Extending the axioms of inconsistency indices for pairwise comparisons

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 axioms has been proposed to define a family of functions representing inconsistency indices. The scope of this paper is to expand the axiomatic framework by adding and justifying a new axiom.