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A Mathematical Analysis of an Election System Proposed by Gottlob Frege

2020; Springer Science+Business Media; Volume: 87; Issue: 6 Linguagem: Inglês

10.1007/s10670-020-00318-0

1572-8420

Paul Harrenstein, Marie-Louise Lackner, Martin Lackner,

Electoral Systems and Political Participation

In 1998 a long-lost proposal for an election law by Gottlob Frege (1848-1925) was rediscovered in the Thüringer Universitäts- 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.