Aggregation of direct and indirect judgments in pairwise comparison matrices with a re-examination of the criticisms by Bana e Costa and Vansnick

In a recent paper by Bana e Costa and Vansnick [C.A. Bana e Costa, J.C. Vansnick, A critical analysis of the eigenvalue method used to derive priorities in AHP, European Journal of Operational Research 187 (3) (2008) 1422–1428], analytic hierarchy process (AHP), particularly its eigenvector method (EM) used for deriving priorities from pairwise comparison matrices, was criticized for the violation of a so-called condition of order preservation (COP). Due to this violation, the EM was considered to have a serious fundamental weakness which makes the use of AHP as a decision support tool very problematic. The consistency ratio (CR) index in the AHP was also criticized for its failure to act as an alert of this violation of COP. In this paper, we look into decision makers’ overall judgments which can be obtained through the aggregation of their direct and indirect judgments and then re-examine Bana e Costa and Vansnick’s numerical examples with a detailed analysis to show the invalidity of their criticisms.