A note on deriving weights from pairwise comparison ratio matrices

This paper addresses the Cook and Kress method regarding the use of mathematical programming to derive weights from pairwise comparison ratio matrices. It notes that the Cook and Kress formulation has the shortcoming that alternative optimal solutions may occur, which would lead to an infinite set of possible weights. This paper proposes to resolve the problem by formulating a Phase II optimization procedure to be solved using quadratic programming. This mathematical formulation is based on the determination of a weight vector that is statistically most likely to cause the associated pairwise comparison matrix. It is concluded that the Cook and Kress method accompanied with the proposed Phase II approach can always derive a unique set of weights from a pairwise comparison matrix.