Harrenstein Paul, Lackner Marie-Louise, Lackner Martin
Department of Computer Science, University of Oxford, Wolfson Building, 15 Parks Road, Oxford, OX1 3QD UK.
Herford College, University of Oxford, Catte Street, Oxford, UK.
Erkenntnis. 2022;87(6):2609-2644. doi: 10.1007/s10670-020-00318-0. Epub 2020 Nov 10.
In 1998 a long-lost proposal for an election law by Gottlob Frege (1848-1925) was rediscovered in the 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.
1998年，戈特洛布·弗雷格（1848 - 1925）一份失传已久的选举法提案在德国耶拿被重新发现。弗雷格提出的选区代表选举方法对少数群体的代表性表现出了显著关注。其核心思想是，投给未当选候选人的选票会结转至下一次选举，而当选候选人则需承担获胜成本。我们证明，这种对过去选举的敏感性从长远来看能保证政治观点的比例代表制。我们发现，通过对弗雷格原方法进行轻微修改，甚至可以实现更强的比例保证。弗雷格方法的这个修改版本还为分配问题提供了一种新颖的解决方案，它不同于所有最著名的分配方法，但仍具有值得注意的比例性质。
