Consistency adjustments for pairwise comparison matrices

This paper is concerned with the development of a ‘best’ rank one transitive approximation to a general paired comparison matrix in a least-squares sense. A direct attack on the non-linear problem is frequently replaced by a sub-optimal linear problem and, here, the best procedure of this kind is obtained. The Newton–Kantorovich method for the solution of the non-linear problem is also studied, including the role of the best linear approximation as a starting point for this method. Numerical examples are included. Copyright © 2002 John Wiley & Sons, Ltd.