A generalization of Condorcet’s Jury Theorem to weighted voting games with many small voters |
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Authors: | Ines Lindner |
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Institution: | (1) Utrecht School of Economics, Boothstraat 6, 3512 BW Utrecht, The Netherlands |
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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.
I wish to thank Maurice Koster, Moshé Machover, Guillermo Owen and two anonymous referees for helpful comments. |
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Keywords: | Condorcet’ s Jury Theorem Weighted voting games Majority games |
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