Social Choice and Welfare

, Volume 52, Issue 4, pp 589–606 | Cite as

Ranking objects from a preference relation over their subsets

  • Giulia BernardiEmail author
  • Roberto Lucchetti
  • Stefano Moretti
Original Paper


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.



We thank two anonymous referees for their valuable comments on a former version of this paper, their suggestions helped us to substantially improve the results.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.Université Paris Dauphine, PSL Research University, CNRS, LAMSADEParisFrance

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