Neatening GMC

[Mike Ossipoff]

It may have been messy when I named various ways that the Generalized
Majority Criterion could be said, so I should carefully state those
ways & distinguish between them, and say how the methods I propose do
by them:

GMC (overall):

A method, including combined methods such as Smith//Condorcet, 
considered as overall methods, meets GMC (overall) if & only
if it will never elect an alternative that has a majority against
it unless every alternative in the Smith set has a majority against
it.

GMC (non-compound):

A method (e.g. Condorcet's choce rule) that isn't a combined method
like Smith//Condorcet meets GMC (non-compound) if it will never
elect an alternative with a majority against it unless every 
alternative in the set from which it is to choose has a majority
against it. [That set from which it is to choose could, of course,
be the entire set of alternatives, or a selection set, such as the
Smith set].

GMC (CW):

A method, compound or otherwise, meets GMC (CW) if & only if it
will never elect an alternative with a majority against it, provided
that there's a Condorcet winner and order-reversal isn't used on
a scale sufficient to affect the election result.

***

Smith//Condorcet meets GMC (combined) & GMC (CW). The
Condorcet choice rule, whether used as a method in itself, or
as part of a compound method, meets GMC (non-compound).

***

Copeland and Regular Champion don't meet the Generalized Majority
Criterion (not to be confused with the Mutual Majority Criterion
that Bruce calls the Generalized Majority Criterion). They don't
meet any of these 3 versions of that criterion.

***

Mike



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