Noname manuscript No. (will be inserted by the editor) Modelling and predicting partial orders from pairwise belief functions Marie-H´ el` ene Masson · S´ ebastien Destercke · Thierry Denoeux Received: date / Accepted: date Abstract In this paper, we introduce a generic way to represent and manip- ulate pairwise information about partial orders (representing rankings, pref- erences, . . . ) 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 com- plete 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. 1 Introduction The need to quantitatively model order structures and make inference about them is present in many fields: rank manipulation in statistics [28], prefer- ence modeling in multi-criteria decision making [18], preference learning [16], decision theory, etc. Orders being complex structures, information about them is often incom- plete or uncertain. However, while the need to consider partial observations of M.-H Masson Universit´ e de Picardie Jules Verne, UMR CNRS 6599 Heudiasyc, Universit´ e de Technologie de Compi` egne , BP 20529 - F-60205 Compi` egne cedex - France E-mail: mmasson@hds.utc.fr S. Destercke UMR CNRS 6599 Heudiasyc, Universit´ e de Technologie de Compi` egne , BP 20529 - F-60205 Compi` egne cedex - France E-mail: sebastien.destercke@hds.utc.fr T. Denoeux UMR CNRS 6599 Heudiasyc, Universit´ e de Technologie de Compi` egne, BP 20529 - F-60205 Compi` egne cedex - France E-mail: thierry.denoeux@hds.utc.fr