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Possible Winners in Approval Voting

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Algorithmic Decision Theory (ADT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8176))

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Abstract

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.

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Author information

Authors and Affiliations

  1. PSL, Université Paris-Dauphine, 75775, Paris Cedex 16, France

    Nathanaël Barrot, Laurent Gourvès, Jérôme Lang, Jérôme Monnot & Bernard Ries

  2. CNRS, LAMSADE UMR 7243, France

    Nathanaël Barrot, Laurent Gourvès, Jérôme Lang, Jérôme Monnot & Bernard Ries

Authors
  1. Nathanaël Barrot
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  2. Laurent Gourvès
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  3. Jérôme Lang
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  4. Jérôme Monnot
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  5. Bernard Ries
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Editor information

Editors and Affiliations

  1. LIP 6, UPMC, 75005, Paris, France

    Patrice Perny

  2. UMONS, Faculty of Engineering, Mathematics and Operations Research, Université de Mons, 9, Rue de Houdain, 7000, Mons, Belgium

    Marc Pirlot

  3. CNRS, LAMSADE, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75016, Paris, France

    Alexis Tsoukiàs

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Barrot, N., Gourvès, L., Lang, J., Monnot, J., Ries, B. (2013). Possible Winners in Approval Voting. In: Perny, P., Pirlot, M., Tsoukiàs, A. (eds) Algorithmic Decision Theory. ADT 2013. Lecture Notes in Computer Science(), vol 8176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41575-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-41575-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41574-6

  • Online ISBN: 978-3-642-41575-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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