Evaluating scales for pairwise comparisons

Abstract

Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision-making methods. The evaluation is very often done linguistically. Several scales have been proposed to translate the linguistic evaluation into a quantitative evaluation. In this paper, we perform an experiment to investigate, under our methodological choices, which type of scale provides the best matching of the decision-maker’s verbal representation. The experiment aims to evaluate the suitability of eight evaluation scales for problems of different sizes. We find that the inverse linear scale provides the best matching verbal representation whenever the objective data are measured by means of pairwise comparisons matrices and a suitable distance between matrices is applied for computing the matching error.