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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.

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  • 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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    1. 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.
    2. 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.
    3. Laslier, Jean-François, 2012. "Why not proportional?," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 90-93.
    4. 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.
    5. Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
    6. Leech, Dennis, 2002. "Computation of Power Indices," The Warwick Economics Research Paper Series (TWERPS) 644, University of Warwick, Department of Economics.
    7. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, September.
    8. 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.
    9. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    10. Leech, Dennis, 2002. "Computation Of Power Indices," Economic Research Papers 269457, University of Warwick - Department of Economics.
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    1. Laslier, Jean-François, 2012. "Why not proportional?," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 90-93.
    2. Katarzyna Cegiełka & Piotr Dniestrzański & Janusz Łyko & Arkadiusz Maciuk & Maciej Szczeciński, 2021. "A neutral core of degressively proportional allocations under lexicographic preferences of agents," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(4), pages 667-685, December.
    3. Markus Brill & Jean-François Laslier & Piotr Skowron, 2018. "Multiwinner approval rules as apportionment methods," Journal of Theoretical Politics, , vol. 30(3), pages 358-382, July.
    4. 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.
    5. 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.
    6. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2017. "Le mécanisme optimal de vote au sein du conseil des représentants d’un système fédéral," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 203-248, Mars-Juin.
    7. 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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