Tiebreakers, Subcycle Rules

[Markus Schulze]

Dear participants,

the Schulze method can be interpreted as a successive
elimination of pairwise defeats.

What is an elimination of a pairwise defeat?
It is obvious, what an elimination of a candidate is. "If a
candidate is eliminated, all ballots are treated as if that
candidate had never stood" (I.D. Hill, "Some Aspects of Elections
- to Fill One Seat or Many," Journal of the Royal Statistical
Society A, vol. 151, part 2, p. 243-275, 1988). To my opinion,
an elimination of a pairwise defeat should be considered, as
if this pairwise defeat is replaced by a pairwise tie. The
disadvantage of this interpretation of an elimination of a
pairwise defeat is the fact, that the Smith set will increase
and not decrease. But this problem can be avoided by using the
Schwartz set instead of the Smith set. Thus, the Schulze method
looks as follows:

Step1: Calculate the Schwartz set among the potential winners
       and eliminate all those candidates, who are not in the
       Schwartz set of the potential winners!

Step2: If there is still more than one potential winner, then
       replace the weakest pairwise defeat (i.e. the pairwise
       defeat with the smallest absolute number of votes for
       the winner of that pairwise comparison) between two
       potential winners with an equality! Pairwise defeats,
       that have already been replaced by an equality, stay
       replaced. Go to Step1!
       Otherwise, if there is only one potential winner, then
       this potential winner wins the election.

But, to my opinion, this interpretation of the Schulze method
as a successive elimination of pairwise defeats doesn't make
this method more simple.

Markus Schulze