On the Number of alpha-Pivotal Players
We show that bounds like those of Al-Najjar and Smorodinsky (J. Econ. Theory, 2000) as well as of Gradwohl et al. (Math. Oper. Res., 2009) on the number of alpha-pivotal agents can be obtained by decomposition of variance. All these bounds have a similar asymptotic behaviour, up to constant factors. Our bound is weaker than that of Al-Najjar and Smorodinsky, but we require only pairwise independent—rather than independent—types. Our result strengthens the bound of Gradwohl et al.
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- Al-Najjar, Nabil I., 2001. "A reputational model of authority," Journal of Economic Behavior & Organization, Elsevier, vol. 46(2), pages 165-191, October.
- Al-Najjar, Nabil I. & Smorodinsky, Rann, 2000. "Provision of a public good with bounded cost," Economics Letters, Elsevier, vol. 67(3), pages 297-301, June.
- Hans Gersbach, 2009. "Democratic Mechanisms," Journal of the European Economic Association, MIT Press, vol. 7(6), pages 1436-1469, December.
- Gerardi, Dino & Yariv, Leeat, 2008. "Information acquisition in committees," Games and Economic Behavior, Elsevier, vol. 62(2), pages 436-459, March.
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