[EM] hey Markus, can you confirm something?...

[Kristofer Munsterhjelm]

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.