[EM] Tideman and GMC

[David Catchpole]

Woops! Obviously, not. The condition of an absolute majority strengthens
the relation >> so that this may not be the case, especially given a
significant number of voters who are disinterested between some
candidates.

However, it is true to say that where >> represented "...a
simple majority or a tie..." and "majority beat path" were redefined
accordingly, the statement below would be true. Consider a vote-cycle

A>>B>>C>>D>>E>>A . In order for D-E-A not to constitute a vote-cycle in
itself,

A>>B>>C>>D>>A. Similarly,
A>>B>>C>>A. So there's a demonstration.

On Sun, 30 Jan 2000, David Catchpole wrote:
> 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...
> 
> 

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