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Journal Article

A resurrection of the Condorcet Jury Theorem

09 Jun 2009-Theoretical Economics (Theoretical Economics)-Vol. 4, Iss: 2, pp 227-252
TL;DR: In this article, the optimal size of a deliberating committee where there is no conflict of interest among individuals and information acquisition is costly is analyzed, and it is shown that any arbitrarily large committee aggregates the decentralized information more efficiently than the committee of size k*-2.
Abstract: This paper analyzes the optimal size of a deliberating committee where (i) there is no conflict of interest among individuals and (ii) information acquisition is costly. The committee members simultaneously decide whether to acquire information, and then make the ex-post efficient decision. The optimal committee size, k*, is shown to be bounded. The main result of this paper is that any arbitrarily large committee aggregates the decentralized information more efficiently than the committee of size k*-2. This result implies that oversized committees generate only small inefficiencies.

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Citations
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Book
01 Jan 2001
TL;DR: This chapter discusses Decision-Theoretic Foundations, Game Theory, Rationality, and Intelligence, and the Decision-Analytic Approach to Games, which aims to clarify the role of rationality in decision-making.
Abstract: Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

3,569 citations

Journal ArticleDOI
TL;DR: This work compares voluntary and compulsory voting in a Condorcet-type model in which voters have identical preferences but differential information, and finds that voluntary voting is welfare superior to compulsory voting when voting is costless and economizes on costs.

92 citations

Journal ArticleDOI
TL;DR: In this article, the authors review recent developments in the theory of committee decision-making, focusing on costly information acquisition, strategic information aggregation, and rules and processes that enhance the quality of the committee decision.
Abstract: This article reviews recent developments in the theory of committee decision-making. A committee consists of self-interested members who make a public decision by aggregating imperfect information dispersed among them according to a pre-specified decision rule. We focus on costly information acquisition, strategic information aggregation, and rules and processes that enhance the quality of the committee decision. Seeming inefficiencies of the committee decision-making process such as over-cautiousness, voting, and delay emerge as partial remedies to these incentive problems. Cet article passe en revue certains developpements recents dans la theorie de la prise de decision en comite. Un comite est defini comme un groupe de membres qui ont des interets particuliers et qui prennent une decision publique en agregeant une information imparfaite et dispersee a travers le groupe selon une regle de decision pre-etablie. Les auteurs portent leur attention sur l’acquisition couteuse d’information, l’agregation de l’information strategique, et les regles et procedures qui accroissent la qualite de la decision en comite. Ce qui apparait comme des inefficacites du processus de prise de decision en comite (sur-precaution, votes, delais) s’avere etre des remedes partiels aux problemes d’incitation.

45 citations

Journal ArticleDOI
TL;DR: This paper showed that the optimal agenda-setting power to the central bank chair is a strictly concave function of the degree of overconfidence and that the quality of advice produced by central bank staff is higher in a flat organization than in a hierarchical one.
Abstract: Monetary policy decisions are typically characterized by three features: (i) decisions are made by a committee, (ii) the committee members often disagree, and (iii) the chairman is almost never on the losing side in the vote. We show that the combination of overconfident policymakers and a chairman with agenda-setting rights can explain all these features. The optimal agenda-setting power to the chairman is a strictly concave function of the degree of overconfidence. We also show that the quality of advice produced by the central bank staff is higher in a flat organization than in a hierarchical one.

37 citations


Cites background from "A resurrection of the Condorcet Jur..."

  • ...∗Sveriges Riksbank. carl-andreas.claussen@riksbank.se †Norwegian University of Science and Technology. egilm@svt.ntnu.no ‡Norges Bank. oistein.roisland@norges-bank.no §Norwegian University of Science and Technology. ragnar.torvik@svt.ntnu.no...

    [...]

  • ...This literature describes under what conditions voting improves on decisions, see e.g. Koriyama and Szentes (2009) and references therein....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the authors study theoretically and experimentally a committee with common interests and show that voters are more likely to acquire information under majority rule, and attempt to counter the bias in favor of one alternative under unanimity rule.
Abstract: We study theoretically and experimentally a committee with common interests. Committee members do not know which of two alternatives is the best, but each member can acquire privately a costly signal before casting a vote under either majority or unanimity rule. In the experiment, as predicted by Bayesian equilibrium, voters are more likely to acquire information under majority rule, and attempt to counter the bias in favor of one alternative under unanimity rule. As opposed to Bayesian equilibrium predictions, however, many committee members vote when uninformed. Moreover, uninformed voting is strongly associated with a lower propensity to acquire information. We show that an equilibrium model of subjective prior beliefs can account for both these phenomena, and provides a good overall fit to the observed patterns of behavior both in terms of rational ignorance and biases.

35 citations

References
More filters
Book
01 Jan 2001
TL;DR: This chapter discusses Decision-Theoretic Foundations, Game Theory, Rationality, and Intelligence, and the Decision-Analytic Approach to Games, which aims to clarify the role of rationality in decision-making.
Abstract: Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

3,569 citations


Additional excerpts

  • ...j=0 μ 2m+ 1 j ¶ p (1− p)2m+1−j  (19) Suppose k (= 2m) is even....

    [...]

Book
01 Jan 1991
TL;DR: In this article, the authors propose a game theoretic approach to games based on the Bayesian model and demonstrate the existence of Nash Equilibria and the Focal Point Effect.
Abstract: Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

3,005 citations

Book
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

Journal ArticleDOI
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

Posted Content
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