Ranking objects from a preference relation over their subsets

In many every day situations it can happen that one wants to rank the elements of a group of people having the possibility to observe them collaborating in subgroups. In this paper we propose a general way to get this ranking over the elements of a group N , starting from an arbitrary preference relation over the subsets of N and taking into account the information provided by this ranking over the subsets. To discuss this issue, we use the standard approach to this type of problems, very common in the social choice framework: we single out some properties that a general solution should have, and we prove that these properties characterize a unique function. Given the very general type of problems that this model can represent, we believe that this is only a starting point for a more extended analysis. In particular, it is clear that different contexts can suggest different properties, thus identifying other ranking methods.