  Ranked data appear in many different applications, including voting and
consumer surveys. There often exhibits a situation in which data are partially
ranked. Partially ranked data is thought of as missing data. This paper
addresses parameter estimation for partially ranked data under a (possibly)
non-ignorable missing mechanism. We propose estimators for both complete
rankings and missing mechanisms together with a simple estimation procedure.
Our estimation procedure leverages a graph regularization in conjunction with
the Expectation-Maximization algorithm. Our estimation procedure is
theoretically guaranteed to have the convergence properties. We reduce a
modeling bias by allowing a non-ignorable missing mechanism. In addition, we
avoid the inherent complexity within a non-ignorable missing mechanism by
introducing a graph regularization. The experimental results demonstrate that
the proposed estimators work well under non-ignorable missing mechanisms.
