A Model of Jury Decisions where all Jurors have the same Evidence

Abstract

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is a shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’.

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References

  1. D. Austen-Smith J. Banks (1996) ArticleTitle‘Information Aggregation, Rationality, and the Condorcet Jury Theorem’ American Political Science Review 90 34–45

    Google Scholar 

  2. P.J. Boland (1989) ArticleTitle‘Majority Systems and the Condorcet Jury Theorem’ Statistician 38 181–189

    Google Scholar 

  3. P.J. Boland F. Proschan Y.L. Tong (1989) ArticleTitle‘Modelling dependence in simple and indirect majority systems’ Journal of Applied Probability 26 81–88

    Google Scholar 

  4. L. Bovens E. Olsson (2000) ArticleTitle‘Coherentism, Reliability and Bayesian Networks’ Mind 109 685–719 Occurrence Handle10.1093/mind/109.436.685

    Article  Google Scholar 

  5. D. Corfield J. Williamson (Eds) (2001) Foundations of Bayesianism Kluwer Dordrecht

    Google Scholar 

  6. Dietrich, F.: 2003, ‘General Representation of Epistemically Optimal Procedures’, Social Choice and Welfare, forthcoming.

  7. D. Estlund (1994) ArticleTitle‘Opinion leaders, independence and Condorcet’s Jury Theorem’ Theory and Decision 36 131–162 Occurrence Handle10.1007/BF01079210

    Article  Google Scholar 

  8. B. Fitelson (2001) ArticleTitle‘A Bayesian Account of Independent Evidence with Application’ Philosophy of Science 68 S123–S140 Occurrence Handle10.1086/392903

    Article  Google Scholar 

  9. B. Grofman G. Owen S.L. Feld (1983) ArticleTitle‘Thirteen Theorems in search of the Truth’ Theory and Decision 15 261–278 Occurrence Handle10.1007/BF00125672

    Article  Google Scholar 

  10. K.K. Lahda (1992) ArticleTitle‘The Condorcet Jury Theorem, Free Speech, and Correlated Votes’ American Journal of Political Science 36 617–634

    Google Scholar 

  11. C. List R.E. Goodin (2001) ArticleTitle‘Epistemic Democracy: Generalizing the Condorcet Jury Theorem’ Journal of Political Philosophy 9 277–306 Occurrence Handle10.1111/1467-9760.00128

    Article  Google Scholar 

  12. List, C.: 2004a, ‘On the Significance of the Absolute Margin’, British Journal for the Philosophy of Science, forthcoming.

  13. List, C.: 2004b, ‘The Epistemology of Special Majority Voting’, Social Choice and Welfare, forthcoming.

  14. S. Nitzan J. Paroush (1984) ArticleTitle‘The Significance of Independent decisions in Uncertain Dichotomous Choice Situations’ Theory and Decision 17 47–60 Occurrence Handle10.1007/BF00140055

    Article  Google Scholar 

  15. G. Owen (1986) ‘Fair Indirect Majority Rules B. Grofman G. Owen (Eds) Information Pooling and Group Decision Making Jai Press Greenwich, CT

    Google Scholar 

  16. Pearl, J.: 2000, ‘Causality: models, reasoning, and inference’, Cambridge (C.U.P.).

Download references

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Correspondence to Franz Dietrich.

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Dietrich, F., List, C. A Model of Jury Decisions where all Jurors have the same Evidence. Synthese 142, 175–202 (2004). https://doi.org/10.1007/s11229-004-1276-z

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Keywords

  • Bayesian Network
  • Classical Model
  • Expert Panel
  • Majority Decision
  • Independence Assumption