  The Mallows-Binomial distribution is the first joint statistical model for
rankings and ratings (Pearce and Erosheva, 2022). Because frequentist
estimation of the model parameters and their uncertainty is challenging, it is
natural to consider the nonparametric bootstrap. However, it is not clear that
the nonparametric bootstrap is asymptotically valid in this setting. This is
because the Mallows-Binomial model is parameterized by continuous quantities
whose discrete order affects the likelihood. In this note, we demonstrate that
bootstrap uncertainty of the maximum likelihood estimates in the
Mallows-Binomial model are asymptotically valid.
