[EM] Why wv is completely expressive

[MIKE OSSIPOFF]

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