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Computing the optimal weights in a utilitarian model of apportionment

Listed author(s):
  • Macé, Antonin
  • Treibich, Rafael

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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File URL: http://www.sciencedirect.com/science/article/pii/S0165489611001168
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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 63 (2012)
Issue (Month): 2 ()
Pages: 141-151

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Handle: RePEc:eee:matsoc:v:63:y:2012:i:2:p:141-151
DOI: 10.1016/j.mathsocsci.2011.10.007
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  1. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
  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. 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.
  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. 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.
  6. Laslier, Jean-François, 2012. "Why not proportional?," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 90-93.
  7. Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
  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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