It occurred to me that there is another method which is similar to weighted pairwise, which uses an approval cutoff rather than a cardinal ratings ballot.
Ballots: ranked ballots with approval cutoff Tally: 1. Pairwise tally using the ranked ballots. Elect the Condorcet winner if one exists. If there is a majority rule cycle: 2. Using the ranked ballots only, construct a map of which candidates beat or tie other candidates. At this point we are only determining the direction of the defeats, not the magnitude. 3. For a given defeat A over B, the magnitude of the defeat is defined by the number of voters who place A above their approval cutoff and B below their approval cutoff. 4. Using this definition of defeat strength, you can resolve the cycle with methods such as minimax, beatpath, or ranked pairs. Perhaps this method has already been proposed? I haven't heard of it specifically, but I know that people on the list have done a lot of work with approval cutoffs. This method requires a ballot that is arguably simpler than weighted pairwise, i.e. rankings plus an approval cutoff. It is also likely to produce similar results in many cases. However, it is by no means an identical method. This method does not allow voters the full range of expression which is the intended purpose of weighted pairwise, that is, the ability to have more than one utility gap. At present, I prefer weighted pairwise. James Green-Armytage ---- Election-methods mailing list - see http://electorama.com/em for list info