. The intention of this criterion is that when some voters cast only a partial ranking then when these partial individual rankings can be completed in such a manner that candidate A is a Schwartz candidate and candidate B is not a Schwartz candidate and these partial individual rankings cannot be completed in such a manner that candidate B is a Schwartz candidate and candidate A is not a Schwartz candidate then candidate B must be elected with zero probability. This guarantees that not unnecessarily a candidate is elected who would not have been a Schwartz candidate when not some voters had cast only a partial ranking because of strategic considerations or other reasons. As far as I remember correctly, it was me (and not Mike Ossipoff) who suggested that "winning votes" should be used for the Schulze method (aka Schwartz sequential dropping, cloneproof Schwartz sequential dropping, beatpath winner, beatpath method). I used the majority beatpath criterion as an argument. Markus Schulze ---- Election-methods mailing list - see http://electorama.com/em for list info
