  Mixtures of ranking models are standard tools for ranking problems. However,
even the fundamental question of parameter identifiability is not fully
understood: the identifiability of a mixture model with two Bradley-Terry-Luce
(BTL) components has remained open. In this work, we show that popular mixtures
of ranking models with two components (BTL, multinomial logistic models with
slates of size 3, or Plackett-Luce) are generically identifiable, i.e., the
ground-truth parameters can be identified except when they are from a
pathological subset of measure zero. We provide a framework for verifying the
number of solutions in a general family of polynomial systems using algebraic
geometry, and apply it to these mixtures of ranking models to establish generic
identifiability. The framework can be applied more broadly to other learning
models and may be of independent interest.
