[EM] two bit ratings

[Craig Layton]

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

Craig