[EM] Majority winner set

MIKE OSSIPOFF nkklrp at hotmail.com
Sun Nov 19 19:50:47 PST 2000

How do that method's properties compare to the Condorcet versions
that we've been discussing: PC, Tideman(wv), SSD, Smith//PC?

One concern is that successive elimination methods are sometimes
nonmonotonic. That would have to be checked out.

In the 3-candidate truncation example, where B is SCW, and the A
voters truncate against B, so that A beats C beats B beats A,
and B majority beats A, and the B voters vote A over C, the elimination
of C, who majority beats no one, leaves B beating A, so B wins.
So, at first glance, SFC isn't violated in that 3-candidate example.
With other situations & other criteria, I don't know.

In the 3-candidate example where A voters order-reverse against
the SCW, B, with a majority voting B over A, and the B voters
refusing to vote a 2nd choice, A can't have a majority against
anyone. But suppose there were subcycle, A1, A2, & A3, all
majority-beating eachother? Your method wouldn't eliminate them then.
PC would come to the rescue. But then why not just use PC or one
of the other Condorcet versions in the 1st place, instead of adding
the extra step.

This is just quick initial impressions.

I feel that it would have to be shown that the proposed method
meets the LO2E-related criteria that Condorcet does, and offers
something more. But it would certainly have to be monotonic. The
successive elimination character of it creates doubts about its
monotonicity, and so monotonicity would have to be demonstrated to
avoid that concern.

Mike Ossipoff

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