Condorcet Jury Theorem: An example in which informative voting is rational but leads to inefficient information aggregation

2014 ◽  
Vol 125 (1) ◽  
pp. 25-28 ◽  
Author(s):  
Johanna M.M. Goertz ◽  
François Maniquet
Episteme ◽  
2018 ◽  
Vol 17 (4) ◽  
pp. 498-518
Author(s):  
Patrick Grim ◽  
Aaron Bramson ◽  
Daniel J. Singer ◽  
William J. Berger ◽  
Jiin Jung ◽  
...  

ABSTRACTEpistemic justifications for democracy have been offered in terms of two different forms of information aggregation and decision-making. The Condorcet Jury Theorem is appealed to as a justification in terms of votes, and the Hong–Page ‘diversity trumps ability’ result is appealed to as a justification in terms of deliberation in the form of collaborative search. Both results, however, are models of full and direct participation across a population. In this paper, we contrast how these results hold up within the familiar structure of a representative hierarchy. We first consider extant analytic work that shows that representation inevitably weakens the voting results of the Condorcet Jury Theorem. We then go on to show that collaborative search, as modeled by Hong and Page, holds its own within hierarchical representation. In a variation on the dynamics of group search, representation even shows a slight edge over direct participation. This contrast illustrates how models of information aggregation vary when put into a representative structure. While some of the epistemic merits of democracy are lost when voting is done hierarchically, modeling results show that representation can preserve and even slightly amplify the epistemic virtues of collaborative search.


1998 ◽  
Vol 92 (2) ◽  
pp. 413-418 ◽  
Author(s):  
Andrew McLennan

“Naïve” Condorcet Jury Theorems automatically have “sophisticated” versions as corollaries. A Condorcet Jury Theorem is a result, pertaining to an election in which the agents have common preferences but diverse information, asserting that the outcome is better, on average, than the one that would be chosen by any particular individual. Sometimes there is the additional assertion that, as the population grows, the probability of an incorrect decision goes to zero. As a consequence of simple properties of common interest games, whenever “sincere” voting leads to the conclusions of the theorem, there are Nash equilibria with these properties. In symmetric environments the equilibria may be taken to be symmetric.


1996 ◽  
Vol 90 (1) ◽  
pp. 34-45 ◽  
Author(s):  
David Austen-Smith ◽  
Jeffrey S. Banks

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.


Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1098
Author(s):  
Keiichi Morimoto

Using a simple model of a coordination game, this paper explores how the information use of individuals affects an optimal committee size. Although enlarging the committee promotes information aggregation, it also stimulates the members’ coordination motive and distorts their voting behavior through higher-order beliefs. On the determination of a finite optimal committee size, the direction and degree of strategic interactions matter. When the strategic complementarity among members is strong, a finite optimal committee size exists. In contrast, it does not exist under strategic substitution. This mechanism is applied to the design of monetary policy committees in a New Keynesian model in which a committee conducts monetary policy under imperfect information.


Author(s):  
Hélène Landemore

This chapter argues that majority rule is a useful complement of inclusive deliberation, not just because majority rule is more efficient timewise, but because it has distinct epistemic properties of its own. It also stresses that majority rule is best designed for collective prediction—that is, the identification of the best options out of those selected during the deliberative phase. Of all the competing alternatives (rule of one or rule of the few), majority rule maximizes the chances of predicting the right answer among the proposed options. The chapter considers several accounts of the epistemic properties of majority rule, including the Condorcet Jury Theorem, the Miracle of Aggregation, and a more fine-grained model based on cognitive diversity.


2001 ◽  
Vol 2 (3) ◽  
pp. 243-249 ◽  
Author(s):  
Ruth Ben-Yashar ◽  
Shmuel Nitzan

Synthese ◽  
2021 ◽  
Author(s):  
Scott Hill ◽  
Renaud-Philippe Garner

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