Optimal Impartial Mechanisms

在许多实际关注的环境中，一群个人所拥有的专业知识与个人的自私利益之间存在着密切的联系，这可能会妨碍以公正的方式提供专业知识。这种现象的例子可以在科学同行评议中找到，这种评议基于这样一种理念，即科学工作的质量最好由科学家或从事这项工作的科学家的同行来判断，在同行评分中，一门课程的学生评估其他学生的工作，从而减轻教师的压力，提高教学质量或扩大班级规模，以及在对员工绩效的评估中，它依靠其他员工的报告来决定奖金支付或晋升。在所有这些例子中，我们感兴趣的是将个人对群体其他成员的公正评估汇总为集体判断，但诚实的报告可能会受到自私利益的损害：科学家的利益是获得科学工作的资助并发表这项工作的结果，学生的利益是在课程中取得好成绩，或者员工的愿望是获得奖金或升职。由于假设个人只要不能影响对自己的最终判断，就会提供公正的评估，这通常是合理的，因此考虑我们所说的汇总个人报告的公正机制是有意义的，这种机制以真实报告符合每个人的最佳利益的方式选择结果。对公正机制的数学研究是微观经济理论中机制设计领域的一部分，并将更大类别的激励兼容机制专门用于报告相当于对一个群体成员的评估，而个人的偏好只涉及该个人的集体判断的设置。关于公正机制的研究相对较新，关于这种机制的文献很少，特别是关于分配固定数量的可分割资源和选择固定数量的个人的机制。拟议的项目着手严格研究更大类设置的最佳公正机制：有或没有弃权的选择，有或没有强度、分配和排名。在这种情况下，如果在所有公正的机制中，公正的机制使解决方案的整体质量最大化，则称为最优机制。关于公正性的新的数学见解将用于开发新的实用机制，以解决同行评审、同行评分和绩效评估等现实问题。这些机制将作为免费在线服务的一部分进行测试并向公众提供，该服务还将用于调查现实世界的公正性要求和新的应用领域。

In many settings of practical concern a close connection exists between the expertise held within a group of individuals and individuals' selfish interests, which may prevent the expertise from being offered in an impartial way. Examples of this phenomenon can be found in scientific peer review, which is based on the very idea that the quality of scientific work is best judged by peers of the scientist or scientists carrying out the work, in peer grading, where students on a course assess the work of other students and thus relieve pressure on teachers and enable better quality teaching or larger class sizes, and in the appraisal of employee performance, which relies on reports from other employees to make decisions regarding bonus payments or promotions. In all of these examples we are interested in aggregating individuals' impartial assessment concerning other members of the group into a collective judgment, but honest reporting may be compromised by selfish interests: the interest of a scientist to receive funding for scientific work and publish the results of this work, the interest of a student to do well on a course, or the desire of an employee to receive a bonus payment or be promoted. As it is often reasonable to assume that individuals will provide impartial assessments as long as they cannot influence the resulting judgment about themselves, it makes sense to consider what we call impartial mechanisms for aggregating individuals' reports, procedures that select an outcome in such a way that truthful reporting is in each individual's best interest. The mathematical study of impartial mechanisms is part of the area of mechanism design in microeconomic theory, and specializes the larger class of incentive-compatible mechanisms to settings where reports amount to an assessment of the members of a group and the preferences of an individual only concern the collective judgment of that individual. The study of impartial mechanisms is relatively new and only a small literature exists on such mechanisms, specifically for the allocation of a fixed amount of a divisible resource and the selection of a fixed number of individuals. The proposed project sets out to rigorously study optimal impartial mechanisms for a larger class of settings: selection with and without abstentions and with or without intensities, assignment, and ranking. An impartial mechanism is called optimal in this context if among all impartial mechanisms it maximizes the overall quality of the solution. New mathematical insights regarding impartiality will be used to develop new practical mechanisms for real-world problems of peer review, peer grading, and performance appraisal. These mechanisms will be tested and made available to the public as part of a free online service, which will also be used to investigate real-world impartiality requirements and new application areas.