Characterization of an inconsistency ranking for pairwise comparison matrices

TL;DR

This paper provides an axiomatic characterization of the inconsistency ranking induced by the Koczkodaj index, establishing a unique linear order for pairwise comparison matrices based on six properties.

Contribution

It introduces six independent axioms that uniquely determine the inconsistency ranking derived from the Koczkodaj index.

Findings

Six axioms uniquely characterize the inconsistency ranking.

The Koczkodaj index's induced ranking is uniquely determined by these properties.

The work clarifies the theoretical foundation of inconsistency measurement in pairwise comparisons.

Abstract

Pairwise comparisons between alternatives are a well-known method for measuring preferences of a decision-maker. Since these often do not exhibit consistency, a number of inconsistency indices has been introduced in order to measure the deviation from this ideal case. We axiomatically characterize the inconsistency ranking induced by the Koczkodaj inconsistency index: six independent properties are presented such that they determine a unique linear order on the set of all pairwise comparison matrices.