# A Mathematical Analysis of an Election System Proposed by Gottlob Frege

arXiv: https://arxiv.org/abs/1907.03643 · HTML: https://mlsanity.com/paper/1907.03643/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [Temporal Fairness in Multiwinner Voting](https://mlsanity.com/paper/2312.04417/) (2023)

## Abstract (arXiv)

In 1998 a long-lost proposal for an election law by Gottlob Frege (1848--1925) was rediscovered in the Th"uringer Universit"ats- und Landesbibliothek in Jena, Germany. The method that Frege proposed for the election of representatives of a constituency features a remarkable concern for the representation of minorities. Its core idea is that votes cast for unelected candidates are carried over to the next election, while elected candidates incur a cost of winning. We prove that this sensitivity to past elections guarantees a proportional representation of political opinions in the long run. We find that through a slight modification of Frege's original method even stronger proportionality guarantees can be achieved. This modified version of Frege's method also provides a novel solution to the apportionment problem, which is distinct from all of the best-known apportionment methods, while still possessing noteworthy proportionality properties.