Simmons, Forest simmonfo at up.edu
Wed Nov 2 13:47:50 PST 2005

Mike asked if Recursive Least Pairwise Opposition from Second Place Alternatives has good properties.
I'm afraid that it fails monotonicity.
However, I have an idea for another similar method that would build in Immunity from Second Place Complaints, but I need some suggestions.
Here's the still unfinished method:
1. For each alternative (i.e. candidate) X let X' denote the candidate that would (by the finished method applied recursively)win the election if alternative X were withdrawn from consideration.
2. For each alternative X, if X is beaten pairwise by X', disqualify X.
3. If some (but not all) alternatives are disqualified, then apply
    (method ??, the same method recursively???)
to determine the winner from among the undisqualified alternatives.
4. If all alternatives are disqualified, then ????
5. If no alternative is disqualified, then ?????
How should we settle the questions in steps 3, 4, and 5?
In particular, it would be nice if it were never the case that all alternatives were disqualified.  Then the method would satisfy Immunity >From Second Place Complaints, and we wouldn't have to wonder what to do in step 4.
I hope that somebody finds this idea interesting enough to try various ways of completing the method.
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