A mathematical analysis of an election system proposed by Gottlob Frege
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 representati...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Springer
2020
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| _version_ | 1797108437913436160 |
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| author | Harrenstein, P Lackner, M-L Lackner, M |
| author_facet | Harrenstein, P Lackner, M-L Lackner, M |
| author_sort | Harrenstein, P |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T07:29:14Z |
| format | Journal article |
| id | oxford-uuid:a2be7603-8cb1-4ad6-b4d8-f2046aba04cd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:29:14Z |
| publishDate | 2020 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:a2be7603-8cb1-4ad6-b4d8-f2046aba04cd2022-12-15T11:00:38ZA mathematical analysis of an election system proposed by Gottlob FregeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a2be7603-8cb1-4ad6-b4d8-f2046aba04cdEnglishSymplectic ElementsSpringer 2020Harrenstein, PLackner, M-LLackner, MIn 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. |
| spellingShingle | Harrenstein, P Lackner, M-L Lackner, M A mathematical analysis of an election system proposed by Gottlob Frege |
| title | A mathematical analysis of an election system proposed by Gottlob Frege |
| title_full | A mathematical analysis of an election system proposed by Gottlob Frege |
| title_fullStr | A mathematical analysis of an election system proposed by Gottlob Frege |
| title_full_unstemmed | A mathematical analysis of an election system proposed by Gottlob Frege |
| title_short | A mathematical analysis of an election system proposed by Gottlob Frege |
| title_sort | mathematical analysis of an election system proposed by gottlob frege |
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