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 A functional equation of tail-balance for continuous signals in the Condorcet Jury Theorem

2020 ◽  
Author(s):  
Steve Alpern ◽  
Bo Chen ◽  
Adam J. Ostaszewski
Keyword(s):  
Functional Equation ◽  
Random Variable ◽  
The State ◽  
Condorcet Jury Theorem ◽  
Signal Distribution ◽  
Binary Signal ◽  
Marquis De Condorcet ◽  
Jury Theorem ◽  
Natural Symmetry ◽  
States Of Nature

Abstract Consider an odd-sized jury, which determines a majority verdict between two equiprobable states of Nature. If each juror independently receives a binary signal identifying the correct state with identical probability p, then the probability of a correct verdict tends to one as the jury size tends to infinity (Marquis de Condorcet in Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix, Imprim. Royale, Paris, 1785). Recently, Alpern and Chen (Eur J Oper Res 258:1072–1081, 2017, Theory Decis 83:259–282, 2017) developed a model where jurors sequentially receive independent signals from an interval according to a distribution which depends on the state of Nature and on the juror’s “ability”, and vote sequentially. This paper shows that, to mimic Condorcet’s binary signal, such a distribution must satisfy a functional equation related to tail-balance, that is, to the ratio $$\alpha (t)$$ α ( t ) of the probability that a mean-zero random variable satisfies X$$>t$$ > t given that $$|X|>t$$ | X | > t . In particular, we show that under natural symmetry assumptions the tail-balances $$\alpha (t)$$ α ( t ) uniquely determine the signal distribution and so the distributions assumed in Alpern and Chen (Eur J Oper Res 258:1072–1081, 2017, Theory Decis 83:259–282, 2017) are uniquely determined for $$\alpha (t)$$ α ( t ) linear.

scholarly journals The Condorcet Jury Theorem with Information Acquisition

Games ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 79
Author(s):  
Jun Chen
Keyword(s):  
Information Acquisition ◽  
Marginal Cost ◽  
Costly Information ◽  
Condorcet Jury Theorem ◽  
Aggregate Information ◽  
Committee Decision ◽  
Private Signals ◽  
Jury Theorem ◽  
Rational Ignorance ◽  
Two Alternatives

We analyze a committee decision in which individuals with common preferences are uncertain which of two alternatives is better for them. Members can acquire costly information. Private signals and information choice are both continuous. As is consistent with Down’s rational ignorance hypothesis, each member acquires less information in a larger committee and tends to acquire zero information when the committee size goes to infinity. However, with more members, a larger committee can gather more aggregate information in equilibrium. The aggregate information is infinite with the size going to infinity if and only if marginal cost at “zero information acquisition” is zero. When the marginal cost at “zero information acquisition” is positive, the probability of making an appropriate decision tends to be less than one.

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.

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 Information Aggregation, Rationality, and the Condorcet Jury Theorem

1996 ◽  
Vol 90 (1) ◽  
pp. 34-45 ◽  
Author(s):  
David Austen-Smith ◽  
Jeffrey S. Banks
Keyword(s):  
Decision Making ◽  
Nash Equilibrium ◽  
Information Aggregation ◽  
Collective Decision Making ◽  
Single Individual ◽  
Condorcet Jury Theorem ◽  
Jury Theorem ◽  
Sincere Voting ◽  
Two Alternatives ◽  
Better Than

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.

Implications

2017 ◽  
Author(s):  
Karl Widerquist ◽  
Grant S. McCall
Keyword(s):  
Property Rights ◽  
The State ◽  
Natural Property ◽  
Government Failure ◽  
State Of Nature ◽  
Best Response ◽  
Lockean Proviso ◽  
Definition Of ◽  
Taking Action ◽  
Disadvantaged People

Earlier chapters of this book found that the Hobbesian hypothesis is false; the Lockean proviso is unfulfilled; contemporary states and property rights systems fail to meet the standard that social contract and natural property rights theories require for their justification. This chapter assesses the implications of those findings for the two theories. Section 1 argues that, whether contractarians accept or reject these findings, they need to clarify their argument to remove equivocation. Section 2 invites efforts to refute this book’s empirical findings. Section 3 discusses a response open only to property rights theorists: concede this book’s empirical findings and blame government failure. Section 4 considers the argument that this book misidentifies the state of nature. Section 5 considers a “bracketing strategy,” which admits that observed stateless societies fit the definition of the state of nature, but argues that they are not the relevant forms of statelessness today. Section 6 discusses the implications of accepting both the truth and relevance of the book’s findings, concluding that the best response is to fulfil the Lockean proviso by taking action to improve the lives of disadvantaged people.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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