  We develop a Bayesian nonparametric extension of the popular Plackett-Luce
choice model that can handle an infinite number of choice items. Our framework
is based on the theory of random atomic measures, with the prior specified by a
gamma process. We derive a posterior characterization and a simple and
effective Gibbs sampler for posterior simulation. We develop a time-varying
extension of our model, and apply it to the New York Times lists of weekly
bestselling books.
