Suppose you run a home exam, where students should report their own scores but can cheat freely. You can, if needed, call a limited number of students to class and verify their actual performance against their reported score. We consider the class of mechanisms where truthful reporting is a dominant strategy, and truthful agents are never penalized -- even off-equilibrium. How many students do we need to verify, in expectation, if we want to minimize the bias, i.e., the difference between agents' competence and their expected grade? When perfect verification is available, we characterize the best possible tradeoff between these requirements and provide a simple parametrized mechanism that is optimal in the class for any distribution of agents' types. When verification is noisy, the task becomes much more challenging. We show how proper scoring rules can be leveraged in different ways to construct truthful mechanisms with a good (though not necessarily optimal) tradeoff.

翻译：假设您组织一场家庭考试，学生需自行报告成绩但可能随意作弊。如有必要，您可以随机抽取部分学生到课堂，将其实际表现与报告成绩进行核实验证。本文研究满足以下条件的机制类：真实报告成为占优策略，且诚实参与者绝不会受到惩罚——即使处于非均衡路径。若我们希望最小化偏差（即参与者实际能力与其期望成绩的差异），则预期需要核验多少学生？当存在完美验证时，我们刻画了这些要求间的最优权衡关系，并提出一种简单的参数化机制，该机制对任意参与者类型分布均在该机制类中达到最优。当验证存在噪声时，问题变得更具挑战性。我们展示了如何通过不同方式运用恰当评分规则，构建具有良好（虽未必最优）权衡特性的真实报告机制。