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Abstract

All the federal unions, like the United States of America or the European Union face the issue of finding the right allocation of seats to their member states. There has been a lot of debates in the United States of America since two centuries in order to find the right mechanism to round off the number of representatives per state proportionally to their populations. This problem is now well documented. The existing methods of the representative apportionment actually are based on the max-utility rule, but they just satisfy one or two Fair Apportionment Axioms. To answer this question, we consider to present a dynamic apportionment method which satisfies the three axioms 1, 3 and 4. The calculable program is also presented.

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References

  • Balinski ML, Young HP (2001) Fair representation, meeting the ideal of one person, one vote, 2nd edn. The Brookings Institution, Washington, DC

    Google Scholar 

  • Berg S, Lepelley D (1994) On probability models in voting theory. Statistica Neerlandica 48(2):133–146

    Article  Google Scholar 

  • Bison F, Bonnet J, and Lepelley D (2004) La détermination du numbre des délégués au sein des structures intercommunales: une application de lindice de pouvoir de Banzhaf. Démocratie et Management local. Revue d’économie régionale et urbaine, pp 259–282

    Google Scholar 

  • Bobay F (2001) La réforme du Conseil de l’Union Européenne `a partir de lathéorie des jeux. Revue Française d’Économie 16:3–58

    Article  Google Scholar 

  • Cervone D, Gehrlein W, Zwicker W (2001) Which scoring rule maximizes Condorcet efficiency Under Zac. Theory Decis 145–185

    Google Scholar 

  • Coxeter H (1935) The functions of Schläfli and Lobatschefsky. Quat J Math 6:13–29

    Article  Google Scholar 

  • Demange G (2001) Commentaire de l’article de F. Bobay. Revue Française d’Économie 16:63–71

    Article  Google Scholar 

  • Feix MR, Lepelley D, Merlin V, Rouet J-L (2004) The probability of conflicts in a U.S. presidential type election. Econ Theory 23(2):227–257

    Article  Google Scholar 

  • Felsenthal DS, Machover M (2001) The treaty of nice and qualified majority voting. Soc Choice Welf 18:431–465

    Article  Google Scholar 

  • Galam S (1990) Social paradoxes of majority rule voting and renormalization group. J Stat Phys 61:943–951

    Article  Google Scholar 

  • Gehrlein W (2002) Condorcet’s paradox and the likelihood of its occurrence: different perspectives on balanced preferences. Theory Decis 52:171–199

    Article  Google Scholar 

  • Hosli MO, Machover M (2002) The nice treaty and voting rules in the council. A reply to moberg. Mimeo, Mannheim

    Google Scholar 

  • Huntington EV (1928) The apportionment of representatives in congress. Trans Am Math Soc 30(1):85–110

    Article  Google Scholar 

  • Lucas WF (1983) Modules in applied mathematics, vol 2, Political and related models (M). Springer, New York

    Google Scholar 

  • Saari DG (2001) Chaotic elections, a mathematician looks at voting. AMS, Providence

    Google Scholar 

Download references

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Correspondence to Qiong Zhang .

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Zhang, Q., Huang, Jm., Wang, Xm. (2013). A Dynamic Method of the Representatives Apportionment. In: Dou, R. (eds) Proceedings of 2012 3rd International Asia Conference on Industrial Engineering and Management Innovation (IEMI2012). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33012-4_48

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