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:通常的情况是,陪审团必须按基本比例( {1, 2, 3, 4, 5} ) 或诸如{ 大、 良好、 平均、 坏} 等常规比例( great, good, 平均, bad ) 来评分一组候选人。 当候选人数量非常大时, 如酒店( booking)、 餐馆( GOGLE) 、 公寓( AIRBNB) 、 司机( UBER) 或文件( EC) 等, 假设每个陪审团成员将为每个候选人提供不同的级别。 每个陪审团成员更可能对某些候选人投弃权票, 投空白票, 或以随机方式, 或作为其专长的函数, 只有一小部分候选人, 并被要求对其中每一个类别进行评分。 推广经典理论理论, 我们研究集合方法, 让一个选民没有资格对全部候选人进行评分, 而候选人没有资格。 此外, 每一位候选人都会选择两种: 空白的选票, 等级, 或弃权, 假设对等级的偏好的偏好, 我们的纸, 我们的分, 将一个大的排序 表示一个相当的排序 等的平的 。