[EM] Beatpath winner

[Andrew Myers]

On Wed, Oct 15, 2003 at 03:51:37PM -0400, Eric Gorr wrote:
> At 3:16 PM -0400 10/15/03, Andrew Myers wrote:
> >In Condorcet elections with the beatpath winner criterion, the
> >computation of the beatpath winner involves finding the strongest
> >beatpath connecting two candidates. To compute this one can run the
> >Floyd-Warshall algorithm on the vote matrix, but with the matrix
> >entries corresponding to a loss zeroed out. This zeroing out seems hard
> >to justify in some ways and I'd like to understand why it's really
> >necessary.
> 
> Do you understand that the Beatpath winner method is attempting to 
> find the alternative that will pairwise beat every other alternative?
> 
> 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".

> You are describing a very close contest. I would imagine that under 
> every voting system where the result was very close, your statement 
> would be true. As such, it does not seem particularly relevant.

You seem to be saying that the alternative definition of beatpaths is
just as good, because it only changes the outcome in close elections.
If that's really true I'd argue that the alternative definition is
actually better because it is computationally simpler. But I suspect not
everyone would agree that this definition of beatpaths is acceptable.

-- Andrew