[EM] new revised ranked pair method in matrix form

Ross Hyman rahyman at sbcglobal.net
Tue Nov 29 06:49:03 PST 2011


Refinement: Don't determine winner until the end.

C_i is the ith candidate.  Initially M is the Identity matrix of size equal to the number of candidates. 

The pairs are ranked in order.  Affirm each group of equally ranked pairs in order, from highest to lowest.   To Affirm a group of equally ranked pairs create the matrix D where D_ij  = 1 for each C_i >C_j that is to be affirmed at this rank.  D_ij=0 otherwise.  Replace the old M matrix with the new one: M + MDM.

After all groups have been affirmed, form the matrix W = M - M^T where M^T is the transpose of M.

The winner is the C_b such that no W_ab is positive.







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