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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
  • 68 Downloads

Abstract

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.

Notes

Acknowledgements

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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