Aggregating partially ordered preferences:impossibility and possibility results

We consider preferences which can be partially ordered and which need to be aggregated. We prove that, under certain conditions, if there are at least two agents and three outcomes, no aggregation system on partially ordered preferences can be fair. These result generalizes Arrow's impossibility theorem for combining total orders. We also provide two sufficient conditions which guarantee fairness for the majority rule over partial orders. This allows us to generalize Sen's theorem for total orders. Finally, we give a generalization of the Muller-Satterthwaite result for social choice functions over partial orders.