论文标题
最大模块化和议会的最佳大小
Maximal modularity and the optimal size of parliaments
论文作者
论文摘要
代表民主国家的一个重要问题是如何确定给定国家的最佳议会规模。根据一个古老的猜想，称为立方根法，存在着一个相当普遍的幂律关系，其成分接近1/3，介于当选的议会和该国人口之间。现代欧洲国家的经验数据支持这种普遍性，但与更大的指数一致。在这项工作中，我们使用复杂网络理论的工具分析了这种有趣的规律性。我们将一个民主国家的人口模拟为一个随机网络，从增长模型中得出，在该模型中，每个节点都从可用的尺寸$ d $中采样了选区会员资格。我们通过分析计算人口的模块化，并发现其与选区数量的功能关系强烈非单调，最大值取决于人口的规模。最大模块化的标准使我们能够预测代表的数量应作为人口规模的幂律，这一发现是通过对现实世界数据的经验分析来定性证实的。
An important question in representative democracies is how to determine the optimal parliament size of a given country. According to an old conjecture, known as the cubic root law, there is a fairly universal power-law relation, with an exponent close to 1/3, between the size of an elected parliament and the country's population. Empirical data in modern European countries support such universality but are consistent with a larger exponent. In this work, we analyze this intriguing regularity using tools from complex networks theory. We model the population of a democratic country as a random network, drawn from a growth model, where each node is assigned a constituency membership sampled from an available set of size $D$. We calculate analytically the modularity of the population and find that its functional relation with the number of constituencies is strongly non-monotonic, exhibiting a maximum that depends on the population size. The criterion of maximal modularity allows us to predict that the number of representatives should scale as a power-law in the size of the population, a finding that is qualitatively confirmed by the empirical analysis of real-world data.
