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Optimal Apportionment

  • Yukio Koriyama

    (Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X)

  • Jean-François Laslier

    (Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X)

  • Antonin Macé

    (Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X)

  • Rafael Treibich

    (Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X)

This paper provides a theoretical foundation which supports the degressive proportionality principle in apportionment problems. The core of the argument is that each individual derives utility from the fact that the collective decision matches her own will with some frequency, with marginal utility decreasing with respect to this frequency. Then classical utilitarianism at the social level recommends decision rules which exhibit degressive proportionality. The model is applied to the case of the 27 states of the European Union.

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Paper provided by HAL in its series Working Papers with number hal-00667852.

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Date of creation: 08 Feb 2012
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Handle: RePEc:hal:wpaper:hal-00667852
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00667852
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  1. Gelman, Andrew & Katz, Jonathan N. & Bafumi, Joseph, 2002. "Standard Voting Power Indexes Don't Work: An Empirical Analysis," Working Papers 1133, California Institute of Technology, Division of the Humanities and Social Sciences.
  2. Jean-François Laslier, 2011. "Why not proportional?," Working Papers hal-00625308, HAL.
  3. Laruelle,Annick & Valenciano,Federico, 2008. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521873871.
  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. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar, number 1489, March.
  6. 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.
  7. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer, vol. 24(1), pages 171-197, January.
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