We propose a Skew-Symmetric Bilinear (SSB) model to represent intransitive preferences on subsets of a ground set of items. More precisely, the SSB model accounts for preference intensities between pairs of subsets. We provide a procedure to learn the parameters of the SSB model from a set of known pairwise preferences between subsets, managing to find a sparse model, and as simple as possible in terms of the degree of interaction between items. The SSB model can be viewed as a concise representation of a weighted tournament on subsets. We study the complexity of determining the winners according to various tournament rules. Numerical tests on synthetic and real-world data are carried out.