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. (shrink)

This entry introduces the reader to the main ideas in Frege's philosophy of logic, mathematics, and language.