Possible Winners in Approval Voting

  • Nathanaël Barrot
  • Laurent Gourvès
  • Jérôme Lang
  • Jérôme Monnot
  • Bernard Ries
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8176)


Given the knowledge of the preferences of a set of voters over a set of candidates, and assuming that voters cast sincere approval ballots, what can we say about the possible (co-)winners? The outcome depends on the number of candidates each voter will approve. Whereas it is easy to know who can be a unique winner, we show that deciding whether a set of at least two candidates can be the set of co-winners is computationally hard. If, in addition, we have a probability distribution over the number of candidates approved by each voter, we obtain a probability distribution over winners; we study the shape of this probability distribution empirically, for the impartial culture assumption. We study variants of the problem where the number of candidates approved by each voter is upper and/or lower bounded. We generalize some of our results to multiwinner approval voting.


Computational social choice Approval voting Voting under incomplete knowledge Computational complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nathanaël Barrot
    • 1
    • 2
  • Laurent Gourvès
    • 2
    • 1
  • Jérôme Lang
    • 2
    • 1
  • Jérôme Monnot
    • 2
    • 1
  • Bernard Ries
    • 1
    • 2
  1. 1.PSLUniversité Paris-DauphineParis Cedex 16France
  2. 2.CNRS, LAMSADE UMR 7243France

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