Studying a set of properties of inconsistency indices for pairwise comparisons

TL;DR

This paper examines properties of inconsistency indices in pairwise comparisons, proposing a new property, analyzing existing indices against these properties, and adjusting one index to meet all criteria.

Contribution

It introduces an additional property for inconsistency indices and evaluates existing indices, modifying one to satisfy all properties.

Findings

Two of four indices fail some properties in current form.

An adjusted index is proposed that satisfies all properties.

The study enhances the theoretical framework for inconsistency measurement.

Abstract

Pairwise comparisons between alternatives are a well-established tool to decompose decision problems into smaller and more easily tractable sub-problems. However, due to our limited rationality, the subjective preferences expressed by decision makers over pairs of alternatives can hardly ever be consistent. Therefore, several inconsistency indices have been proposed in the literature to quantify the extent of the deviation from complete consistency. Only recently, a set of properties has been proposed to define a family of functions representing inconsistency indices. The scope of this paper is twofold. Firstly, it expands the set of properties by adding and justifying a new one. Secondly, it continues the study of inconsistency indices to check whether or not they satisfy the above mentioned properties. Out of the four indices considered in this paper, in its present form, two fail to satisfy some properties. An adjusted version of one index is proposed so that it fulfills them.