Multidimensional political apportionment

Javier Cembrano, José Correa and Victor Verdugo
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Javier Cembrano: a Institute of Mathematics, Technische Universität Berlin, 10623 Berlin, Germany;
José Correa: b Department of Industrial Engineering, Universidad de Chile, 8370456 Santiago, Chile;
Victor Verdugo: c Institute of Engineering Sciences, Universidad de O’Higgins, 2841959 Rancagua, Chile

Proceedings of the National Academy of Sciences, 2022, vol. 119, issue 15, e2109305119

Abstract: A cornerstone in the modern political organization of societies is the existence of a deliberative assembly, reflecting the needs of different population segments. As modern societies become more complex, representation according to dimensions beyond political affiliation and geography is demanded; examples include gender balance and ethnicity. As this dimensionality increases, the task becomes more challenging and requires more sophisticated mathematical tools. In this paper, we initiate the study of multidimensional apportionments and show that, in three and more dimensions, their existence is not guaranteed. However, our main result states that it is possible to elect a house nearly respecting proportionality of representation along several dimensions simultaneously. We finally illustrate the potential of our approach with recent election data.

Keywords: apportionment; integer programming; social choice (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:nas:journl:v:119:y:2022:p:e2109305119

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