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

[MIKE OSSIPOFF]

Markus quoted me:

> > Why doesn't that work when A is replaced with {A1,A2,A3}? Because
> > they're in a cycle of majority defeats. Their majority defeats could
> > be greater than that of B. B's majority defeat could be weaker than
> > any other defeat in the election, and B could win by having the weakest
> > maximum defeat.
> >
> > Of course if B is in the sincere Smith set,

Sorry--I meant "the voted Smith set".

> > qualifying him to win
> > if his greatest defeat is the least among that set, then A1, A2, &
> > A3 are also in the sincere Smith set, since they beat B.

Again, I meant "voted Smith set".

>
>But this situation is also possible under the Tideman method.

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.

Tideman(wv) meets BC. Tideman(wv) can be reworded:

Drop the strongest defeat that's the weakest defeat in a cycle.
Repeat till there are no cycles.

[end of definition]

Obviously no defeat can be dropped unless it's the weakest defeat in
a cycle.

The above Tideman wording is the one that demonstrates BC compliance,
and it's probably the briefest one too. But the definition at

http://www.electionmethods.org

...is more obviously & naturally motivated.

Mike Ossipoff




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

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