# On Inconsistency Indices and Inconsistency Axioms in Pairwise Comparisons

arXiv: https://arxiv.org/abs/1703.05204 · HTML: https://mlsanity.com/paper/1703.05204/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2017.

## Built on by (most cited first, 1 of 1)

- [An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices' Properties in Pairwise Comparisons Methods](https://mlsanity.com/paper/2408.13297/) (2024)

## Abstract (arXiv)

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.