  Learning how to aggregate ranking lists has been an active research area for
many years and its advances have played a vital role in many applications
ranging from bioinformatics to internet commerce. The problem of discerning
reliability of rankers based only on the rank data is of great interest to many
practitioners, but has received less attention from researchers. By dividing
the ranked entities into two disjoint groups, i.e., relevant and
irrelevant/background ones, and incorporating the Mallows model for the
relative ranking of relevant entities, we propose a framework for rank
aggregation that can not only distinguish quality differences among the rankers
but also provide the detailed ranking information for relevant entities.
Theoretical properties of the proposed approach are established, and its
advantages over existing approaches are demonstrated via simulation studies and
real-data applications. Extensions of the proposed method to handle partial
ranking lists and conduct covariate-assisted rank aggregation are also
discussed.
