[EM] Smith//PC , GSFC, & SDSC

[Markus Schulze]

Dear Mike,

you wrote (6 Oct 2000):
> I'm not sure just which situation you mean. Your statement is probably
> the result of my typo in which I said "sincere Smith set" above,
> when I meant "voted Smith set".
>
> If you doubt that Tideman meets GSFC & SDSC, then I assure you that
> Tideman(wv) meets those 2 criteria, and all of the majority defensive
> strategy criteria. I admit that Tideman(m) meets none of those criteria.
> I don't propose Tideman(m).
>
> Any  BC complying method meets SDSC because the members of that
> majority can make B have a majority defeat (by ranking A over B) and
> can make sure that B won't have a majority defeat (by not ranking B).
> Since B beats no one by majority, then his majority defeat can't be
> the weakest defeat in a cycle.
>
> 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?

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de