# Phragm'en's Voting Methods and Justified Representation

arXiv: https://arxiv.org/abs/2102.12305 · HTML: https://mlsanity.com/paper/2102.12305/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2021.

## Built on by (most cited first, 12 of 12)

- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Temporal Fairness in Multiwinner Voting](https://mlsanity.com/paper/2312.04417/) (2023)
- [Generative AI voting: fair collective choice is resilient to LLM biases and inconsistencies](https://mlsanity.com/paper/2406.11871/) (2024)
- [Full Proportional Justified Representation](https://mlsanity.com/paper/2501.12015/) (2025)
- [Harm Ratio: A Novel and Versatile Fairness Criterion](https://mlsanity.com/paper/2410.02977/) (2024)
- [Proportional Committee Elections with Positive and Negative Votes](https://mlsanity.com/paper/2503.01985/) (2025)
- [Fair Voting Methods as a Catalyst for Democratic Resilience: A Trilogy on Legitimacy, Impact and AI Safeguarding](https://mlsanity.com/paper/2512.17461/) (2025)
- [Computing Thiele Rules on Interval Elections and their Generalizations](https://mlsanity.com/paper/2605.03067/) (2026)
- [Strengthening Full Justified Representation: Efficient Verification and Computation](https://mlsanity.com/paper/2608.11500/) (2026)
- [Data as Voters: Core Set Selection Using Approval-Based Multi-Winner Voting](https://mlsanity.com/paper/2304.09995/) (2023)
- [A General Theory of Proportionality with Additive Utilities](https://mlsanity.com/paper/2602.08504/) (2026)
- [From Validator Selection to Portfolio Collection Optimization in Proof-of-Stake Blockchains](https://mlsanity.com/paper/2606.08282/) (2026)

## Abstract (arXiv)

In the late 19th century, Swedish mathematician Lars Edvard Phragm'en proposed a load-balancing approach for selecting committees based on approval ballots. We consider three committee voting rules resulting from this approach: two optimization variants - one minimizing the maximal load and one minimizing the variance of loads - and a sequential variant. We study Phragm'en's methods from an axiomatic point of view, focusing on properties capturing proportional representation. We show that the sequential variant satisfies proportional justified representation, which is a rare property for committee monotonic methods. Moreover, we show that the optimization variants satisfy perfect representation. We also analyze the computational complexity of Phragm'en's methods and provide mixed-integer programming based algorithms for computing them.