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

For many years, pairwise comparison methods have been widely used for eliciting preferences and ranking alternatives in decision-making problems. These methods estimate priority weights from a pairwise comparison matrix and are now standard tools in multi-criteria decision analysis. 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.