Axiomatic properties of inconsistency indices for pairwise comparisons
This work addresses the reliability of decision-making processes by providing a theoretical framework to assess inconsistency indices, which is incremental as it builds on existing methods without introducing new paradigms.
The paper tackles the problem of evaluating inconsistency in pairwise comparisons for decision-making by proposing five axioms to characterize inconsistency indices, and it proves that some existing indices satisfy these axioms while others do not, potentially leading to incorrect evaluations.
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.