  In this paper we address the identifiability and efficient learning problems
of finite mixtures of Plackett-Luce models for rank data. We prove that for any
$k\geq 2$, the mixture of $k$ Plackett-Luce models for no more than $2k-1$
alternatives is non-identifiable and this bound is tight for $k=2$. For generic
identifiability, we prove that the mixture of $k$ Plackett-Luce models over $m$
alternatives is generically identifiable if $k\leq\lfloor\frac {m-2}
2\rfloor!$. We also propose an efficient generalized method of moments (GMM)
algorithm to learn the mixture of two Plackett-Luce models and show that the
algorithm is consistent. Our experiments show that our GMM algorithm is
significantly faster than the EMM algorithm by Gormley and Murphy (2008), while
achieving competitive statistical efficiency.
