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A Recursive Measure of Voting Power that Satisfies Reasonable Postulates

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  • Arash Abizadeh
  • Adrian Vetta

Abstract

We design a recursive measure of voting power based on partial as well as full voting efficacy. Classical measures, by contrast, incorporate solely full efficacy. We motivate our design by representing voting games using a division lattice and via the notion of random walks in stochastic processes, and show the viability of our recursive measure by proving it satisfies a plethora of postulates that any reasonable voting measure should satisfy. These include the iso-invariance, dummy, dominance, donation, minimum-power bloc, and quarrel postulates.

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  • Arash Abizadeh & Adrian Vetta, 2021. "A Recursive Measure of Voting Power that Satisfies Reasonable Postulates," Papers 2105.03006, arXiv.org, revised May 2022.
    • Handle: RePEc:arx:papers:2105.03006
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    References listed on IDEAS

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    1. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 171-197, January.
    2. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, October.
    3. Annick Laruelle & Federico Valenciano, 2001. "Shapley-Shubik and Banzhaf Indices Revisited," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 89-104, February.
    4. Leech, Dennis, 1990. "Power Indices and Probabilistic Voting Assumptions," Public Choice, Springer, vol. 66(3), pages 293-299, September.
    5. Guillermo Owen, 1975. "Multilinear extensions and the banzhaf value," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(4), pages 741-750, December.
    6. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
    7. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    8. Dan Felsenthal & Moshé Machover & William Zwicker, 1998. "The Bicameral Postulates and Indices of a Priori Voting Power," Theory and Decision, Springer, vol. 44(1), pages 83-116, January.
    9. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    10. Dan S. Felsenthal & Moshé Machover, 2004. "A Priori Voting Power: What Is It All About?," Political Studies Review, Political Studies Association, vol. 2(1), pages 1-23, January.
    11. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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    Cited by:

    1. Arash Abizadeh & Adrian Vetta, 2023. "The blocker postulates for measures of voting power," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 595-623, May.

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