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Optimal Apportionment

Author

Listed:
  • Yukio Koriyama

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique)

  • Antonin Macé

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique)

  • Rafael Treibich

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique)

  • Jean-François Laslier

    (CNRS - Centre National de la Recherche Scientifique, X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique)

Abstract

This paper provides a theoretical foundation that supports the degressive proportionality principle in apportionment problems, such as the allocation of seats in a federal parliament. The utility assigned by an individual to a constitutional rule is a function of the frequency with which each collective decision matches the individual's own will. The core of the argument is that, if the function is concave, then classical utilitarianism at the social level recommends decision rules that exhibit degressive proportionality with respect to the population size.

Suggested Citation

  • Yukio Koriyama & Antonin Macé & Rafael Treibich & Jean-François Laslier, 2013. "Optimal Apportionment," Post-Print halshs-01321784, HAL.
    • Handle: RePEc:hal:journl:halshs-01321784
    as

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    References listed on IDEAS

    as
    1. Claus Beisbart & Stephan Hartmann, 2010. "Welfarist evaluations of decision rules under interstate utility dependencies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(2), pages 315-344, February.
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    6. Laslier, Jean-François, 2012. "Why not proportional?," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 90-93.
    7. Maaser, Nicola & Napel, Stefan, 2012. "A note on the direct democracy deficit in two-tier voting," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 174-180.
    8. Gelman, Andrew & Katz, Jonathan N. & Bafumi, Joseph, 2004. "Standard Voting Power Indexes Do Not Work: An Empirical Analysis," British Journal of Political Science, Cambridge University Press, vol. 34(4), pages 657-674, October.
    9. Macé, Antonin & Treibich, Rafael, 2012. "Computing the optimal weights in a utilitarian model of apportionment," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 141-151.
    10. Barr, Jason & Passarelli, Francesco, 2009. "Who has the power in the EU?," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 339-366, May.
    11. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    12. Victoriano Ramírez & Antonio Palomares & Maria L. Márquez, 2006. "Degressively Proportional Methods for the Allotment of the European Parliament Seats Amongst the EU Member States," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 205-220, Springer.
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    Keywords

    federal parliament; theoretical foundation;

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