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

[Markus Schulze]

Dear Mike,

you wrote (6 Oct 2000):
> GSFC:
>
> 5 candidates: A1,A2,A3,B, & C.
> 
> A1,A2, & A3 are in a cycle of majority defeats, and they're the
> sincere Smith set. A majority prefers a member of {A1,A2,A3) to B,
> and no one falisifes a preference.
> 
> Now, if, instead of {A1,A2,A3}, we just had a 1-candidate sincere
> Smith set, A, then Smith//PC would pass the criterion in that example.
> Because A can't have a majority defeat, since he's SCW and no
> one falsifies a preference. Since B has a majority defeat, and
> A doesn't, then A can't win. Of course if B is in the voted Smith
> set, then so must A be, since A beats B.
> 
> 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, 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.

But this situation is also possible under the Tideman method.

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