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Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality

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  • Wenruo Lyu

    (Graduate School of Advanced Integrated Studies in Human Survivability, Kyoto University, Kyoto 606-8306, Japan)

  • Liang Zhao

    (Graduate School of Advanced Integrated Studies in Human Survivability, Kyoto University, Kyoto 606-8306, Japan)

Abstract

The allocation of seats in a legislative body to groups based on their size is a crucial issue in legal and political studies. However, recent findings suggest that an optimal allocation of seats may not be proportional to the size of the groups. For instance, the European Parliament (EP) utilizes a subproportional system known as degressive proportionality. Unfortunately, current apportionment methods for the EP lack a rigorous axiomatic analysis and fail to adequately address equality. Building upon recent research on equality in subproportional settings, this paper proposed a novel generalization of existing axioms and divisor methods for proportionality to encompass subproportionality with relative equality. Specifically, we consider a function f ( p ) = a + b p γ on the standard number of seats for a group of size p , where a , b and γ are given non-negative constants, and a is an integer. This theory is exemplified through an empirical study focused on the EP.

Suggested Citation

  • Wenruo Lyu & Liang Zhao, 2023. "Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality," Mathematics, MDPI, vol. 11(15), pages 1-13, July.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3270-:d:1202204
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    References listed on IDEAS

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    1. Carrie Arnold, 2017. "The mathematicians who want to save democracy," Nature, Nature, vol. 546(7657), pages 200-202, June.
    2. Emmanuelle Auriol & Robert Gary-Bobo, 2012. "On the optimal number of representatives," Public Choice, Springer, vol. 153(3), pages 419-445, December.
    3. Grimmett, G.R. & Oelbermann, K.-F. & Pukelsheim, F., 2012. "A power-weighted variant of the EU27 Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 136-140.
    4. G. R. Grimmett & F. Pukelsheim & V. Ram'irez Gonz'alez & W. S{l}omczy'nski & K. .Zyczkowski, 2017. "A 700-seat no-loss composition for the 2019 European Parliament," Papers 1710.03820, arXiv.org.
    5. Raphael Godefroy & Nicolas Klein, 2018. "Parliament Shapes And Sizes," Economic Inquiry, Western Economic Association International, vol. 56(4), pages 2212-2233, October.
    6. Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
    7. Theil, Henri, 1969. "The Desired Political Entropy," American Political Science Review, Cambridge University Press, vol. 63(2), pages 521-525, June.
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