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Reasonable doubt

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  • 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
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    References listed on IDEAS

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