Abstract
We extend Condorcet’s Jury Theorem (Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. De l’imprimerie royale, 1785) to weighted voting games with voters of two kinds: a fixed (possibly empty) set of ‘major’ voters with fixed weights, and an ever-increasing number of ‘minor’ voters, whose total weight is also fixed, but where each individual’s weight becomes negligible. As our main result, we obtain the limiting probability that the jury will arrive at the correct decision as a function of the competence of the few major players. As in Condorcet’s result the quota q = 1/2 is found to play a prominent role.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
de Condorcet N.C. (1785) Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. De l’imprimerie royale, Paris
Dubey P., Shapley L.S. (1979) Mathematical properties of the Banzhaf power index. Math Oper Res 4(2): 99–131
Fey M. (2003) A note on the Condorcet Jury Theorem with supermajority voting rules. Soc Choice Welfare 20(1): 27–32
Petrov V.V. (1995) Limit theorems of probability theory. Clarendon Press, Oxford
Rae D.W. (1969) Decision rules and individual values in constitutional choice. Am Polit Sci Rev 63: 40–56
Author information
Authors and Affiliations
Corresponding author
Additional information
I wish to thank Maurice Koster, Moshé Machover, Guillermo Owen and two anonymous referees for helpful comments.
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Lindner, I. A generalization of Condorcet’s Jury Theorem to weighted voting games with many small voters. Economic Theory 35, 607–611 (2008). https://doi.org/10.1007/s00199-007-0239-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00199-007-0239-2