[EM] monotonic order of the Landau set

[Forest Simmons]

Sorry, something hijacked the text editor and sent the cursor on a rampage
with a mind of it's own

So let's try that again:

As in River we start by locking in certain defeats.  As in River no
candidate needs to be defeated more than once to be excluded from the
winner's circle.  Also as in River we lock in the strongest defeats first.
We consider all defeats by cover to be stronger than defeats that are not
part of the covering relation.  If a candidate is covered by two or more
(other) we consider the defeating candidate with the greatest approval to
have the strongest defeat.

So ballots must must allow us to infer both pairwise defeats and an
approval order.  [Any other monotonicically generated order of the
candidates may be substituted for approval if so desired.]

1.  For each covered candidate X, find the highest approval candidate Y
that defeats X, and lock in this defeat Y>X.

2.  We now have a partial river structure of several components, each of
which drains into an uncovered candidate.  Instead of completing the river
drainage system by locking in other (weaker) defeats, we define an order on
these uncovered candidates.  Think of these uncovered candidates as mouths
of rivers entering into a universal ocean.

3. Each river mouth (uncovered candidate) receives a score, namely the
highest approval of any candidate in any of its tributaries.

4. Order these uncovered candidates in the order of their respective scores.

5. What does montone mean in this context?  If one of the uncovered
candidates is elevated in approval or by pairwise defeat over another
uncovered candidate with lower score, than when the new order is found, the
first candidate will still be higher in the new order than the second
candidate.
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