The analytic hierarchy process: Does adjusting a pairwise comparison matrix to improve the consistency ratio help?

• Published in: Computers & operations research 1997-08, Vol.24 (8), p.749-755
• Main Authors: Finan, J.S., Hurley, W.J.
• Format: Article
• Language: English
• Subjects: Applied sciences; Comparative analysis; Decision analysis; Decision making; Decision theory. Utility theory; Exact sciences and technology; Hierarchies; Monte Carlo simulation; Operational research and scientific management; Operational research. Management science; Studies
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/S0305-0548(96)00090-1

Consider an AHP decision-maker who is uncertain about his or her preferences. In fact, suppose he or she is only able to specify unbiased estimates of these preferences. Then given the decision-maker's final pairwise comparison matrix having a consistency ratio less than 0.10, is it possible for the reliability of the analysis to be improved by using some artificial means to lower the consistency ratio (i.e. a minimum perturbation of pairwise comparison matrix elements which reduces the consistency ratio by a given amount)? In this paper we argue that the answer to this question is yes. To make our point, we employ a Monte Carlo simulation of a decision-maker who picks random judgments out of a distribution centered at his or her true judgment. The simulation results suggest that, if the final consistency ratio is less than 0.10, additional artificial manipulation to lower the consistency ratio will improve, on average, the reliability of the analysis.