# Model inference for ranking from pairwise comparisons

arXiv: https://arxiv.org/abs/2512.15269 · HTML: https://mlsanity.com/paper/2512.15269/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Builds on (most cited first, 6 of 6)

- [The Computer Science and Physics of Community Detection: Landscapes, Phase Transitions, and Hardness](https://mlsanity.com/paper/1702.00467/) (2017)
- [A physical model for efficient ranking in networks](https://mlsanity.com/paper/1709.09002/) (2017)
- [Luck, skill, and depth of competition in games and social hierarchies](https://mlsanity.com/paper/2312.04711/) (2023)
- [Generalized communities in networks](https://mlsanity.com/paper/1505.07478/) (2015)
- [Belief propagation for permutations, rankings, and partial orders](https://mlsanity.com/paper/2110.00513/) (2021)
- [The Bradley-Terry Stochastic Block Model](https://mlsanity.com/paper/2511.03467/) (2025)

## Abstract (arXiv)

We consider the problem of ranking objects from noisy pairwise comparisons, for example, ranking tennis players from the outcomes of matches. We follow a standard approach to this problem and assume that each object has an unobserved strength and that the outcome of each comparison depends probabilistically on the strengths of the comparands. However, we do not assume to know a priori how skills affect outcomes. Instead, we present an efficient algorithm for simultaneously inferring both the unobserved strengths and the function that maps strengths to probabilities. Despite this problem being under-constrained, we present experimental evidence that the conclusions of our Bayesian approach are robust to different model specifications. We include several case studies to exemplify the method on real-world data sets.