1) Determine the winner.[...]
2) Order the losing candidates from the one with the strongest beatpath against
the winner, to the one with the weakest.
3) Assign the winning candidate a score equal to its beatpath against the
strongest losing candidate.
49% Bush 12% Gore>Bush>Nader 12% Gore>Nader>Bush 27% Nader>Gore>Bush
The results by my proposal would be displayed:
1) Gore 51% 2) Bush 49% 3) Nader 27%
That's not quite right. What I show there is the pairwise counts of each of Gore's contests. Which is really what I want; that seems like the best measure when there is a Condorcet winner. That said, it would look very strange to the casual viewer if a loser had a higher score than a winner. So I would add the following fourth step to my process above:
4) Replace all non-winning candidates' scores with the number of votes they received against the winning candidate, unless this amount is larger than the winner's score.
So, my ranking of the example on Rob's site would now become:
1) Abby 511 2) Brad 463 3) Cora 460 4) Dave 436 5) Erin 410
It's a bit more pleasing to the eye, isn't it?
This is admittedly a mishmash of a couple different measures, but I think it does a good job of getting a monotone ranking out of pairwise ballots. At least, I'll think that until someone comes up with a good counterexample.
-Adam
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