# Ranking with multiple types of pairwise comparisons

arXiv: https://arxiv.org/abs/2206.13580 · HTML: https://mlsanity.com/paper/2206.13580/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 38 references that are in the map.
- First posted on arXiv 27 Jun 2022.

## Builds on (most cited first, 4 of 4)

- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [The structure and dynamics of multilayer networks](https://mlsanity.com/paper/1407.0742/) (2014)
- [Functional Multiplex PageRank](https://mlsanity.com/paper/1608.06328/) (2016)
- [Centralities of Nodes and Influences of Layers in Large Multiplex Networks](https://mlsanity.com/paper/1703.05833/) (2017)

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

- [Luck, skill, and depth of competition in games and social hierarchies](https://mlsanity.com/paper/2312.04711/) (2023)
- [Exact and rapid linear clustering of networks with dynamic programming](https://mlsanity.com/paper/2301.10403/) (2023)
- [ExPairT-LLM: Exact Learning for LLM Code Selection by Pairwise Queries](https://mlsanity.com/paper/2511.10855/) (2025)
- [A theoretical guarantee for SyncRank](https://mlsanity.com/paper/2509.22766/) (2025)
- [All against the machine: the Solo score for rating skill in variable environments](https://mlsanity.com/paper/2610.04523/) (2026)

## Abstract (arXiv)

The task of ranking individuals or teams, based on a set of comparisons between pairs, arises in various contexts, including sporting competitions and the analysis of dominance hierarchies among animals and humans. Given data on which competitors beat which others, the challenge is to rank the competitors from best to worst. Here we study the problem of computing rankings when there are multiple, potentially conflicting modes of comparison, such as multiple types of dominance behaviors among animals. We assume that we do not know a priori what information each behavior conveys about the ranking, or even whether they convey any information at all. Nonetheless we show that it is possible to compute a ranking in this situation and present a fast method for doing so, based on a combination of an expectation-maximization algorithm and a modified Bradley-Terry model. We give a selection of example applications to both animal and human competition.