弗雷格选举制度的数学分析
A Mathematical Analysis of an Election System Proposed by Gottlob Frege
摘要：
1998年，德国耶拿的图林根大学和州立图书馆重新发现了戈特洛布·弗雷格（Gottlob Frege，1848- 1925）遗失已久的选举法提案。弗雷格提出的选举选区代表的方法对少数民族的代表性有着显著的关注。其核心思想是，投给未当选候选人的选票将被结转到下一次选举，而当选候选人则要承担获胜的成本。我们证明，这种对过去选举的敏感性保证了从长远来看政治意见的比例代表。我们发现，通过对弗雷格的原始方法稍加修改，甚至可以实现更强的比例保证。弗雷格的方法的这个修改版本也提供了一个新的解决方案的分摊问题，这是不同于所有最著名的分摊方法，同时仍然拥有值得注意的比例属性。
英文摘要：
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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