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arXiv · 1907.03643

A Mathematical Analysis of an Election System Proposed by Gottlob Frege

Paul Harrenstein·Marie-Louise Lackner·Martin Lackner
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Abstract

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.

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Paul Harrenstein, Marie-Louise Lackner, Martin Lackner. 2019-07-08. A Mathematical Analysis of an Election System Proposed by Gottlob Frege. https://arxiv.org/abs/1907.03643

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