One phrase people use for this problem is "rank aggregation." It often comes up in the context of search engines and document retrieval, where you might have multiple ways of ranking search results. 

I'd add more details, but I'd just be repeating the nice answer to this previous MathOverflow question:
https://mathoverflow.net/questions/15955/defining-average-rank-when-not-every-ranking-covers-the-whole-set