[EM] Condorcet cyclic drop rule
LAYTON Craig
Craig.LAYTON at add.nsw.gov.au
Tue Mar 27 16:38:29 PST 2001
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.
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