# [EM] Question about Schulze beatpath method

Ross Hyman rahyman at sbcglobal.net
Thu Feb 16 05:02:13 PST 2012

```If one removed all pairwise defeats that contradict the Schulze beathpath order and then constructed a new beatpath order from the reduced set of defeats, would the new beatpath order always be consistent with (although not necessarily the same as) the previous beatpath order?  Could this method, repeatedly applied, be used to construct a monotonic and clone proof strict linear ordering if the original beatpath order produced a partial linear ordering?
Example: If the defeat order is
A>B, A>C
B>D, C>D
D>A
B>C
E>D
A>E
B>E
C>E
The beatpath ordering is:  E>A>(B,C)>D.  This is a partial order since the order of B and C is not completely specified by beatpath.  Removing all defeats that are not consistent with the partial beatpath order produces:
A>B, A>C
B>D, C>D
B>C
E>D
The beatpath order derived from these defeats is: ((A>B>C),E)>D
The two partial orderings E>A>(B,C)>D and ((A>B>C),E)>D are consistent and together produce the linear ordering E>A>B>C>D.

```