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A Model of Adversarial Committees
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A Model of Adversarial Committees
Jaehoon Kim
1
Center for Business, Government, and Society, MEDS Department,
Kellogg School of Management, Northwestern University, Evanston, Illinois, 60208
Abstract
We generalize the Condorcet Jury Theorem to an environment where each voter has privateinformation about the true state of the world and two groups of voters have opposing state-contingent preferences. We show that in equilibrium under unanimity rule, the probability ofmaking a wrong choice for the majority-type voters is bounded below and above. Under anynon-unanimous rule, we show that in a large electorate, if the majority-type voters are attentiveto their private information, and the fraction of the majority-type voters is greater than thefraction of votes required to pass the alternative, then the probability of choosing the correctalternative from the majority-type voter’s perspective gets close to one, as in the case of pref-erence aggregation in complete information. Otherwise, non-unanimous voting rules (except forsimple majority rule) fail to aggregate information. Finally we show that only simple majorityrule is minority-dominance proof. Journal of Economic Literature Classification Numbers: C72,D72.
Key words: Adversarial committee, Condorcet Jury Theorem, Information aggregation,Minority-dominance proofness
1
Introduction
Among many things the Condorcet Jury Theorem has been spotlighted as an epitome ofinformation aggregation. Since Austen-Smith and Banks (1995) have shown that sincerevoting behavior is generally not supported as a Nash equilibrium phenomenon, scholars
Previous version of this paper was presented at the Annual Meetings of 2004 Midwest Political
Science Association, Chicago, Il.
Email address: ## email not listed ## (Jaehoon Kim ).
1
Special thanks go to John Duggan, Mark Fey, and Larry Rothenberg for their support during
the course of developing this paper. Also I would like to thank my colleagues at the Universityof Rochester for helpful comments. All errors are my own.
7 September 2004
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A Model of Adversarial Committees
Jaehoon Kim
1
Center for Business, Government, and Society, MEDS Department,
Kellogg School of Management, Northwestern University, Evanston, Illinois, 60208
Abstract
We generalize the Condorcet Jury Theorem to an environment where each voter has private
information about the true state of the world and two groups of voters have opposing state-
contingent preferences. We show that in equilibrium under unanimity rule, the probability of
making a wrong choice for the majority-type voters is bounded below and above. Under any
non-unanimous rule, we show that in a large electorate, if the majority-type voters are attentive
to their private information, and the fraction of the majority-type voters is greater than the
fraction of votes required to pass the alternative, then the probability of choosing the correct
alternative from the majority-type voter’s perspective gets close to one, as in the case of pref-
erence aggregation in complete information. Otherwise, non-unanimous voting rules (except for
simple majority rule) fail to aggregate information. Finally we show that only simple majority
rule is minority-dominance proof. Journal of Economic Literature Classification Numbers: C72,
D72.
Key words: Adversarial committee, Condorcet Jury Theorem, Information aggregation,
Minority-dominance proofness
1
Introduction
Among many things the Condorcet Jury Theorem has been spotlighted as an epitome of
information aggregation. Since Austen-Smith and Banks (1995) have shown that sincere
voting behavior is generally not supported as a Nash equilibrium phenomenon, scholars
Previous version of this paper was presented at the Annual Meetings of 2004 Midwest Political
Science Association, Chicago, Il.
Email address: ## email not listed ## (Jaehoon Kim ).
1
Special thanks go to John Duggan, Mark Fey, and Larry Rothenberg for their support during
the course of developing this paper. Also I would like to thank my colleagues at the University
of Rochester for helpful comments. All errors are my own.
7 September 2004
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