# On Axiomatization of Inconsistency Indicators for Pairwise Comparisons

arXiv: https://arxiv.org/abs/1307.6272 · HTML: https://mlsanity.com/paper/1307.6272/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2013.

## Built on by (most cited first, 5 of 5)

- [Manipulation of individual judgments in the quantitative pairwise comparisons method](https://mlsanity.com/paper/2211.01809/) (2022)
- [Establishing a leader in a pairwise comparisons method](https://mlsanity.com/paper/2403.14885/) (2024)
- [An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices' Properties in Pairwise Comparisons Methods](https://mlsanity.com/paper/2408.13297/) (2024)
- [Classifying Inconsistency in AHP Pairwise Comparison Matrices Using Machine Learning](https://mlsanity.com/paper/2505.06293/) (2025)
- [Geometric mean-based pairwise comparison method with the reference values -- statistical approach](https://mlsanity.com/paper/2607.10038/) (2026)

## Abstract (arXiv)

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.