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

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  • Barbera, Salvador
  • Matthew O. Jackson

Abstract

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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Bibliographic Info

Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 1196.

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Length: 29 pages
Date of creation: Apr 2004
Date of revision:
Publication status: Published: Published in Journal of Political Economy, V. 114, #2, (2006), pp. 317-339.
Handle: RePEc:clt:sswopa:1196

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Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
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Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
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Keywords: weighted voting; voting rules; voting weights; European Union;

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References

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  1. B�rd Harstad, 2005. "Majority Rules and Incentives," The Quarterly Journal of Economics, MIT Press, vol. 120(4), pages 1535-1568, November.
  2. Bård Harstad, 2007. "Harmonization and Side Payments in Political Cooperation," American Economic Review, American Economic Association, vol. 97(3), pages 871-889, June.
  3. Jackson, Matthew O. & Barbera, Salvador, 2002. "Choosing How Choose: Self-Stable Majority Rules," Working Papers 1145, California Institute of Technology, Division of the Humanities and Social Sciences.
  4. Annick Laruelle & Mika Widgrén, 1998. "Is the allocation of voting power among EU states fair?," Public Choice, Springer, vol. 94(3), pages 317-339, March.
  5. Philippe Aghion & Patrick Bolton, 2003. "Incomplete Social Contracts," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 38-67, 03.
  6. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer, vol. 24(1), pages 171-197, January.
  7. 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.
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