Maximal modularity and the optimal size of parliaments

Author:

Gamberi Luca,Förster Yanik-Pascal,Tzanis Evan,Annibale Alessia,Vivo Pierpaolo

Abstract

AbstractAn 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 equal 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 analyse 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.

Funder

Engineering and Physical Sciences Research Council

UK Research and Innovation

Publisher

Springer Science and Business Media LLC

Subject

Multidisciplinary

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Variational kinetic clustering of complex networks;The Journal of Chemical Physics;2023-03-14

2. On the optimal size of legislatures: An illustrated literature review;European Journal of Political Economy;2023-03

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