Axiomatization of inconsistency indicators for pairwise comparisons

This study proposes axioms for inconsistency indicators in pairwise comparisons. The new observation (by Szybowski), that “no PC submatrix may have a worse inconsistency indicator than the given PC matrix” is an essential simplification of the axiomatization. The goal of formulating axioms for all future definitions of new inconsistency indicators is difficult and as illusive as the inconsistency concept itself. This study improves the axiomatization proposed by Koczkodaj and Szwarc in 2014. As a side product, the new axiom allows to prevent approximation error aberrations of an arbitrarily large value in the input data.