[EM] An odd case for Ranked-Pairs
ericgorr at cox.net
Tue Jan 14 10:40:11 PST 2003
This example was recently brought to my attention. Consider:
The pairwise matrix is:
0 4 4 2 3 4
2 0 4 3 4 5
2 2 0 4 3 4
4 3 2 0 3 2
3 2 3 3 0 3
2 1 2 4 3 0
Now, with Ranked-Pairs, the only kept-defeat will be B:F.
However, once all of the defeats have been considered, there will be
no kept-defeats for <someone>:E, which allows E to participate in a
tie (according to my computations).
Now, the problem with this appears to be that E also does not have
any pairwise-victories, which would seem to indicate that it should
not have the opportunity to be selected as the victor.
Now, it would seem to me that, in the case of a tie, I should verify
that each option in the tie did have at least one pairwise-victory
and if they did not, eliminate them from the tie.
Would anyone else agree or have I made a mistake in here somewhere?
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