Axiomatic properties of inconsistency indices for pairwise comparisons

TL;DR

This paper introduces five axioms to evaluate inconsistency indices in pairwise comparisons, analyzing existing indices against these criteria to determine their suitability for reliable decision-making.

Contribution

It proposes axiomatic properties for inconsistency indices and assesses existing measures, highlighting which are appropriate for evaluating preferences.

Findings

Some indices satisfy all axioms, indicating reliability.

Others fail to meet the axioms, questioning their validity.

The axioms help distinguish suitable inconsistency measures.

Abstract

Pairwise comparisons are a well-known method for the representation of the subjective preferences of a decision maker. Evaluating their inconsistency has been a widely studied and discussed topic and several indices have been proposed in the literature to perform this task. Since an acceptable level of consistency is closely related with the reliability of preferences, a suitable choice of an inconsistency index is a crucial phase in decision making processes. The use of different methods for measuring consistency must be carefully evaluated, as it can affect the decision outcome in practical applications. In this paper, we present five axioms aimed at characterizing inconsistency indices. In addition, we prove that some of the indices proposed in the literature satisfy these axioms, while others do not, and therefore, in our view, they may fail to correctly evaluate inconsistency.