# A characterization of the Logarithmic Least Squares Method

arXiv: https://arxiv.org/abs/1704.05321 · HTML: https://mlsanity.com/paper/1704.05321/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 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)

We provide an axiomatic characterization of the Logarithmic Least Squares Method (sometimes called row geometric mean), used for deriving a preference vector from a pairwise comparison matrix. This procedure is shown to be the only one satisfying two properties, correctness in the consistent case, which requires the reproduction of the inducing vector for any consistent matrix, and invariance to a specific transformation on a triad, that is, the weight vector is not influenced by an arbitrary multiplication of matrix elements along a 3-cycle by a positive scalar.