[EM] two bit ratings

[Forest Simmons]

On Fri, 21 Sep 2001, Richard Moore wrote:

> Craig Layton wrote:
> 
> > I expect you're right, but isn't the Condorcet Criterion phrased something
> > like "if there is a sincere Condorcet winner, and all voters vote sincerely,
> > then the sincere Condorcet winner must win"?
> 
> 
> Why should the CC definition include the word "sincere" at 
> all? Isn't the use of "sincere CW", coupled with the 
> conditional "all voters vote sincerely", redundant? What 
> does this definition say that is different from "If there's 
> an expressed CW, then the expressed CW must win"?
> 

This definition has its problems, too.  By the rules of classical logic,
if a method doesn't allow the expression of a  CW, then that method would
satisfy this definition.

So perhaps we should say that a method satisfies the CC if and only if

(1) the method's ballots do allow complete expression of preference order
among the candidates

AND

(2) whenever a candidate is an expressed CW, then that candidate must be
the method's winner.

In that case it would be OK to allow truncation, but not OK to force
truncation.

So my two bit method would satisfy the CC only for four or fewer
candidates. If we have more than four candidates, we have to allow more
bits of expression to maintain the CC.

Forest