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Condorcet's jury theorem
About: Condorcet's jury theorem is a research topic. Over the lifetime, 314 publications have been published within this topic receiving 13095 citations.
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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
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
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
TL;DR: Kemeny's rule as discussed by the authors is the unique social welfare function that satisfies a variant of independence of irrelevant alternatives together with several other standard properties, and is the most likely ranking of the alternatives.
Abstract: Condcrcet's criterion states that an alternative that defeats every other by a simple majority is the socially optimal choice. Condorcet argued that if the object of voting is to determine the “best” decision for society but voters sometimes make mistakes in their judgments, then the majority alternative (if it exists) is statistically most likely to be the best choice. Strictly speaking, this claim is not true; in some situations Bordas rule gives a sharper estimate of the best alternative. Nevertheless, Condorcet did propose a novel and statistically correct rule for finding the most likely ranking of the alternatives. This procedure, which is sometimes known as “Kemeny's rule,” is the unique social welfare function that satisfies a variant of independence of irrelevant alternatives together with several other standard properties.
618 citations
TL;DR: In this article, a Condorcet social choice function elects the candidate that beats every other candidate under simple majority when such a candidate exists, and several extensions of the simple majority principle have been proposed.
Abstract: A Condorcet social choice function elects the candidate that beats every other candidate under simple majority when such a candidate exists. Various extensions of Condorcet’s simple majority principle that deal with situations that have no simple majority winner have been proposed.Nine Condorcet social choice functions are analyzed and compared on the basis of how well they satisfy a number of conditions for social choice functions. The conditions include several generalizations of Condorcet’s Principle. Remarks on the relative merits of the nine basic functions are included.
549 citations