The Classic Framework

2018 ◽  
Author(s):  
Robert E. Goodin ◽  
Kai Spiekermann
Keyword(s):  
Group Size ◽  
Majority Vote ◽  
Asymptotic Result ◽  
Correct Decision ◽  
Independence Assumption ◽  
Condorcet Jury Theorem ◽  
Correct Alternative ◽  
Jury Theorem

In the classic setup of the Condorcet Jury Theorem, voters decide by majority vote between two different options. The Competence Assumption is that all voters are more likely than not to identify the correct alternative with the same probability. The Independence Assumption is that the votes are statistically independent. The Sincerity Assumption is that the voters always vote for the alternative they believe to be correct. Two results follow if these conditions are met. First, the Non-asymptotic Result says that the probability of a correct decision increases in group size. Second, the Asymptotic Result says that this probability converges to 1. We show that this convergence happens very quickly.

scholarly journals A Condorcet Jury Theorem for Large Poisson Elections with Multiple Alternatives

Games ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 2
Author(s):  
Johanna M. M. Goertz
Keyword(s):  
The State ◽  
Previous Literature ◽  
Plurality Rule ◽  
Condorcet Jury Theorem ◽  
Correct Alternative ◽  
State Of Nature ◽  
Voting Game ◽  
Common Interests ◽  
Jury Theorem ◽  
Two Alternatives

Herein, we prove a Condorcet jury theorem (CJT) for large elections with multiple alternatives. Voters have common interests that depend on an unknown state of nature. Each voter receives an imprecise private signal about the state of nature and then submits one vote (simple plurality rule). We also assume that this is a Poisson voting game with population uncertainty. The question is whether the simple plurality rule aggregates information efficiently so that the correct alternative is elected with probability tending to one when the number of voters tends to infinity. The previous literature shows that the CJT holds for large elections with two alternatives, but there is also an example of a large election with three alternatives that has an inefficient equilibrium. We show that there always exists an efficient equilibrium, independent of the number of alternatives. Under certain circumstances (informative types), it is unique in elections with two alternatives. The existence of inefficient equilibria in elections with more than two alternatives is generic.

scholarly journals The metaethical dilemma of epistemic democracy

2021 ◽  
pp. 1-19
Author(s):  
Christoph Schamberger
Keyword(s):  
Moral Realism ◽  
Epistemic Democracy ◽  
Condorcet Jury Theorem ◽  
Correct Alternative ◽  
Jury Theorem ◽  
High Chance ◽  
Moral Facts

Abstract Epistemic democracy aims to show, often by appeal to the Condorcet Jury Theorem, that democracy has a high chance of reaching correct decisions. It has been argued that epistemic democracy is compatible with various metaethical accounts, such as moral realism, conventionalism and majoritarianism. This paper casts doubt on that thesis and reveals the following metaethical dilemma: if we adopt moral realism, it is doubtful that voters are, on average, more than 0.5 likely to track moral facts and identify the correct alternative. By contrast, if we adopt conventionalism or majoritarianism, we cannot expect that voters are both competent and sincere. Either way, the conditions for the application of Condorcet’s theorem are not met.

Independence Revisited

2018 ◽  
Author(s):  
Robert E. Goodin ◽  
Kai Spiekermann
Keyword(s):  
Final Section ◽  
The State ◽  
Statistical Independence ◽  
Decision Situation ◽  
Independence Assumption ◽  
Condorcet Jury Theorem ◽  
Condorcet’S Jury Theorem ◽  
Common Causes ◽  
The World ◽  
Jury Theorem

The Independence Assumption is the most misunderstood premise of the Condorcet Jury Theorem. This chapter shows, first, that absence of direct voter interaction is neither necessary nor sufficient for Independence. Second, we explain that the statistical independence required is conditional: in Condorcet’s jury theorem, conditional on the state of the world; in other jury theorems, conditional on the evidence, on common causes, or on the whole decision situation. This insight leads, third, to the ‘Best Responder Corollary’, a jury theorem that is better suited to dealing with the inevitable interdependence of votes caused by common causes. In the final section, we discuss epistemic implications.

Extensions

2018 ◽  
Author(s):  
Robert E. Goodin ◽  
Kai Spiekermann
Keyword(s):  
Decision Procedures ◽  
Borda Count ◽  
Asymptotic Result ◽  
Condorcet Jury Theorem ◽  
Jury Theorem

The classic Condorcet Jury Theorem comes with demanding assumptions. This chapter shows that similar results can be derived if the assumptions are weakened. First, if the Competence Assumption is weakened by allowing for heterogeneous voter competence, the Asymptotic Result of the jury theorem still obtains (though the Non-asymptotic Result does only under very specific assumptions). Second, the number of alternatives can be more than two for a structurally similar jury theorem, using plurality voting. Third, different decision procedures, such as the Borda count or the Condorcet pairwise criterion, still lead to the Asymptotic Result. While the Borda count and the Condorcet pairwise criterion have a slight epistemic advantage over plurality voting, for large competent groups this difference is negligible.

Second Mechanism of Democratic Reason: Majority Rule

2012 ◽  
Author(s):  
Hélène Landemore
Keyword(s):  
Majority Rule ◽  
Cognitive Diversity ◽  
Condorcet Jury Theorem ◽  
Fine Grained ◽  
Model Based ◽  
Jury Theorem ◽  
The Right

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.

The invalidity of the Condorcet Jury Theorem under endogenous decisional skills

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

scholarly journals Virtue signalling and the Condorcet Jury theorem

Synthese ◽  
2021 ◽  
Author(s):  
Scott Hill ◽  
Renaud-Philippe Garner
Keyword(s):  
Condorcet Jury Theorem ◽  
Jury Theorem
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