Ranking objects from a preference relation over their subsets

In many everyday situations, we need to rank individuals or single items having the possibility to observe the behavior of groups. In this paper we propose a way to get this ranking over the elements of a set X, starting from an arbitrary preference relation over the subsets of X and taking into account the information provided by this ranking over the subsets. To this purpose, we use a very common approach in the social choice framework: we single out some properties that a general solution should satisfy, and we prove that these properties characterize a unique solution. Given the generality of the approach, we believe that this paper is only a starting point for a more extended analysis. In particular, it is clear that different contexts can suggest other properties, thus identifying alternative ranking methods.