[EM] Help requested: rankings corresponding to pairwise array

[Ted Stern]

Hi,

Say I have a pairwise array that looks like

   |  A  |  B  |  C  |  D  |
===+=====+=====+=====+=====+
 A |  60 |  45 |  46 |  60 |
---+-----+-----+-----+-----+ 
 B |  55 |  55 |  55 |  49 |
---+-----+-----+-----+-----+ 
 C |  54 |  45 |  54 |  52 |
---+-----+-----+-----+-----+ 
 D |  40 |  51 |  48 |  51 |
---+-----+-----+-----+-----+ 

For this example, I assume that a tie between candidates is counted as
one vote for each candidate, and the diagonal entry is equal to the
maximum non-diagonal entry on that row.  This is a way to extract
Approval from the pairwise array.

The exact numbers are not important.  What really matters to me is
that the candidates in descending order of approval are A, B, C, D,
and the pairwise outcomes look like

   |  A  |  B  |  C  |  D  |
===+=====+=====+=====+=====+
 A |  -  |  L  |  L  |  W  |
---+-----+-----+-----+-----+ 
 B |  W  |  -  |  W  |  L  |
---+-----+-----+-----+-----+ 
 C |  W  |  L  |  -  |  W  |
---+-----+-----+-----+-----+ 
 D |  L  |  W  |  L  |  -  |
---+-----+-----+-----+-----+

The reason I'm looking for a set of ranked ballots that lead to this
outcome is that I believe it might be a counterexample to Forest
Simmons' Enhanced DMC proposal.

If there is a set of rankings that lead to this array, then B would be
the winner under Schulze, Ranked Pairs, River and DMC, but Enhanced
DMC would pick either A or C.

Ted
-- 
araucaria dot araucana at gmail dot com