[EM] two bit ratings
Craig Layton
craigl at froggy.com.au
Fri Sep 21 00:15:00 PDT 2001
>> 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
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