This work focuses on a robust learning methodology in a collaborative filtering context. We wish to predict preferences between alternatives characterized by binary attributes, where each attribute represents the opinion of a reference user on the alternative. The model whose parameters we learn is general enough to be compatible with any strict weak order on the attribute vectors, thanks to the consideration of opinion synergies. Moreover, we accept not to predict some preferences if the data collected are not compatible with a reliable prediction. A predicted preference will be considered reliable if all the simplest models explaining the training data agree on it. Following the robust ordinal regression methodology, our predictions are based on an ordinal dominance relation between alternatives introduced by Fishburn and LaValle (1996) which relies on an uncertainty set encompassing the possible values of the parameters of the multi-attribute utility function.