[EM] Condorcet cyclic drop rule

[MIKE OSSIPOFF]

>I've been curious about the Condorcet drop rule with cycles. Previously 
>I've
>just computed a pair win table but not implemented rules to handle cycles.
>
>At: http://russp.org/ElectionMethods.org/CondorcetEx.htm
>****
>* Plain Condorcet (PC)
>* The Plain Condorcet method of ambiguity resolution is the
>* simplest method: drop the weakest (smallest magnitude)
>* defeat, repeating if necessary until one of the candidates
>* is unbeaten.
>****
>
>It seems like there are two ways to define weakest defeat:
>1. The defeat with the smallest difference.
>2. The defeat with the smallest ratio (closest to one).

There are at least 2 additional ways:

3. Defeat support (number of voters voting for that defeat)
4. Defeat opposition (number of voters voting against that defeat).

Markus, Steve Eppley, Norm Petry, Rob Lanphier & I all prefer
defeat support as the measure of a defeat's strength.

That's largely because that measure of defeat strength confers some
important strategy criterion compliances.

It's also because defeat support is what is important tothe 
lesser-of-2-evils voter. He's willing to do whatetever it takes to reliably
& effectively vote against his greater evil.

It's also because it's the measure that minimizes the number of
overruled voters. A voter is overruled if he's voted for one of the
winner's defeats (doubly overruled if he's voted for 2 of the winner's
defeats, etc).

Defeat Support is what Condorcet himself specified. Norm & Markus
posted quotations about that. They're in the archives for last year.

Now, if we didn't care about overruled voters, lesser-of-2-evils
problem, etc., then margins would be good. Margins is better than
ratio. Margins combines ratio & turnout. Two defeats have the same
ratio but one has a bigger turnout. The bigger turnout gives that
defeat more validity, and that defeat has a bigger margin.

Mike Ossipoff

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