# Information Aggregation and Equilibrium Selection in Committees

01 Jan 2007-

About: The article was published on 2007-01-01 and is currently open access. It has received None citations till now. The article focuses on the topics: Equilibrium selection.

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04 Mar 2009

TL;DR: Condorcet's paradox (the non-transitivity of majority preferences) is seen as the direct ancestor of Arrow's paradox as discussed by the authors, and it was rediscovered as a foundational work in the theory of voting and societal preferences.

Abstract: A central figure in the early years of the French Revolution, Nicolas de Condorcet (1743–94) was active as a mathematician, philosopher, politician and economist. He argued for the values of the Enlightenment, from religious toleration to the abolition of slavery, believing that society could be improved by the application of rational thought. In this essay, first published in 1785, Condorcet analyses mathematically the process of making majority decisions, and seeks methods to improve the likelihood of their success. The work was largely forgotten in the nineteenth century, while those who did comment on it tended to find the arguments obscure. In the second half of the twentieth century, however, it was rediscovered as a foundational work in the theory of voting and societal preferences. Condorcet presents several significant results, among which Condorcet's paradox (the non-transitivity of majority preferences) is now seen as the direct ancestor of Arrow's paradox.

1,782 citations

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TL;DR: The Condorcet Jury Theorem states that majorities are more likely than any single individual to select the "better" of two alternatives when there exists uncertainty about which of the two alternatives is in fact preferred as discussed by the authors.

Abstract: The Condorcet Jury Theorem states that majorities are more likely than any single individual to select the "better" of two alternatives when there exists uncertainty about which of the two alternatives is in fact preferred Most extant proofs of this theorem implicitly make the behavioral assumption that individuals vote "sincerely" in the collective decision making, a seemingly innocuous assumption, given that individuals are taken to possess a common preference for selecting the better alternative However, in the model analyzed here we find that sincere behavior by all individuals is not rational even when individuals have such a common preference In particular, sincere voting does not constitute a Nash equilibrium A satisfactory rational choice foundation for the claim that majorities invariably "do better" than individuals, therefore, has yet to be derived

948 citations

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TL;DR: In this article, the existence of a swing voter's curse is demonstrated: less informed indifferent voters strictly prefer to abstain rather than vote for either candidate even when voting is costless, and the equilibrium result that a substantial fraction of the electorate will abstain even though all abstainers strictly prefer voting for one candidate over voting for another.

Abstract: The authors analyze two-candidate elections in which some voters are uncertain about the realization of a state variable that affects the utility of all voters. They demonstrate the existence of a swing voter's curse: less informed indifferent voters strictly prefer to abstain rather than vote for either candidate even when voting is costless. The swing voter's curse leads to the equilibrium result that a substantial fraction of the electorate will abstain even though all abstainers strictly prefer voting for one candidate over voting for another. Copyright 1996 by American Economic Association.

793 citations

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TL;DR: The authors showed that the probability of acquitting an innocent defendant may actually increase with the size of the jury and that a wide variety of voting rules, including simple majority rule, lead to much lower probabilities of both kinds of error.

Abstract: It is often suggested that requiring juries to reach a unanimous verdict reduces the probability of convicting an innocent defendant while increasing the probability of acquitting a guilty defendant. We construct a model that demonstrates how strategic voting by jurors undermines this basic intuition. We show that the unanimity rule may lead to a high probability of both kinds of error and that the probability of convicting an innocent defendant may actually increase with the size of the jury. Finally, we demonstrate that a wide variety of voting rules, including simple majority rule, lead to much lower probabilities of both kinds of error.

679 citations

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TL;DR: In this article, the authors analyzed two-candidate elections in which voters are uncertain about the realization of a state variable that affects the utility of all voters and showed that the fraction of voters whose vote depends on their private information goes to zero as the size of the electorate goes to infinity.

Abstract: We analyze two-candidate elections in which voters are uncertain about the realization of a state variable that affects the utility of all voters. Each voter has noisy private information about the state variable. We show that the fraction of voters whose vote depends on their private information goes to zero as the size of the electorate goes to infinity. Nevertheless, elections fully aggregate information in the sense that the chosen candidate would not change if all private information were common knowledge. Equilibrium voting behavior is to a large extent determined by the electoral rule, i.e., if a candidate is required to get at least x percent of the vote in order to win the election, then in equilibrium this candidate gets very close to x percent of the vote with probability close to one. Finally, if the distribution from which preferences are drawn is uncertain, then elections will generally not satisfy full information equivalence and the fraction of voters who take informative action does not converge to zero.

599 citations