[EM] Tideman and GMC

[David Catchpole]

On Sun, 30 Jan 2000, Markus Schulze wrote:

> The exact mathematical formulation of beat path GMC looks as follows:
> 
>    "X >> Y" means that an absolute majority of the voters
>    strictly prefers candidate X to candidate Y.
>    "There is a majority beat path from X to Y" means that
>    (1) X >> Y or 
>    (2) there is a set of candidates C[1],...,C[n] with
>        X >> C[1] >> ... >> C[n] >> Y.
> 
>    If there is a majority beat path from candidate A to
>    candidate B and no majority beat path from candidate B
>    to candidate A, then candidate B must not be elected.

Can someone refresh my memory- where a candidate A has a majority beat
path to candidate B and B has a majority beat path to A, does this imply,
or not imply, that a candidate C exists such that A>>B, B>>C, C>>A or
B>>A, A>>C, C>>A? I suspect it does, but I may be wrong...