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Fair Apportionment in the Italian Senate : Which Reform Should Be Implemented?


  • Fabrice Barthelemy

    () (THEMA, Universite de Cergy-Pontoise)

  • Gabriele Esposito

    () (EHESS and GREQAM)

  • Mathieu Martin

    () (THEMA, Universite de Cergy-Pontoise)

  • Vincent Merlin

    () (CREM, Université de Caen)


In this paper we analyze the fairness of the 2007 reform proposal concerning the apportionment of the seats between the regions for the Italian Senate. Theory of power indices is used to compare the actual case with the proposed one. Two scenarios are proposed, senators belonging to the same region voting in blocks and senators voting according party lines, using both the Impartial Culture and the Impartial Anonymous Culture models. Our objective is to determine which apportionment is closer to the equal distribution of power among the citizens. In addition, we will seek for apportionments that are closer to the ideal representation than the ones proposed by politicians. We will also derive the probability that different apportionments produce a referendum paradox, i.e. exhibit a majority in the Senate different from the national popular majority.

Suggested Citation

  • Fabrice Barthelemy & Gabriele Esposito & Mathieu Martin & Vincent Merlin, 2011. "Fair Apportionment in the Italian Senate : Which Reform Should Be Implemented?," THEMA Working Papers 2011-16, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  • Handle: RePEc:ema:worpap:2011-16

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    References listed on IDEAS

    1. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 431-464.
    2. Dan S Felsenthal & Moshé Machover, 2004. "Analysis of QM rules in the draft constitution for Europe proposed by the European Convention, 2003," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 1-20, August.
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    More about this item


    Power index; Banzhaf; Italian Senate; apportionment; voting paradox; Monte Carlo simulation.;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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