[EM] two bit ratings

[Forest Simmons]

Craig, 

I think that what you are saying is what we have all been taking for
granted, and is true 99.9999 percent of the time. 

But consider the possibility that the voters truncate for strategical
reasons even when they do have significant preferences among the truncated
candidates, and that the information from the polls might be so far off
(or the voters so confused on strategy) that the truncation choices were
unwise enough to eliminate the true CW, or lucky enough to eliminate a low
utility CW. 

I admit it is extremely unlikely, but if it is possible, then the method
doesn't technically satisfy the absolute version of the Condorcet
Criterion. 

Am I overlooking something here?

Forest

On Fri, 21 Sep 2001, Craig Layton wrote:

> >> If there is a candidate A such that for any other candidate B, it is the
> >> case that candidate A is preferred over candidate B on more ballots than
> >> candidate B is preferred over candidate A, then candidate A is the
> >> method's designated winner.
> >>
> >> This is the closest we can get to the Condorcet Criterion for any method
> >> that doesn't require complete rankings.
> >
> >
> >It is interesting to note that Approval meets this "Relaxed
> >Condorcet Criterion". But I have to temper my enthusiasm by
> >noting that, so does Plurality.
> 
> 
> I'm not sure that the Condorcet Criterion needs to be relaxed to incorporate
> methods allowing truncation.  If a voter truncates her ballot, I think she
> could be construed as making a definite choice not to express a preference
> between the unranked candidates, ie she is choosing to rank them equally.
> Using this interpretation, there really is no such thing as a truncated
> ballot, just one where the voter votes some candidates equally (or implies
> that she considers some candidates to be equal).  Related to this is a
> question about what constitutes a full, sincere ranking.  For instance,
> consider the following sincere utilities;
> 
> A 100
> B 70
> C 20
> D  1
> E  0
> 
> Is A>B>C>D=E any less of a complete sincere vote than A>B>C>D>E?  Truncation
> will usually only occur when the voter has no strong preference between the

Forest's comment: It's the "usually" in this sentence that bothers me. The
other reason for truncation is strategy, in methods like "Approval
Completed Condorcet"  where the approval cutoff is marked by truncation. 
A low utility CW could be cut off in a zero information election. 

Mike's winning votes SSD makes similar use of truncation in defense
strategies, although the chances of eliminating a true CW would be
infinitesimal because of the Strategy Free Criterion, etc.


> bottom candidates, or not enough information to distinguish them.  As a
> result, they are bunched at the bottom like the preceeding example.
> 
> Craig
> 
>