[EMAIL PROTECTED]">I was thinking about this recently. If a completion method is going to be biased towardThere may be a Condorcet completion method that satisfies the same criteria and is better on SU, but
somehow I doubt it.
higher SU, then it will have to be able to pick a winner outside the Smith set occasionally.
Say the Smith set includes A, B, and C. Say D loses to each of these three, but only by
a very slim margin. It is possible that D has a higher SU than either A, B, or C.
One idea I'm thinking about is to define a minimum cost dropping algorithm. Let's say
you could make A the winner by dropping C's defeat of A, but that defeat has a margin
of 5 votes. And let's say you could make D the winner by dropping A's, B's, and C's
defeates of D, and each of those defeats is by only 1 vote. In the minimum cost algorithm,
the total cost of declaring a winner would be the sum of the margins of the dropped
defeats, so the cost of declaring D the winner (3) would be lower than that of A (5). If
the B and C defeats also have margins of 4 or higher, then D would be the winner. If
two candidates tie for the lowest cost then of course you can take the pairwise contest
results between just those candidates.
I like this method intuitively, but don't have any ideas about what criteria (other than
Condorcet and I believe monotonicity) it may or may not satisfy. It seems to me that
it is somewhat similar to path voting. Any comments?
Richard
