On Axiomatization of Inconsistency Indicators for Pairwise Comparisons

TL;DR

This paper critically examines inconsistency measures in pairwise comparisons, proposing an axiomatic framework independent of specific methods, and demonstrates the invalidity of the eigenvalue-based inconsistency measure used in AHP.

Contribution

It introduces an axiomatization for inconsistency indicators that does not depend on particular approximation methods, challenging the validity of the eigenvalue-based inconsistency measure.

Findings

Eigenvalue-based inconsistency measure is proven incorrect.

Axiomatization of inconsistency indicators is proposed.

Framework is independent of specific comparison methods.

Abstract

We examine the notion of inconsistency in pairwise comparisons and propose an axiomatization which is independent of any method of approximation or the inconsistency indicator definition (e.g., Analytic Hierarchy Process, AHP). It has been proven that the eigenvalue-based inconsistency (proposed as a part of AHP) is incorrect.