It is common that a jury must grade a set of candidates in a cardinal scale such as {1,2,3,4,5} or an ordinal scale such as {Great, Good, Average, Bad }. When the number of candidates is very large such as hotels (BOOKING), restaurants (GOOGLE), apartments (AIRBNB), drivers (UBER), or papers (EC), it is unreasonable to assume that each jury member will provide a separate grade for each candidate. Each jury member is more likely to abstain for some candidates, cast a blank vote, or be associated at random, or as a function of its expertise, with only a small subset of the candidates and is asked to grade each of those. Extending the classical theory, we study aggregation methods in which a voter will not be eligible to grade all the candidates, and the candidates are not eligible for the same sets of voters. Moreover, each candidate on which they are eligible, the voter will have the choice between: a blank vote, grade the candidate, or abstain. Assuming single-peaked preferences over the grades, we axiomatically characterise a broad class of strategy-proof grading mechanisms satisfying axioms such as unanimity, anonymity, neutrality, participation or consistency. Finally, when a strict ranking is necessary (to distinguish let say between two borderline papers in a conference), some tie-breaking rules, extending the leximin and majority judgment, are defined and are shown to be equivalent to some strategy-proof grading functions on a richer space of outcome. Our paper will propose new rules, called phantom-proxy mechanisms, to aggregate the votes in the examples above or others, which differ from the usual average mark, that are easily manipulable. Moreover, the phantom-proxy are able to reduce the injustices caused by some candidates juries too generous or severe.

翻译：评审团常需在基数标度（如{1,2,3,4,5}）或序数标度（如{优,良,中,差}）上对一组候选人进行评分。当候选人数量非常庞大时（如酒店（BOOKING）、餐厅（GOOGLE）、公寓（AIRBNB）、司机（UBER）或论文（EC）），假设每位评审成员为每位候选人单独评分是不合理的。评审成员更可能对某些候选人弃权、投空白票，或随机（或根据其专业领域）仅与一小部分候选人相关联，并被要求对这些候选人进行评分。扩展经典理论，我们研究了投票者无权对所有候选人评分、且候选人也不面向相同投票者群体的聚合方法。此外，对于其有权评分的每位候选人，投票者可在以下三种选择中进行：投空白票、评分或弃权。假设对评分的偏好为单峰性，我们在公理上刻画了一类广泛的防策略评分机制，这些机制满足一致性、匿名性、中立性、参与性或一致性等公理。最后，当需要严格排序时（例如区分会议上两篇临界论文），我们定义了扩展了词典序和多数评判的平局打破规则，并证明其在更丰富的结果空间上等价于某些防策略评分函数。本文提出的新规则——幻影代理机制——用于聚合上述例子中的投票（或其他场景），其区别于易于操纵的常规平均分。此外，幻影代理能够减少因部分过于宽厚或严苛的评审团对候选人造成的不公正。