  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.

Artificial Intelligence