Passive and Active Ranking from Pairwise Comparisons

In the problem of ranking from pairwise comparisons, the learner has access to pairwise preferences among n objects and is expected to output a total order of these objects. This problem has a wide range of applications not only in computer science but also in other areas such as social science and economics. In this report, we will give a survey of passive and active learning algorithms for ranking from pairwise comparisons. We will first survey algorithms for learning to rank in a general setting, and then we will discuss ranking problems with special structures like bounded noise, the Bradley-Terry-Luce model, and embedding in a low dimensional Euclidean space. Finally, we will briefly survey efficient algorithms for practical applications.