[EM] A question about Random Pair

[Kristofer Munsterhjelm]

Say we run Random Pair n times for a given election. Furthermore, say 
that the set of candidates that win most often is called GP_n (greatest 
probability in n tries), and say that GP is equal to GP_n as n 
approaches infinity.

What deterministic election method would always elect GP?

Presumably, when some candidate X is the CW, GP consists of X alone. But 
does GP consist of the Smith set when in a cycle? I doubt it, but I'm 
not sure. This is equivalent to a question of whether Random Pair passes 
a (probabilistic) version of Smith.