We study functions that produce a ranking of $n$ individuals from $n$ such rankings and are impartial in the sense that the position of an individual in the output ranking does not depend on the input ranking submitted by that individual. When $n \geq 4$, two properties concerning the quality of the output in relation to the input can be achieved in addition to impartiality: individual full rank, which requires that each individual can appear in any position of the output ranking; and monotonicity, which requires that an individual cannot move down in the output ranking if it moves up in an input ranking. When $n \geq 5$, monotonicity can be dropped to strengthen individual full rank to weak unanimity, requiring that a ranking submitted by every individual must be chosen as the output ranking. Mechanisms achieving these results can be implemented in polynomial time. Both results are best possible in terms of their dependence on $n$. The second result cannot be strengthened further to a notion of unanimity that requires agreement on pairwise comparisons to be preserved.

翻译：我们研究从$n$个个体的排名中生成一个$n$个个体排名的函数，这些函数具有公正性，即个体在输出排名中的位置不依赖于该个体提交的输入排名。当$n \geq 4$时，除了公正性外，还可以实现两个关于输出质量与输入相关性的性质：个体全排名，要求每个个体可以出现在输出排名的任何位置；以及单调性，要求如果个体在某个输入排名中上升，则其在输出排名中不能下降。当$n \geq 5$时，可以放弃单调性，将个体全排名加强为弱一致性，要求每个个体提交的排名必须被选为输出排名。实现这些结果的机制可以在多项式时间内完成。这两个结果在依赖于$n$的意义上都是最优的。第二个结果不能进一步加强为要求保留成对比较一致的一致性概念。