[EM] Condorcet cyclic drop rule

[LAYTON Craig]

Tom wrote:

>However if some voters bullet vote:
>Example ballots: AC=3, A=2, BA=4, CB=3
>
>Pair elections:
>A:B=5:7 - diff=2, ratio=1.4
>B:C=4:6 - diff=2, ratio=1.5
>A:C=9:3 - diff=6, ratio=3
>
>Which is the weakest defeat? (With some work I could come up with a case
>that the difference and ratio pick different defeats, but a tied difference
>is still interesting.)
>
>I would judge the weakest defeat as the one in the election with more
voters
>participating. Therefore the 5:7 defeat is "weaker" than the 4:6 defeat.
>
>Do these examples look correct? Might weakest ratio be a better criterion
>than weakest difference?

Some people interpret the weakest defeat to be the one in which the smallest
number of voters voted for the winning candidate.  By this definition, the
4:6 defeat is weaker.  The rationale is that you are overruling less voters
when you ignore this result.

However, I'm not sure I agree with this.  How should we interpret tied
preferences (eg A=B>C>D=E)?  There is one view (with which I'm inclined to
agree) that gives each candidate in a pairwise tie 0.5 votes.  Truncating
your vote is the same as tieing all of the unranked candidates - the
previous example should be equivalent to A=B>C.  If you count the ballots in
this fashion, all of the ways to interpret pairwise defeats are equivalent -
ratios, winning votes, margins.