Optimal Decision Mechanisms for Committees: Acquitting the Guilty
Deniz Kattwinkel, Alexander Winter
TL;DR
The paper studies optimal decision rules in a Condorcet Jury setting where agents privately observe signals and may be biased toward one alternative. It shows that, despite potential non-monotonicity, the principal can attain the best payoff with an interval voting mechanism defined by two cutoffs, implementing $A$ when the number of $A$-votes $k$ falls within $[k_L, k_U]$ (with possible mixing inside the interval). When there is a conflict of interest and the principal’s doubt threshold is high, the optimal interval rule becomes non-monotone, reflecting strategic incentives to report truthfully. The results link ancient judicial procedure to modern mechanism design and have practical implications for boards, committees, and juries by highlighting when anti-unanimous, interval-based rules outperform standard monotone rules.
Abstract
A group of privately informed agents chooses between two alternatives. How should the decision rule be designed if agents are known to be biased in favor of one of the options? We address this question by considering the Condorcet Jury Setting as a mechanism design problem. Applications include the optimal decision mechanisms for boards of directors, political committees, and trial juries. While we allow for any kind of mechanism, the optimal mechanism is a voting mechanism. In the terminology of the trial jury example: When jurors (agents) are more eager to convict than the lawmaker (principal), then the defendant should be convicted if and only if neither too many nor too few jurors vote to convict. This kind of mechanism accords with a judicial procedure from ancient Jewish law.