robert bristow-johnson wrote:
In a Condorcet election in which a cycle occurs, if there are only three
candidates in the Smith set, or even if there are more but the defeat
path is a simple single loop, is the outcome of the election any
different if decided by Schulze rules than if decided by Tideman ruules
(Ranked Pairs)?
Of course, this question is open for anyone to answer.
AFAIK, if there are three candidates in a cycle, RP and Schulze returns
the same: they break the cycle by its weakest defeat. This is obvious
for RP, because the weakest defeat (least victory) gets sorted last. For
Schulze, consider the Schwartz set implementation (CSSD) as described on
http://en.wikipedia.org/wiki/Schulze_method#The_Schwartz_set_heuristic .
Since there's a cycle and all three candidates are involved in it, steps
one and two can't be done, so 3 is done, which also discards the weakest
defeat.
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