  We consider the problem of statistical inference for ranking data,
specifically rank aggregation, under the assumption that samples are incomplete
in the sense of not comprising all choice alternatives. In contrast to most
existing methods, we explicitly model the process of turning a full ranking
into an incomplete one, which we call the coarsening process. To this end, we
propose the concept of rank-dependent coarsening, which assumes that incomplete
rankings are produced by projecting a full ranking to a random subset of ranks.
For a concrete instantiation of our model, in which full rankings are drawn
from a Plackett-Luce distribution and observations take the form of pairwise
preferences, we study the performance of various rank aggregation methods. In
addition to predictive accuracy in the finite sample setting, we address the
theoretical question of consistency, by which we mean the ability to recover a
target ranking when the sample size goes to infinity, despite a potential bias
in the observations caused by the (unknown) coarsening.
