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Minimizing the threat of a positive majority deficit in two-tier voting systems with equipopulous units

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  • Claus Beisbart
  • Luc Bovens

Abstract

The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College. Copyright Springer Science+Business Media, LLC 2013

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  • Claus Beisbart & Luc Bovens, 2013. "Minimizing the threat of a positive majority deficit in two-tier voting systems with equipopulous units," Public Choice, Springer, vol. 154(1), pages 75-94, January.
    • Handle: RePEc:kap:pubcho:v:154:y:2013:i:1:p:75-94
    DOI: 10.1007/s11127-011-9810-2
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    References listed on IDEAS

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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. Claus Beisbart & Luc Bovens, 2008. "A power measure analysis of Amendment 36 in Colorado," Public Choice, Springer, vol. 134(3), pages 231-246, March.
    3. 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.
    4. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    5. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    6. Edelman, Paul H., 2004. "Voting power and at-large representation," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 219-232, March.
    7. Annick Laruelle & Federico Valenciano, 2004. "Inequality in voting power," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 413-431, April.
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    Cited by:

    1. Laurent, Thibault & Le Breton, Michel & Lepelley, Dominique & de Mouzon, Olivier, 2017. "Exploring the Effects on the Electoral College of National and Regional Popular Vote Interstate Compact: An Electoral Engineering Perspective," TSE Working Papers 17-861, Toulouse School of Economics (TSE), revised May 2018.
    2. Olivier Mouzon & Thibault Laurent & Michel Breton & Dominique Lepelley, 2019. "Exploring the effects of national and regional popular vote Interstate compact on a toy symmetric version of the Electoral College: an electoral engineering perspective," Public Choice, Springer, vol. 179(1), pages 51-95, April.
    3. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2017. "Le mécanisme optimal de vote au sein du conseil des représentants d’un système fédéral," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 203-248, Mars-Juin.
    4. Le Breton, Michel & Van Der Straeten, Karine, 2014. "Influence Vs. Utility in the Evaluation of Voting Rules: A New Look at the Penrose Formula," TSE Working Papers 14-511, Toulouse School of Economics (TSE).

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