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.
