Geometric mean-based pairwise comparison method with the reference values -- statistical approach

2026/07/30 by Konrad Kułakowski, Kamil Pustelnik, Jacek Szybowski
Mathematics · Computer Science · #stat.ME #cs.AI #math.ST #stat.TH

paper · pdf

31 pages

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

For many years, the decision-making method based on pairwise comparison of alternatives has been frequently and readily used for decision-making with the participation of 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 the phenomenon of inconsistency in pairwise comparisons and the preference distance between different alternatives. In this paper, we define indicators that measure the quality of the obtained weight vector, which, thanks to the statistical approach, have an understandable interpretation.

Citations

• Mean-based incomplete pairwise comparisons method with the reference values
• Managing Null Entries in Pairwise Comparisons
• A scaling method for priorities in hierarchical structures

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• Mean-based incomplete pairwise comparisons method with the reference values
• Some Notes on the Similarity of Priority Vectors Derived by the Eigenvalue Method and the Geometric Mean Method
• Geometric mean method for judgement matrices: Formulas for errors
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• On the Convergence of the Pairwise Comparisons Inconsistency Reduction Process