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Jury Theorems

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  • Dietrich, Franz
  • Spiekermann, Kai

Abstract

We give a review of jury theorems, including Condorcet's (1785) classic theorem and several later refinements and departures. The review comes with a critique of jury theorems from a social-epistemology perspective. We assess the plausibility of the theorems' conclusions and premises and the potential of jury theorems to serve as formal arguments for the 'wisdom of crowds'. In particular, we argue (i) that there is a fundamental tension between voters' independence and voters' competence, hence between the two premises of typical jury theorems; (ii) that the (asymptotic) conclusion that 'huge groups are infallible', reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (non-asymptotic) conclusion that 'larger groups are more reliable', also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the 'wisdom of crowds'.

Suggested Citation

  • Dietrich, Franz & Spiekermann, Kai, 2016. "Jury Theorems," MPRA Paper 72951, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:72951
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    References listed on IDEAS

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    1. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    2. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
    3. Serguei Kaniovski, 2010. "Aggregation of correlated votes and Condorcet’s Jury Theorem," Theory and Decision, Springer, vol. 69(3), pages 453-468, September.
    4. Nitzan, Shmuel & Paroush, Jacob, 1982. "Optimal Decision Rules in Uncertain Dichotomous Choice Situations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 289-297, June.
    5. Ben-Yashar, Ruth C & Nitzan, Shmuel I, 1997. "The Optimal Decision Rule for Fixed-Size Committees in Dichotomous Choice Situations: The General Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 175-186, February.
    6. Ladha, Krishna K., 1995. "Information pooling through majority-rule voting: Condorcet's jury theorem with correlated votes," Journal of Economic Behavior & Organization, Elsevier, vol. 26(3), pages 353-372, May.
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    More about this item

    Keywords

    jury theorems; Condorcet jury theorem; social epistemology; wisdom of crowds;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D79 - Microeconomics - - Analysis of Collective Decision-Making - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • K0 - Law and Economics - - General

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