> > Any BC complying method meets GSFC, because, since B is majority-beaten
> > from the sincere Smith set (this time I mean sincere Smith set), and,
> > since no one falsifies a preference, it's impossible for any member
> > of the sincere Smith set to have a majority defeat from outside that
> > set. That means that there can't be a majority beatpath from B to the
> > sincere Smith set candidate who beats B. That means that B's defeat
> > from the sincere Smith set can't be the weakest defeat in a cycle.
>
>Which properties are necessary and sufficient for an example for being
>an example showing that a given election method violates GSFC? Which
>properties are necessary and sufficient for an example for being an
>example showing that a given election method violates SDSC?
Again, I'm not quite sure what you're asking. I've demonstrated that
Tideman(wv) meets GSFC & SDSC, and that Smith//PC doesn't. Any examples
that comply with the example outlines that I posted for Smith//PC
will be sufficient to show that Smith//PC fails GSFC & SDSC.
In general, any example that complies with the premise of a
criterion, and in which the method being tested doesn't meet the
requirement of the criterion will be sufficient to show that that
method fails the criterion. Also, such an example is necessary to show
that. In fact, that's what it takes to show that any method fails
any criterion. For more detail, I refer you to the definitions of
the criteria.
Speaking of necessary & suffient conditions, BC compliance is a
sufficient condition for compliance with all 4 of the majority
defensive strategy, for the reasons that I've stated. (Of course
any method that meets GSFC meets SFC, and any method that meets
SDSC meets WDSC).
Mike Ossipoff
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