[EM] requesing help in converting pairwise matrix into preference rankings
Markus Schulze
markus.schulze at alumni.tu-berlin.de
Thu Sep 18 00:36:01 PDT 2003
Dear James Green-Armytage,
let's say that there are 4 candidates.
When you add a ballot and its inverted ballot then
each entry of the pairwise matrix is increased by 1.
Let's say that you want to increase the entry B:E.
Then you can simply add a ballot where B and E are
ranked in an adjacent manner and its inverted ballot.
When you then switch the positions of B and E in the
inverted ballot, then the entry B:E is increased by 2,
the entry E:B is increased by 0, and every other entry
is increased by 1.
Example:
Suppose you want to increase the entry B:E without
changing the other entries relatively to each other.
When you add the ballots B>E>A>D and D>A>E>B then
each entry is increased by 1. Therefore, when you
add B>E>A>D and D>A>B>E then you increase the
strength of the pairwise defeat B:E without changing
the strengths of the other pairwise defeats relatively
to each other.
With this method, it is possible to create successively
any matrix of pairwise defeats (as long as you are
interested only in the directions and the margins of
the pairwise defeats). This method has been proposed by
Blake Cretney a few years ago.
Markus Schulze
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