Abstract We propose a collaborative filtering (CF) recommendation framework which is based on viewing user feedback on products as ordinal, rather than the more common numerical view. Such an ordinal view frequently provides a more natural reflection of the user intention when providing qualitative ratings, allowing users to have different internal scoring scales. Moreover, we can address scenarios where assigning numerical scores to different types of user feedback would not be easy. The framework can wrap most collaborative filtering algorithms, enabling algorithms previously designed for numerical values to handle ordinal values. We demonstrate our framework by wrapping a leading matrix factorization CF method. A cornerstone of our method is its ability to predict a full probability distribution of the expected item ratings, rather than only a single score for an item. One of the advantages this brings is a novel approach to estimating the confidence level in each individual prediction. Compared to previous approaches to confidence estimation, ours is more principled and empirically superior in its accuracy. We demonstrate the efficacy of the approach on two of the largest publicly available datasets: the Netflix data and the Yahoo! Music data.