Geometric mean-based pairwise comparison method with the reference values -- statistical approach
2026-07-10 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors look at a common decision-making method where experts compare options in pairs to decide which is better. Instead of just using the usual math approach with eigenvectors, they use a statistical method involving reference values and geometric means to figure out the priority of each option. This new view helps them understand both how inconsistent the comparisons are and how different the options actually are. They also create simple indicators to measure how good the final rankings are, making it easier to interpret the results.
Pairwise comparisonAnalytic Hierarchy ProcessPrincipal eigenvectorGeometric meanInconsistencyPreference distanceWeight vectorStatistical approachDecision making
Authors
Konrad Kułakowski, Jacek Szybowski
Abstract
For many years, the pairwise comparison method has been widely used for decision-making involving experts. The best-known example of this method is the Analytic Hierarchy Process (AHP). In this now classic approach, the weights of alternatives are calculated using the principal eigenvector of the comparison matrix. In this paper, we present a statistical view of the pairwise comparison method, using reference values and the geometric mean to calculate alternative priorities. Thanks to this approach, we can simultaneously capture both the phenomenon of inconsistency in pairwise comparisons and the preference distance between alternatives. In this paper, we define indicators that measure the quality of the obtained weight vector, which, thanks to the statistical approach, have a clear and intuitive interpretation.