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On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union

  • Salvador Barbera

    (CODE, Departament d’Economia i d'Historia Economica, Universitat Autònoma de Barcelona)

  • Matthew O. Jackson

    (Division of Humanities and Social Sciences, California Institute of Technology)

Consider a voting procedure where countries, states, or districts comprising a union each elect representatives who then participate in later votes at the union level on their behalf. The countries, provinces, and states may vary in their populations and composition. If we wish to maximize the total expected utility of all agents in the union, how to weight the votes of the representatives of the different countries, states or districts at the union level? We provide a simple characterization of the efficient voting rule in terms of the weights assigned to different districts and the voting threshold (how large a qualified majority is needed to induce change versus the status quo). Next, in the context of a model of the correlation structure of agents preferences, we analyze how voting weights relate to the population size of a country. We then analyze the voting weights in Council of the European Union under the Nice Treaty and the recently proposed constitution, and contrast them under different versions of our model, and compare them to the weights derived from poll data.

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Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2004.76.

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Date of creation: May 2004
Date of revision:
Handle: RePEc:fem:femwpa:2004.76
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  1. 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.
  2. Aghion, Philippe & Bolton, Patrick, 2003. "Incomplete Social Contracts," Scholarly Articles 4554123, Harvard University Department of Economics.
  3. Bård Harstad, 2007. "Harmonization and Side Payments in Political Cooperation," American Economic Review, American Economic Association, vol. 97(3), pages 871-889, June.
  4. Salvador Barbera & Matthew O. Jackson, 2002. "Choosing How to Choose: Self Stable Majority Rules," Microeconomics 0211003, EconWPA.
  5. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer, vol. 24(1), pages 171-197, January.
  6. Bård Harstad, 2005. "Majority Rules and Incentives," The Quarterly Journal of Economics, Oxford University Press, vol. 120(4), pages 1535-1568.
  7. Laruelle, Annick & Widgren, Mika, 1996. "Is the allocation of voting power among EU states fair?," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1996022, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
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