pairwise matrices and ballots
DEMOREP1 at aol.com
DEMOREP1 at aol.com
Thu Feb 24 23:00:53 PST 2000
MIKE OSSIPOFF wrote:
> Blake wrote:
>
> >Often people want to create examples involving pairwise methods,
> >usually to show that the method behaves badly in some situation.
> >Since not all pairwise matrices are possible, it is customary to
> >provide a set of ballots instead of just providing a pairwise matrix.
>
> For any pairwise preference matrix, it's possible to devise
> a set of rankings that will give that pairwise preference matrix.
> So, for pairwise methods, it's unnecessary to furnish rankings
> for an example--the pairwise preference table is sufficient.
I don't know where you got that idea. Try the following example:
A B C
A X 1 3
B 2 X 1
C 1 3 X
----
The matrix produces
2 BA(C) and/or B > (A=C)
1 AB(C) and/or A > (B=C)
3 AC(B) and/or A > (C=B)
1 CA(B) and/or C > (A=B)
3 CB(A) and/or C > (B=A)
1 BC(A) and/or B > (C=A)
The possibility of truncated votes makes producing a matrix before having
actual or example votes very difficult or impossible. Roughly like taking a
photo of a chess board after X moves and trying to go backward to get the
exact order of the moves.
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