If all you care about are margins, then you can build up the pairwise array
from atomic pairs of voters.
For example, I consider ABCD and DCAB to be an atom for AB because all
other pairwise races cancel out, yielding the following margins matrix:
| A | B | C | D |
===+=+=+=+=+
A | 0 | +2 | 0 | 0 |
---+-+-+-+-+
B | -2 | 0 | 0 | 0 |
---+-+-+-+-+
C | 0 | 0 | 0 | 0 |
---+-+-+-+-+
D | 0 | 0 | 0 | 0 |
---+-+-+-+-+
But I don't know how this fits in with the way you calculate approval.
~ Andy Jennings
On Mon, Oct 10, 2011 at 2:51 PM, Ted Stern araucaria.arauc...@gmail.comwrote:
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
--
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