We propose a model for learning user preference rankings for the purpose of making product recommendations. The model allows us to learn from pairwise preference statements or from (incomplete) rankings over more than two items. We present two algorithms for performing inference in this model, both with excellent scaling in the number of users and items. The superior predictive performance of the new method is demonstrated on the well-known sushi preference data set. In addition, we show how the model can be used effectively in an active learning setting where we select only a small number of informative items for learning.