[EM] Sequential dropping towards a spanning tree - another immune method related to ranked pairs and river

[Markus Schulze]

Dear Jobst,

you wrote (17 May 2004):
> That seems to be right indeed -- I should have realized this
> myself. At least the winners are identical since (a) whenever
> the defeat under consideration is in the current Schwartz set,
> there is also a beatpath in the other direction, hence the
> defeat can be dropped without destroying the last contained
> spanning tree, and (b) whenever the defeat under consideration
> is not in the current Schwartz set, its removeal doesn't change
> the Schwartz set...
>
> So -- was the characterization of the beatpath winner as the root
> of the spanning tree with lexicographically maximal increasing
> weight sequence known already -- if so, I apologize :-)

Well, the spanning tree heuristic for the beatpath method is very
interesting because --like for the river method-- the leaves of the
arborescence represent candidates who can be eliminated without
changing the winner and the branches represent sets of candidates
who can be eliminated without changing the winner. Therefore, you
only have to use a property XYZ that is sufficient for being a
leaf of this arborescence and immediately you can formulate an
"independence from candidates with property XYZ" criterion. Hahaha.

Markus Schulze