When is Condorcet's Jury Theorem valid?

1998 ◽  
Vol 15 (4) ◽  
pp. 481-488 ◽  
Author(s):  
Daniel Berend ◽  
Jacob Paroush
Keyword(s):  
Condorcet’S Jury Theorem ◽  
Jury Theorem

Threshold Phenomena and Influence: Perspectives from Mathematics, Computer Science, and Economics

2005 ◽  
Author(s):  
Gil Kalai ◽  
Shmuel Safra
Keyword(s):  
Computer Science ◽  
Political Science ◽  
Monotone Function ◽  
Majority Voting ◽  
Simple Majority ◽  
Condorcet’S Jury Theorem ◽  
Threshold Phenomenon ◽  
Threshold Phenomena ◽  
Aggregation Of Information ◽  
Jury Theorem

Threshold phenomena refer to settings in which the probability for an event to occur changes rapidly as some underlying parameter varies. Threshold phenomena play an important role in probability theory and statistics, physics, and computer science, and are related to issues studied in economics and political science. Quite a few questions that come up naturally in those fields translate to proving that some event indeed exhibits a threshold phenomenon, and then finding the location of the transition and how rapid the change is. The notions of sharp thresholds and phase transitions originated in physics, and many of the mathematical ideas for their study came from mathematical physics. In this chapter, however, we will mainly discuss connections to other fields. A simple yet illuminating example that demonstrates the sharp threshold phenomenon is Condorcet's jury theorem, which can be described as follows. Say one is running an election process, where the results are determined by simple majority, between two candidates, Alice and Bob. If every voter votes for Alice with probability p > 1/2 and for Bob with probability 1 — p, and if the probabilities for each voter to vote either way are independent of the other votes, then as the number of voters tends to infinity the probability of Alice getting elected tends to 1. The probability of Alice getting elected is a monotone function of p, and when there are many voters it rapidly changes from being very close to 0 when p < 1/2 to being very close to 1 when p > 1/2. The reason usually given for the interest of Condorcet's jury theorem to economics and political science [535] is that it can be interpreted as saying that even if agents receive very poor (yet independent) signals, indicating which of two choices is correct, majority voting nevertheless results in the correct decision being taken with high probability, as long as there are enough agents, and the agents vote according to their signal. This is referred to in economics as asymptotically complete aggregation of information.

scholarly journals Epistemic democracy and political legitimacy

2015 ◽  
Author(s):  
◽  
Sheng Zhang
Keyword(s):  
Political Legitimacy ◽  
The State ◽  
Epistemic Value ◽  
Democratic Legitimacy ◽  
Epistemic Democracy ◽  
Condorcet’S Jury Theorem ◽  
Jury Theorem ◽  
The Common ◽  
Egalitarian Principle

My dissertation aims to answer two questions: (1) Is democracy epistemically valuable? (2) Is the epistemic value of democracy, if it has any, necessary for justifying its legitimacy? I argue that democracy in certain form can be epistemically valuable. However, I also argue that the epistemic value of democracy is not necessary for justifying its legitimacy. To defend the epistemic value of democracy, I propose a postdeliberation version of Condorcet's jury theorem. I argue that this version of the jury theorem can avoid the common challenges against the classic version. To reject the necessity of epistemic value for democratic legitimacy, I argue that, given that the epistemic value of democracy is subject to disagreement, it cannot be used to justify legitimacy. In addition, I provide a purely proceduralist argument for democratic legitimacy, which appeals to the egalitarian principle that every citizens ought to be equally respected by the state. This argument, if succeeds, shows that the epistemic value of democracy is not necessary for justifying democratic legitimacy.

Monotonicity in Condorcet’s Jury Theorem with dependent voters

2006 ◽  
Vol 28 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Daniel Berend ◽  
Luba Sapir
Keyword(s):  
Condorcet’S Jury Theorem ◽  
Jury Theorem

scholarly journals An Interpretation of Weights in Linear Opinion Pooling

Episteme ◽  
2020 ◽  
pp. 1-15
Author(s):  
Jan-Willem Romeijn
Keyword(s):  
Condorcet’S Jury Theorem ◽  
Bayesian Update ◽  
Opinion Pooling ◽  
Jury Theorem ◽  
New Interpretation ◽  
Modelling Assumptions

Abstract This paper explores the fact that linear opinion pooling can be represented as a Bayesian update on the opinions of others. It uses this fact to propose a new interpretation of the pooling weights. Relative to certain modelling assumptions the weights can be equated with the so-called truth-conduciveness known from the context of Condorcet's jury theorem. This suggests a novel way to elicit the weights.

scholarly journals Condorcet’s jury theorem: General will and epistemic democracy

2018 ◽  
Vol 61 (4) ◽  
pp. 147-170
Author(s):  
Miljan Vasic
Keyword(s):  
Real Life ◽  
Historical Source ◽  
General Will ◽  
Epistemic Democracy ◽  
Condorcet’S Jury Theorem ◽  
Life Conditions ◽  
Jury Theorem ◽  
Epistemic Theory ◽  
Theory Of Democracy

My aim in this paper is to explain what Condorcet?s jury theorem is, and to examine its central assumptions, its significance to the epistemic theory of democracy and its connection with Rousseau?s theory of general will. In the first part of the paper I will analyze an epistemic theory of democracy and explain how its connection with Condorcet?s jury theorem is twofold: the theorem is at the same time a contributing historical source, and the model used by the authors to this day. In the second part I will specify the purposes of the theorem itself, and examine its underlying assumptions. Third part will be about an interpretation of Rousseau?s theory, which is given by Grofman and Feld relying on Condorcet?s jury theorem, and about criticisms of such interpretation. In the fourth, and last, part I will focus on one particular assumption of Condorcet?s theorem, which proves to be especially problematic if we would like to apply the theorem under real-life conditions; namely, the assumption that voters choose between two options only.

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