A mathematical analysis of an election system proposed by Gottlob Frege

P Harrenstein, ML Lackner, M Lackner - Erkenntnis, 2020 - Springer
Erkenntnis, 2020Springer
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 …
Abstract
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.
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