Maximal modularity and the optimal size of parliaments

Abstract 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 equal to 1/3, between the size of an elected...

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Autores principales:	Luca Gamberi, Yanik-Pascal Förster, Evan Tzanis, Alessia Annibale, Pierpaolo Vivo
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/93cdeca6804046b6be873874d8221115
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spelling	oai:doaj.org-article:93cdeca6804046b6be873874d82211152021-12-02T18:30:45ZMaximal modularity and the optimal size of parliaments10.1038/s41598-021-93639-12045-2322https://doaj.org/article/93cdeca6804046b6be873874d82211152021-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-93639-1https://doaj.org/toc/2045-2322Abstract 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 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.Luca GamberiYanik-Pascal FörsterEvan TzanisAlessia AnnibalePierpaolo VivoNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Luca Gamberi Yanik-Pascal Förster Evan Tzanis Alessia Annibale Pierpaolo Vivo Maximal modularity and the optimal size of parliaments
description	Abstract 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 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.
format	article
author	Luca Gamberi Yanik-Pascal Förster Evan Tzanis Alessia Annibale Pierpaolo Vivo
author_facet	Luca Gamberi Yanik-Pascal Förster Evan Tzanis Alessia Annibale Pierpaolo Vivo
author_sort	Luca Gamberi
title	Maximal modularity and the optimal size of parliaments
title_short	Maximal modularity and the optimal size of parliaments
title_full	Maximal modularity and the optimal size of parliaments
title_fullStr	Maximal modularity and the optimal size of parliaments
title_full_unstemmed	Maximal modularity and the optimal size of parliaments
title_sort	maximal modularity and the optimal size of parliaments
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/93cdeca6804046b6be873874d8221115
work_keys_str_mv	AT lucagamberi maximalmodularityandtheoptimalsizeofparliaments AT yanikpascalforster maximalmodularityandtheoptimalsizeofparliaments AT evantzanis maximalmodularityandtheoptimalsizeofparliaments AT alessiaannibale maximalmodularityandtheoptimalsizeofparliaments AT pierpaolovivo maximalmodularityandtheoptimalsizeofparliaments
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Maximal modularity and the optimal size of parliaments

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