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A theory of unanimous jury voting with an ambiguous likelihood

Author

Listed:
  • Simona Fabrizi

    (The University of Auckland)

  • Steffen Lippert

    (The University of Auckland)

  • Addison Pan

    (Xi’an Jiaotong-Liverpool University, International Business School Suzhou (IBSS), Business Building (BS)
    AUT)

  • Matthew Ryan

    (AUT
    Centre for Mathematical Social Science at the University of Auckland)

Abstract

We examine collective decision-making in a jury voting game under the unanimity rule when voters have ambiguous beliefs. Unlike in existing studies (Ellis in Theoretical Economics 11:865–895, 2016; Fabrizi et al., in: AUT Economics Working Paper, 2021; Ryan in Theory and Decision 90:543–577, 2021), the locus of ambiguity is the likelihood function (signal precision) rather than the prior. This significantly alters the properties of symmetric equilibria. While prior ambiguity may induce multiple equilibria (Fabrizi et al., in: AUT Economics Working Paper, 2021; Ryan in Theory and Decision 90:543–577, 2021) we show that, under likelihood ambiguity, there exists a unique non-trivial symmetric responsive equilibrium that takes the same form as in the absence of ambiguity (Feddersen and Pesendorfer in The American Political Science Review 92:23–35, 1998). Moreover, likelihood ambiguity partially offsets the pernicious effects of pivotality on decision quality: the frequency of Type I error (convicting the innocent) is typically lower than in the absence of ambiguity.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:theord:v:93:y:2022:i:3:d:10.1007_s11238-021-09857-6
    DOI: 10.1007/s11238-021-09857-6
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    References listed on IDEAS

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    1. 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.
    2. Laohakunakorn, Krittanai & Levy, Gilat & Razin, Ronny, 2019. "Private and common value auctions with ambiguity over correlation," Journal of Economic Theory, Elsevier, vol. 184(C).
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    4. Ralph W. Bailey & Jürgen Eichberger & David Kelsey, 2005. "Ambiguity and Public Good Provision in Large Societies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(5), pages 741-759, December.
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    9. 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.
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    16. Addison Pan, 2019. "A Note on Pivotality," Games, MDPI, vol. 10(2), pages 1-8, June.
    17. 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.
    18. Simona Fabrizi & Steffen Lippert & Addison Pan & Matthew Ryan, 2024. "Unanimity under Ambiguity," Working Papers 2024-01, Auckland University of Technology, Department of Economics.
    19. Laohakunakorn, Krittanai & Levy, Gilat & Razin, Ronny, 2019. "Private and common value auctions with ambiguity over correlation," LSE Research Online Documents on Economics 101410, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Takashi Ui, 2023. "Strategic Ambiguity in Global Games," Papers 2303.12263, arXiv.org, revised Jul 2024.
    2. Simona Fabrizi & Steffen Lippert & Addison Pan & Matthew Ryan, 2021. "Unanimity under Ambiguity," Working Papers 2021-07, Auckland University of Technology, Department of Economics.
    3. Simona Fabrizi & Steffen Lippert & Addison Pan & Matthew Ryan, 2024. "Unanimity under Ambiguity," Working Papers 2024-01, Auckland University of Technology, Department of Economics.

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    More about this item

    Keywords

    Ambiguity; Voting; Belief updating; Pivotality;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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