In this paper, we introduce a generic way to represent and manipulate pairwise information about partial orders (representing rankings, preferences, ...) with belief functions. We provide generic and practical tools to make inferences from this pairwise information and illustrate their use on the machine learning problems that are label ranking and multi-label prediction. Our approach differs from most other quantitative approaches handling complete or partial orders, in the sense that partial orders are here considered as primary objects and not as incomplete specifications of ideal but unknown complete orders.