This poll is forcing me to think about the difference between various Condorcet methods, which is something I've been putting off. On the topic of margins vs. winning votes: Draw an equilateral triangle. The top vertex represents all ties. The lower right represents winning votes, and the lower left represents losing votes. Drop a vertical line from the top of the triangle to the base. Each pairwise contest can be mapped into a point on the right-hand side of the triangle. (Each point can be labeled with an order indicating the winner, so that the point representing A vs. B is labeled AB if A wins, BA if B wins). For points in a cycle, dropping the contest with the smallest margin is equivalent to dropping the left-most point in the cycle. The left-most point is closest to the vertical line. If this point is XY, then it is the point in the cycle for which the fewest votes would have to change to move it to the left-hand side of the triangle (at which point we replace it with its mirror image point YX on the right-hand side). Another way to picture this is to imagine all the points in the cycle orthogonally projected onto the triangle's base, an operation equivalent to splitting the tie votes evenly between the two candidates. Using winning votes is equivalent to a projection down and to the left along a 60 degree slope to the base of the triangle. This is equivalent to converting all the tie votes to losing votes. I think the margins approach is better because it treats tie votes as ambiguous, rather than as losing votes. One other approach would be to allocate the tie votes to the winner and loser in proportion to the actual numbers of winning and losing votes, which is a projection onto the triangle's base from a focus at the top corner of the triangle. Richard
