[EM] minmax

[MIKE OSSIPOFF]

Markus--

Thanks for posting Fishburn's 1977 definition of minmax. It's becoming 
obvious that minmax is undefined unless every ranking ranks all of the 
candidates.

As for the name "Condorcet's method", Condorcet's own description of his 
drop-weakest proposal takes precedece over Fishburn's definition. 
Condorcet's drop-weakest proposal was PC.

Kevin said:

When this rule is used even with partial rankings, this is what I call
"MinMax (pairwise opposition)" or "MMPO." It fails Condorcet, but not too
badly, I'd say. An advantage of this method is that it satisfies 
Later-no-harm:
Adding lower preferences to a ranking can't harm any higher preferences.
For that reason I think it's a good three-candidate method. (The MinMax 
clone
problem kicks in beyond three candidates.)

I reply:

Well, the people who have already defined minmax (including Nalebuff, Levin, 
and Fishburn) have given us only definitions that don't apply when there are 
truncated ballots. So can you really call the above-quoted method "minmax"? 
Even if you say that minmax means something when there are truncated 
ballots, that doesn't mean that we can say _what_ it means with truncated 
ballots, because those who give us our definition of minmax won't say.

But, aside from that, if we accept that the above is minmax with truncation, 
then, Kevin must agree that minmax isn't PC, since PC meets Condorcet's 
Criterion.

Mike Ossipoff

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