Abstract
In voting bodies, when voting weights are reallocated, it may be observed that the voting power of some members, as measured by the Shapley-Shubik and Banzhaf power indices, increases while their voting weight decreases. By a simple constructive proof, this paper shows that such a “paradox of redistribution” can always occur in any voting body if the number of voters, n, is sufficiently large. Simulation results show that the paradox is quite frequent (up to 30 percent) and increases with n (at least for small n). Examples are given where the Banzhaf and Shapley-Shubik indices are not consistent in demonstrating the paradox.
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References
Brams, S. J., and Affuso, P. J. “Power and Size: A New Paradox,” Theory and Decision, 7, 1976, pp. 29–56.
Dreyer, J., and Schotter, A. “Power Relationships in the International Monetary Fund: The Consequences of Quota Changes,” manuscript in progress.
Lucas, W. “Measuring Power in Weighted Voting Systems,” Technical Report #227, School of Operations Research and Industrial Engineering, Cornell University, September, 1974.
Raanan, J. “The Inevitability of the Paradox of New Members,” Technical Report #311, School of Operations Research and Industrial Engineering, Cornell University, September, 1976.
Additional information
Department of Economics, New York University. Professor Schotter's participation in this paper was made possible by partial support of the Office of Naval Research Contract N00014-76-C-0033 given to New York University.
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Fischer, D., Schotter, A. The inevitability of the “paradox of redistribution” in the allocation of voting weights. Public Choice 33, 49–67 (1978). https://doi.org/10.1007/BF00118357
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DOI: https://doi.org/10.1007/BF00118357