[EM] The RP example, winnner doesn't beat anyone.
nkklrp at hotmail.com
Tue Jan 14 19:49:17 PST 2003
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?
RP can choose a winner that isn't a member of the initial Schwartz set,
and that's somewhat unaesthetic. But doing so doesn't cause any
problems of the kind that I'm trying to get rid of.
I should add that, though RP can choose outside the initial Schwartz
set, it never chooses outside the Smith set, the smallest set of
candidates such that every candidate in the set beats everyone outside
A remedy to keep victory in the Schwartz set would be to add that
requirement to a method's definition, so that RP could be used
to choose from among the Schwartz set.
Myself, I don't consider it a real problem when RP chooses outside
the Schwartz set, and so I wouldn't complicate the definition by
adding that requirement, unless people object about non-Schwartz-set
It takes time to do a 5-candidate example, so I'll have to comment
more tomorrow instead of tonight on other aspects of the example.
Someone pointed out that it takes pairwise ties to make RP choose
outside the Schwartz set. Those are vanishingly unlikely in public
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