Why Condorcet(wv) is conditionally completely expressive: We rule out order-reversal as a strategy. Say everyone sincerely ranks all of the candidates. Of course that always elects the sincere CW. Because there's a CW, and no indifference between him & anyone else, that CW has a majority against everyone. If there's no falsification of preferences, it's impossible for the CW to have a voted majority against him. The definitioni of a conditionally completely expressive method stipulates that we rule out order-reversal as a strategy. Since there's no indifference involving the CW, that means that there's also no falsification of preferences involving the CW. And that means that it's impossible for the CW to have a voted majority against him. Say that some voters want to make a circular tie by truncating, in hopes of electing some candidate X, whom they prefer to the CW. The CW has a voted majority against X, and no one has a voted majority against the CW, for the reasons described in the paragraph before last. With BeatpathWinner, that means that no one, including X, can have as strong a beatpath to the CW as the CW has to X (a 1-defeat beatpath). X can't win. With SSD & RP, that means that the CW's defeat of X can't be the weakest defeat in a cycle, since no one beats the CW as strongly as the CW beats X. As described in an earlier posting, SSD & RP never drop a defeat that isn't, and wasn't initially, the weakest defeat in a cycle. X can't win. With PC, the CW doesn't have as strong a defeat as X does, and so X can't win. Order-reversal is ruled out. Truncation can't elect X, and can't , in general, benefit anyone who does it. Extending one's ranking farther isn't possible, since everyone is already ranking all the candidates. No one can gain by changing their strategy. Mike Ossipoff _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx
