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A Model of Jury Decisions Where All Jurors Have The Same Evidence

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  • Christian List
  • Franz Dietrich

Abstract

In the classical Condorcet jury model, different jurors votes are independent random variables, where each juror has the same probability p>1/2 of voting for the correct alternative. The probability that the correct alternative will win under majority voting converges to 1 as the number of jurors increases. Hence the probability of an incorrect majority vote can be made arbitrarily small, a result that may seem unrealistic. A more realistic model is obtained by relaxing the assumption of independence and relating the vote of every juror to the same body of evidence. In terms of Bayesian trees, the votes are direct descendants not of the true state of the world (guilty or not guilty), but of the body of evidence, which in turn is a direct descendant of the true state of the world. This permits the possibility of a misleading body of evidence. Our main theorem shows that the probability that the correct alternative will win under majority voting converges to the probability that the body of evidence is not misleading, which may be strictly less than 1.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 2002-W23.

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Date of creation: 01 Sep 2002
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Handle: RePEc:oxf:wpaper:2002-w23

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Keywords: Condorcet jury theorem; conditional independence; interpretation of evidence; Bayesian trees;

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References

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  1. Daniel Berend & Jacob Paroush, 1998. "When is Condorcet's Jury Theorem valid?," Social Choice and Welfare, Springer, vol. 15(4), pages 481-488.
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Cited by:
  1. Dietrich Franz & Spiekermann Kai, 2010. "Epistemic Democracy with Defensible Premises," Research Memorandum 066, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Daniel Berend & Luba Sapir, 2007. "Monotonicity in Condorcet’s Jury Theorem with dependent voters," Social Choice and Welfare, Springer, vol. 28(3), pages 507-528, April.
  3. Franz Dietrich, 2006. "General Representation of Epistemically Optimal Procedures," Social Choice and Welfare, Springer, vol. 26(2), pages 263-283, April.
  4. Dietrich, Franz & Spiekermann, Kai, 2012. "Independent opinions? on the causal foundations of belief formation and jury theorems," MPRA Paper 40137, University Library of Munich, Germany, revised Oct 2010.
  5. Wojciech Charemza & Daniel Ladley, 2012. "MPC Voting, Forecasting and Inflation," Discussion Papers in Economics 12/23, Department of Economics, University of Leicester, revised Jan 2013.
  6. Bezalel Peleg & Shmuel Zamir, 2009. "On Bayesian-Nash Equilibria Satisfying the Condorcet Jury Theorem: The Dependent Case," Discussion Paper Series dp527, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  7. Christian List, 2002. "On the Significance of the Absolute Margin," Public Economics 0211004, EconWPA.

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