[EM] Tideman and GMC

[Blake Cretney]

David Catchpole wrote:

> 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...

> 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

Consider the following example

40 A B C D
35 C D A B
25 D B A C

Resulting majorities are, using -> to denote a simple pairwise
majority

A->B 75-25
A->C 65-35
B->C 65-35
C->D 75-25
D->A 60-40
D->B 60-40

There is a path from A to B, via A->B
There is a path from B to A, via B->C, C->D, D->A
However, there is no candidate X, s.t. B->X, X->A

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Blake Cretney