# Sufficient conditions for a Heuristic Rating Estimation Method application

arXiv: https://arxiv.org/abs/2605.08991 · HTML: https://mlsanity.com/paper/2605.08991/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 25 references that are in the map.
- First posted on arXiv 9 May 2026.

## Builds on (most cited first, 3 of 3)

- [Pairwise Comparisons Simplified](https://mlsanity.com/paper/1311.6863/) (2013)
- [Multiple-criteria Heuristic Rating Estimation](https://mlsanity.com/paper/2205.10428/) (2022)
- [Mean-based incomplete pairwise comparisons method with the reference values](https://mlsanity.com/paper/2207.10783/) (2022)

## Abstract (arXiv)

A series of papers has introduced the Heuristic Rating Estimation method, which evaluates a set of alternatives based on pairwise comparisons and the weights of reference alternatives. We formulate the conditions under which the HRE method can be applied correctly. The research considers both arithmetic and geometric algorithms for complete and incomplete pairwise comparison methods. The illustrative examples show that the estimations of inconsistency in the arithmetic variant are optimal.