[EM] Beatpath winner

[Kevin Venzke]

Andrew,

 --- Andrew Myers <andru at cs.cornell.edu> a écrit : 
> On Wed, Oct 15, 2003 at 03:51:37PM -0400, Eric Gorr wrote:
> > Do you agree that if an alternative does pairwise beat every other 
> > alternative that it should win?
> 
> Understood and agreed. But both of those conditions are still met if we
> allow beatpaths to go "backwards" along links with the strength of the
> losing votes.  It comes down to the definition of what a beatpath is,
> and it seems that either way of doing things will resolve the cycles in
> the graph.  I'm wondering if there is a simple argument that the usual
> definition is "right".

It looks like Rob provided a simple argument:

2 B>C>A
3 A>BC
3 AB>C
3 C>AB

Although A beats all, if a beatpath can use losing paths, B's beatpath to A
is stronger than A's to B.

Specifically, A has paths 2 to B and 6 to C, and C's path to B is also 2.
B beats C with 5 votes, and can crawl up the A>C path which is still strength
5.

Thus we cut the losing paths to ensure that a beats-all candidate will win.

Kevin Venzke
stepjak at yahoo.fr


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