HodgeRank (see https://math.pku.edu.cn/teachers/yaoy/publications/HodgeRank...) is somewhat related to PageRank but is a natural way to approach this problem. I haven't tested it for anything but would expect it to handle noisy comparisons fairly well.

HodgeRank is a very different beast. It is nothing like Pagerank. Its input is not a citation/link graph but a list of paired ordered preferences.

In HodgeRank the goal is to combine a large list of pairwise preferences how to obtain the most representative total order.