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Welfare ordering of voting weight allocations

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  • Kazuya Kikuchi

Abstract

This paper studies the allocation of voting weights in a committee representing groups of different sizes. We introduce a partial ordering of weight allocations based on stochastic comparison of social welfare. We show that when the number of groups is sufficiently large, this ordering asymptotically coincides with the total ordering induced by the cosine proportionality between the weights and the group sizes. A corollary is that a class of expectation-form objective functions, including expected welfare, the mean majority deficit and the probability of inversions, are asymptotically monotone in the cosine proportionality.

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  • Kazuya Kikuchi, 2022. "Welfare ordering of voting weight allocations," Papers 2208.05316, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2208.05316
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    1. Claus Beisbart & Luc Bovens, 2007. "Welfarist evaluations of decision rules for boards of representatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(4), pages 581-608, December.
    2. Marc Feix & Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet, 2004. "The probability of conflicts in a U.S. presidential type election," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 227-257, January.
    3. Salvador Barbera & Matthew O. Jackson, 2006. "On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 317-339, April.
    4. Olivier Mouzon & Thibault Laurent & Michel Le Breton & Dominique Lepelley, 2020. "The theoretical Shapley–Shubik probability of an election inversion in a toy symmetric version of the US presidential electoral system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 363-395, March.
    5. 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.
    6. Serguei Kaniovski & Alexander Zaigraev, 2018. "The probability of majority inversion in a two-stage voting system with three states," Theory and Decision, Springer, vol. 84(4), pages 525-546, June.
    7. Sascha Kurz & Nicola Maaser & Stefan Napel, 2017. "On the Democratic Weights of Nations," Journal of Political Economy, University of Chicago Press, vol. 125(5), pages 1599-1634.
    8. Moshe Koppel & Abraham Diskin, 2009. "Measuring disproportionality, volatility and malapportionment: axiomatization and solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 281-286, August.
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