Characterization of an inconsistency ranking for pairwise comparison matrices

Pairwise comparisons between alternatives are a well-known method of decision-making. Since the preferences do often not exhibit consistency, a number of inconsistency indices have been defined in order to measure the deviation from this ideal case. Recently, some axioms have been proposed to identify indices that evaluate inconsistency correctly. Inconsistency rankings are weak orders on the set of pairwise comparison matrices with respect to their inconsistency level and can be defined by any inconsistency index. This study characterizes a specific inconsistency ranking by providing six independent axioms such that they determine a unique weak order on the set of all pairwise comparison matrices.