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Unanimity under Ambiguity

Author

Listed:
  • Simona Fabrizi

    (Department of Economics and Centre for Mathematical Social Science, University of Auckland, New Zealand)

  • Steffen Lippert

    (Department of Economics and Centre for Mathematical Social Science, University of Auckland, New Zealand.)

  • Addison Pan

    (International Office and Centre for Mathematical Social Science, University of Auckland, New Zealand.)

  • Matthew Ryan

    (School of Economics and Finance, Auckland University of Technology, New Zealand, and Centre for Mathematical Social Science, University of Auckland, New Zealand.)

Abstract

This paper considers a binary decision to be made by a committee- canonically, a jury- through a voting procedure. Each juror must vote on whether a defendant is guilty or not guilty. The voting rule aggregates the votes to determine whether the defendant is convicted or acquitted. We focus on the unanimity rule (convict if and only if all vote guilty), and we consider jurors who share ambiguous prior beliefs as in Ellis (2016). Our contribution is twofold. First, we identify all symmetric equilibria of these voting games. Second, we show that ambiguity may drastically undermine McLennan's (1998) results on decision quality: unlike in the absence of ambiguity, the ex ante optimal symmetric strategy profile need not be an equilibrium; indeed, there are games for which it is possible to reduce both types of error starting from any (non-trivial) equilibrium.

Suggested Citation

  • Simona Fabrizi & Steffen Lippert & Addison Pan & Matthew Ryan, 2024. "Unanimity under Ambiguity," Working Papers 2024-01, Auckland University of Technology, Department of Economics.
    • Handle: RePEc:aut:wpaper:2024-01
    as

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    File URL: https://www.aut.ac.nz/__data/assets/pdf_file/0010/873685/working-paper-24_01.pdf
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    References listed on IDEAS

    as
    1. Guarnaschelli, Serena & McKelvey, Richard D. & Palfrey, Thomas R., 2000. "An Experimental Study of Jury Decision Rules," American Political Science Review, Cambridge University Press, vol. 94(2), pages 407-423, June.
    2. Feddersen, Timothy & Pesendorfer, Wolfgang, 1998. "Convicting the Innocent: The Inferiority of Unanimous Jury Verdicts under Strategic Voting," American Political Science Review, Cambridge University Press, vol. 92(1), pages 23-35, March.
    3. Addison Pan, 2019. "A Note on Pivotality," Games, MDPI, vol. 10(2), pages 1-8, June.
    4. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    5. Coughlan, Peter J., 2000. "In Defense of Unanimous Jury Verdicts: Mistrials, Communication, and Strategic Voting," American Political Science Review, Cambridge University Press, vol. 94(2), pages 375-393, June.
    6. Simona Fabrizi & Steffen Lippert & Addison Pan & Matthew Ryan, 2022. "A theory of unanimous jury voting with an ambiguous likelihood," Theory and Decision, Springer, vol. 93(3), pages 399-425, October.
    7. Austen-Smith, David & Banks, Jeffrey S., 1996. "Information Aggregation, Rationality, and the Condorcet Jury Theorem," American Political Science Review, Cambridge University Press, vol. 90(1), pages 34-45, March.
    8. Jacob K. Goeree & Leeat Yariv, 2011. "An Experimental Study of Collective Deliberation," Econometrica, Econometric Society, vol. 79(3), pages 893-921, May.
    9. S. Nageeb Ali & Jacob K. Goeree & Navin Kartik & Thomas R. Palfrey, 2008. "Information Aggregation in Standing and Ad Hoc Committees," American Economic Review, American Economic Association, vol. 98(2), pages 181-186, May.
    10. ,, 2016. "Condorcet meets Ellsberg," Theoretical Economics, Econometric Society, vol. 11(3), September.
    11. Matthew Ryan, 2021. "Feddersen and Pesendorfer meet Ellsberg," Theory and Decision, Springer, vol. 90(3), pages 543-577, May.
    12. McLennan, Andrew, 1998. "Consequences of the Condorcet Jury Theorem for Beneficial Information Aggregation by Rational Agents," American Political Science Review, Cambridge University Press, vol. 92(2), pages 413-418, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    : ambiguous priors; voting problems; decision quality;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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