[EM] monotonic order of the Landau set

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[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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