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Computing the optimal weights in a utilitarian model of apportionment

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  • Macé, Antonin
  • Treibich, Rafael

Abstract

We consider a model of optimal apportionment in which individuals derive utility from the probability that the collective decision matches their own will. We suggest an iterative algorithm for the numerical optimization of the utilitarian social welfare function and apply it to the case of the European Parliament. Our results confirm that the optimal system of weights exhibits a form of degressive proportionality.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:matsoc:v:63:y:2012:i:2:p:141-151
    DOI: 10.1016/j.mathsocsci.2011.10.007
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    References listed on IDEAS

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    1. Laslier, Jean-François, 2012. "Why not proportional?," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 90-93.
    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. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, April.
    4. Claus Beisbart & Luc Bovens, 2007. "Welfarist evaluations of decision rules for boards of representatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(4), pages 581-608, December.
    5. Yukio Koriyama & Jean-François Laslier & Antonin Macé & Rafael Treibich, 2013. "Optimal Apportionment," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 584-608.
    6. Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
    7. Annick Laruelle & Federico Valenciano, 2010. "Egalitarianism and utilitarianism in committees of representatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 221-243, July.
    8. Leech, Dennis, 2002. "Computation of Power Indices," The Warwick Economics Research Paper Series (TWERPS) 644, University of Warwick, Department of Economics.
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    Cited by:

    1. 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.
    2. Laslier, Jean-François, 2012. "Why not proportional?," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 90-93.
    3. Yukio Koriyama & Jean-François Laslier & Antonin Macé & Rafael Treibich, 2013. "Optimal Apportionment," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 584-608.
    4. 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.
    5. 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.
    6. 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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