[EM] Beatpath for dummies

[Roy]

I haven't seen a description of beatpath that is really easy to 
visualize, so I pondered the concept a while and came up with my 
own version. It's very similar to the Dodgson-like method I describe 
in my last post (RE Don't ignore the margins), except instead of 
eliminating by row or column total, margin entries are eliminated in
order of increasing size.

This elimination method is at least in the spirit of beatpath, and may
be functionally equivalent to it, apart from my use of run-offs.

Start with a matrix of winning margins. Eliminate Condorcet winners
and losers until none are left. Winners accumulate in top-to-bottom
ranking order; losers accumulate separately, bottom-to-top.

Keep a copy of the original matrix to use in run-offs (below).

Eliminate all occurrences of the smallest margin from the working
matrix. This eliminates the weakest paths: candidates who do not win
any contests by a larger margin are beatpath losers, because there are
no paths from them to anywhere else that are stronger than that
margin. Similarly, those who do not lose any contest by a larger
margin are beatpath winners. During this step, if you like, you can
say, "You are the weakest link. G'bye!"

Collect any losers (those with no remaining victories) and, if there
are more than one, conduct a run-off among them, using numbers from
the original matrix, to determine the order in which they will be
added to the losers. Collect any winners and do likewise. Remove
winners and losers from the working matrix.

Repeat Elimination and Collection until the working matrix is empty.