Studying a set of properties of inconsistency indices for pairwise comparisons
This work addresses the need for reliable inconsistency measures in decision-making processes, but it is incremental as it builds on existing properties and indices.
The paper tackles the problem of quantifying inconsistency in pairwise comparisons by expanding a set of defining properties for inconsistency indices and testing existing indices against them, finding that two out of four indices fail some properties and proposing an adjusted version for one.
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.