[EM] The Unique Winning Alliance method

[Markus Schulze]

Dear Rob,

I see the following problem with the Nash Set:

   Situation 1: A > B, A > D, B > C, C > A, D > B, D > C.
   The Nash Set is ACD.

   Situation 2: Some voters rank candidate C higher so
   that "D > C" is changed to "C > D". Now, the Nash Set
   is ABC.

In so far as I haven't made any presumptions about the
strengths of the pairwise defeats, it is (at least for
all those election methods X that are not identical to
RandomCandidate in the circular 3-candidate case A>B>C>A)
trivial to create an example where Nash//X chooses
candidate C in situation 1 and doesn't choose candidate C
in situation 2 resp. where Nash//X decreases the winning
probability of candidate C from situation 1 to situation 2
so that Nash//X violates monotonicity.

Do you agree with my conclusions?

Markus Schulze