# Phragm'en's and Thiele's election methods

arXiv: https://arxiv.org/abs/1611.08826 · HTML: https://mlsanity.com/paper/1611.08826/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2016.

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

- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Full Proportional Justified Representation](https://mlsanity.com/paper/2501.12015/) (2025)
- [Proportional Committee Elections with Positive and Negative Votes](https://mlsanity.com/paper/2503.01985/) (2025)
- [Computing Thiele Rules on Interval Elections and their Generalizations](https://mlsanity.com/paper/2605.03067/) (2026)
- [Reverse Sequential Proportional Approval Voting Rule: Proportionality and Approximation Guarantees](https://mlsanity.com/paper/2609.35331/) (2026)

## Abstract (arXiv)

The election methods introduced in 1894--1895 by Phragm'en and Thiele, and their somewhat later versions for ordered (ranked) ballots, are discussed in detail. The paper includes definitions and examples and discussion of whether the methods satisfy some properties, including monotonicity, consistency and various proportionality criteria. The relation with STV is also discussed. The paper also contains historical information on the methods.