IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v95y2023i3d10.1007_s11238-023-09926-y.html
   My bibliography  Save this article

Reasonable doubt

Author

Listed:
  • Liqun Liu

    (Xiamen University)

Abstract

We study the strategic interactions within testing in a model of political agency. A principal decides between convicting and acquitting an agent of unknown innocence based on a noisy signal that is manipulable by the agent’s unobserved actions. We identify conditions under which the principal sets a threshold conviction strategy in the form of “beyond a reasonable doubt.” We show that, in spite of strategic concerns, the amount of information that a principal can glean from the test is entirely determined by the threshold; in equilibrium, the threshold is set where the signal realization conveys just enough information to validate a conviction. As such, the game of testing is analytically equivalent to the principal’s statistical inference problem. We next examine how exogenous shocks on preference parameters affect the principal’s equilibrium threshold and welfare. In general, the principal benefits from being better at distinguishing types; whether she should increase or decrease the threshold depends crucially on whether the agent’s distribution of signals varies with types in the absence of manipulation.

Suggested Citation

  • Liqun Liu, 2023. "Reasonable doubt," Theory and Decision, Springer, vol. 95(3), pages 485-514, October.
    • Handle: RePEc:kap:theord:v:95:y:2023:i:3:d:10.1007_s11238-023-09926-y
    DOI: 10.1007/s11238-023-09926-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-023-09926-y
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-023-09926-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mookherjee, Dilip & Png, I P L, 1994. "Marginal Deterrence in Enforcement of Law," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 1039-1066, October.
    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. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    4. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    5. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    6. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    7. Scott Ashworth & Ethan Bueno de Mesquita & Amanda Friedenberg, 2017. "Accountability and Information in Elections," American Economic Journal: Microeconomics, American Economic Association, vol. 9(2), pages 95-138, May.
    8. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    9. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 355-374.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mailath, George J. & Nöldeke, Georg, 2006. "Extreme Adverse Selection, Competitive Pricing, and Market Breakdown," Working papers 2006/09, Faculty of Business and Economics - University of Basel.
    2. Mailath, George J. & Nöldeke, Georg, 2008. "Does competitive pricing cause market breakdown under extreme adverse selection?," Journal of Economic Theory, Elsevier, vol. 140(1), pages 97-125, May.
    3. Samuel Häfner & Curtis R. Taylor, 2022. "On young Turks and yes men: optimal contracting for advice," RAND Journal of Economics, RAND Corporation, vol. 53(1), pages 63-94, March.
    4. Schmidbauer, Eric & Lubensky, Dmitry, 2018. "New and improved?," International Journal of Industrial Organization, Elsevier, vol. 56(C), pages 26-48.
    5. Yun Wang, 2015. "Bayesian Persuasion with Multiple Receivers," Working Papers 2015-03-24, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    6. Eduardo Perez-Richet, 2014. "Interim Bayesian Persuasion: First Steps," American Economic Review, American Economic Association, vol. 104(5), pages 469-474, May.
    7. Shmuel Leshem, 2010. "The benefits of a right to silence for the innocent," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 398-416, June.
    8. Winand Emons & Claude Fluet, 2019. "Strategic communication with reporting costs," Theory and Decision, Springer, vol. 87(3), pages 341-363, October.
    9. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    10. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
    11. Li Hao & Wing Suen, 2009. "Viewpoint: Decision-making in committees," Canadian Journal of Economics, Canadian Economics Association, vol. 42(2), pages 359-392, May.
    12. Anton Kolotilin & Tymofiy Mylovanov & Andriy Zapechelnyuk & Ming Li, 2017. "Persuasion of a Privately Informed Receiver," Econometrica, Econometric Society, vol. 85(6), pages 1949-1964, November.
    13. Hedlund, Jonas, 2017. "Bayesian persuasion by a privately informed sender," Journal of Economic Theory, Elsevier, vol. 167(C), pages 229-268.
    14. Sun, Wuqin & Wang, Dazhong & Zhang, Yue, 2018. "Optimal profit sharing mechanisms with type-dependent outside options," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 57-66.
    15. Archishman Chakraborty & Rick Harbaugh, 2014. "Persuasive Puffery," Marketing Science, INFORMS, vol. 33(3), pages 382-400, May.
      • Archishman Chakraborty & Rick Harbaugh, 2012. "Persuasive Puffery," Working Papers 2012-05, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
    16. Terence Johnson, 2009. "Matching Through Position Auctions," Working Papers 001, University of Notre Dame, Department of Economics, revised Jan 2011.
    17. Jianan Wang, 2022. "Partially verifiable deliberation in voting," Public Choice, Springer, vol. 190(3), pages 457-481, March.
    18. Archishman Chakraborty & Rick Harbaugh, 2010. "Persuasion by Cheap Talk," American Economic Review, American Economic Association, vol. 100(5), pages 2361-2382, December.
      • Archishman Chakraborty & Rick Harbaugh, 2006. "Persuasion by Cheap Talk," Working Papers 2006-10, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy, revised Oct 2009.
    19. Ambrus, Attila & Egorov, Georgy, 2017. "Delegation and nonmonetary incentives," Journal of Economic Theory, Elsevier, vol. 171(C), pages 101-135.
    20. de Haan, Thomas & Offerman, Theo & Sloof, Randolph, 2011. "Noisy signaling: Theory and experiment," Games and Economic Behavior, Elsevier, vol. 73(2), pages 402-428.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:95:y:2023:i:3:d:10.1007_s11238-023-09926-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.