<html><head></head><body>Rob LeGrand wrote:<br>
<blockquote type="cite" cite="mid:20010427010836.9008.qmail@web11003.mail.yahoo.com"><pre wrap="">There may be a Condorcet completion method that satisfies the same criteria and is better on SU, but<br>somehow I doubt it.</pre>
</blockquote>
I was thinking about this recently. If a completion method is going to be biased toward<br>
higher SU, then it will have to be able to pick a winner outside the Smith set occasionally.<br>
Say the Smith set includes A, B, and C. Say D loses to each of these three, but only by<br>
a very slim margin. It is possible that D has a higher SU than either A, B, or C.<br>
<br>
One idea I'm thinking about is to define a minimum cost dropping algorithm. Let's say<br>
you could make A the winner by dropping C's defeat of A, but that defeat has a margin<br>
of 5 votes. And let's say you could make D the winner by dropping A's, B's, and C's<br>
defeates of D, and each of those defeats is by only 1 vote. In the minimum cost algorithm,<br>
the total cost of declaring a winner would be the sum of the margins of the dropped<br>
defeats, so the cost of declaring D the winner (3) would be lower than that of A (5). If<br>
the B and C defeats also have margins of 4 or higher, then D would be the winner. If<br>
two candidates tie for the lowest cost then of course you can take the pairwise contest<br>
results between just those candidates.<br>
<br>
I like this method intuitively, but don't have any ideas about what criteria (other than<br>
Condorcet and I believe monotonicity) it may or may not satisfy. It seems to me that<br>
it is somewhat similar to path voting. Any comments?<br>
<br>
Richard<br>
<br>
</body></html>