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In this paper we propose a Bayesian nonparametric model for clusteringpartial ranking data. We start by developing a Bayesian nonparametric extensionof the popular Plackett-Luce choice model that can handle an infinite number ofchoice items. Our framework is based on the theory of random atomic measures,with the prior specified by a completely random measure. We characterise theposterior distribution given data, and derive a simple and effective Gibbssampler for posterior simulation. We then develop a Dirichlet process mixtureextension of our model and apply it to investigate the clustering ofpreferences for college degree programmes amongst Irish secondary schoolgraduates. The existence of clusters of applicants who have similar preferencesfor degree programmes is established and we determine that subject matter andgeographical location of the third level institution characterise theseclusters.

Bayesian nonparametric Plackett-Luce models for the analysis of preferences for college degree programmes