# Proportional Rankings

arXiv: https://arxiv.org/abs/1612.01434 · HTML: https://mlsanity.com/paper/1612.01434/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2016.

## Built on by (most cited first, 10 of 10)

- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Online Approval Committee Elections](https://mlsanity.com/paper/2202.06830/) (2022)
- [Drawing a Map of Elections](https://mlsanity.com/paper/2504.03809/) (2025)
- [Core-Stable Committees under Restricted Domains](https://mlsanity.com/paper/2108.01987/) (2021)
- [Full Proportional Justified Representation](https://mlsanity.com/paper/2501.12015/) (2025)
- [Representative Ranking for Deliberation in the Public Sphere](https://mlsanity.com/paper/2503.18962/) (2025)
- [Selecting the Most Conflicting Pair of Candidates](https://mlsanity.com/paper/2405.05870/) (2024)
- [Strengthening Full Justified Representation: Efficient Verification and Computation](https://mlsanity.com/paper/2608.11500/) (2026)
- [A General Theory of Proportionality with Additive Utilities](https://mlsanity.com/paper/2602.08504/) (2026)
- [Reverse Sequential Proportional Approval Voting Rule: Proportionality and Approximation Guarantees](https://mlsanity.com/paper/2609.35331/) (2026)

## Abstract (arXiv)

In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that cohesive groups of voters are represented proportionally in each initial segment of the ranking. Proportional rankings are desirable in situations where initial segments of different lengths may be relevant, e.g., hiring decisions (if it is unclear how many positions are to be filled), the presentation of competing proposals on a liquid democracy platform (if it is unclear how many proposals participants are taking into consideration), or recommender systems (if a ranking has to accommodate different user types). We study the proportional representation provided by several ranking methods and prove theoretical guarantees. Furthermore, we experimentally evaluate these methods and present preliminary evidence as to which methods are most suitable for producing proportional rankings.