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Optimal Apportionment

Author

Listed:
  • Yukio Koriyama

    (Department of Economics, Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Antonin Macé

    () (Department of Economics, Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Rafael Treibich

    (Department of Economics, Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Jean-François Laslier

    (CNRS - Centre National de la Recherche Scientifique, Department of Economics, Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

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
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01321784
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    References listed on IDEAS

    as
    1. Barr, Jason & Passarelli, Francesco, 2009. "Who has the power in the EU?," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 339-366, May.
    2. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 171-197, January.
    3. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    4. 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.
    5. Felsenthal, Dan S. & Machover, Moshe, 1999. "Minimizing the mean majority deficit: The second square-root rule," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 25-37, January.
    6. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    7. Laslier, Jean-François, 2012. "Why not proportional?," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 90-93.
    8. 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.
    9. 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(04), pages 657-674, October.
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    Cited by:

    1. repec:eee:gamebe:v:106:y:2017:i:c:p:239-259 is not listed on IDEAS
    2. Biró, Péter & Kóczy, László Á. & Sziklai, Balázs, 2015. "Fair apportionment in the view of the Venice Commission’s recommendation," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 32-41.
    3. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2016. "Le Mécanisme Optimal de Vote au Sein du Conseil des Représentants d'un Système Fédéral," TSE Working Papers 16-617, Toulouse School of Economics (TSE), revised Dec 2016.
    4. repec:spr:sochwe:v:50:y:2018:i:2:d:10.1007_s00355-017-1087-z is not listed on IDEAS
    5. Laslier, Jean-François, 2012. "Why not proportional?," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 90-93.
    6. 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.
    7. repec:spr:homoec:v:34:y:2017:i:1:d:10.1007_s41412-017-0036-5 is not listed on IDEAS
    8. repec:bla:econom:v:84:y:2017:i:333:p:78-103 is not listed on IDEAS
    9. repec:eee:matsoc:v:87:y:2017:i:c:p:22-30 is not listed on IDEAS
    10. Casella, Alessandra & Laslier, Jean-François & Macé, Antonin, 2017. "Democracy for Polarized Committees: The Tale of Blotto's Lieutenants," Games and Economic Behavior, Elsevier, vol. 106(C), pages 239-259.
    11. Matthias Weber, 2014. "Choosing Voting Systems behind the Veil of Ignorance: A Two-Tier Voting Experiment," Tinbergen Institute Discussion Papers 14-042/I, Tinbergen Institute.
    12. 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.
    13. Antonin Macé & Rafael Treibich, 2018. "On the Weights of Sovereign Nations," Working Papers halshs-01630090, HAL.
    14. Marcus Pivato, 2016. "Asymptotic utilitarianism in scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 431-458, August.
    15. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2016. "Le Mécanisme Optimal de Vote au Sein du Conseil des Représentants d'un Système Fédéral," TSE Working Papers 16-617, Toulouse School of Economics (TSE), revised Dec 2016.
    16. Sascha Kurz & Nicola Maaser & Stefan Napel & Matthias Weber, 2014. "Mostly Sunny: A Forecast of Tomorrow's Power Index Research," Tinbergen Institute Discussion Papers 14-058/I, Tinbergen Institute.

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    Keywords

    federal parliament; theoretical foundation;

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