Dear Norman,
the aim of this e-mail is to prove, that Schulze wins
cannot be cyclic. It is sufficient to prove that if
Candidate A defeats candidate B via beat-paths and
candidate B defeats candidate C via beat-paths, then
candidate A defeats candidate C via beat-paths.
**
First:
Dear Blake,
you wrote (28 Aug 1998):
I suggest that the way to judge the randomness of a method should
be by outcome. If given a certain example, method X has
5 possible outcomes, while method Y has only 3, I would conclude that
in that case at least, X has behaved more randomly.
The
Dear Markus,
Thank-you for providing a proof of the impossibility of 3-candidate cycles
in a beat-path matrix.
This result is interesting, because it suggests that if your proof could be
generalised to apply to cycles of any size, this would greatly simplify the
calculation of the Schwartz-set
