Optimal Impartial Mechanisms

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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.