On Inconsistency Indices and Inconsistency Axioms in Pairwise Comparisons

TL;DR

This paper introduces a new inconsistency measure for pairwise comparisons, proposes an additional axiom, and evaluates existing indices against this axiom to improve decision-making reliability.

Contribution

It presents a novel inconsistency measure, adds an upper boundary axiom to the set of axioms, and compares indices based on this new criterion.

Findings

The new inconsistency measure satisfies key properties.

Selected indices comply with the new upper boundary axiom.

Numerical comparison highlights differences among indices.

Abstract

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several inconsistency indices were proposed as an alternative to Saaty inconsistency index and inconsistency ratio for reciprocal pairwise comparisons matrices. This paper aims to: firstly, introduce a new measure of inconsistency of pairwise comparisons and to prove its basic properties; secondly, to postulate an additional axiom, an upper boundary axiom, to an existing set of axioms; and the last, but not least, the paper provides proofs of satisfaction of this additional axiom by selected inconsistency indices as well as it provides their numerical comparison.