[EM] RP & CSSD pick A,B,C,& D

[MIKE OSSIPOFF]

In the 6 candidate example recently posted, Ranked-Pairs and
BeatpathWinner/CSSD both pick A,B,C,&D.

E doesn't win in RP because the defeat against E isn't in a cycle
and therefore won't be exempt from being kept.

E doesn't win in a BeatpathWinner count because the defeat against
E is also an unreturned beatpath to E.

And E doesn't win in the CSSD or SSD count because E isn't in the
Schwartz set.

In SD, E doesn't win because the defeat against it isn't in a cycle
and therefore can't be dropped.

For the above reasons, with those methods, a candidate can't win
if he has a pairwise defeat against him, but has no pairwise victories.

In that example, PC & Smith//PC choose A,B,C,D,&E.

But in all Condorcet versions, a candidate wins if he has no
pairwise decisions for or against him.

I once said that it seems to me that if there are 2 or more candidates
who have no defeats against them, and some of those have no
pairwise victories, and some have a pairwise victory, then the tie
should consist of the one(s) who have/has a pairwise victory.
Of course that only matters in small comittees, or maybe sometimes in
organizations.

Mike Ossipoff




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