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International Conference on Algorithmic Decision Theory

ADT 2013: Algorithmic Decision Theory pp 57–70Cite as

Possible Winners in Approval Voting

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

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.

Keywords

  • Computational social choice
  • Approval voting
  • Voting under incomplete knowledge
  • Computational complexity

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  • DOI: 10.1007/978-3-642-41575-3_5
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References

  1. Bachrach, Y., Betzler, N., Faliszewski, P.: Probabilistic possible-winner determination. In: Proc. of AAAI 2010 (2010)

    Google Scholar 

  2. Baumeister, D., Erdèlyi, G., Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Computational aspects of approval voting. In: Laslier, J.-F., Sanver, R. (eds.) Handbook of Approval Voting, pp. 199–251. Springer (2010)

    Google Scholar 

  3. Baumeister, D., Rothe, J.: Taking the final step to a full dichotomy of the possible winner problem in pure scoring rules. In: Proceedings of ECAI 2010 (2010)

    Google Scholar 

  4. Betzler, N., Dorn, B.: Towards a dichotomy of finding possible winners in elections based on scoring rules. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 124–136. Springer, Heidelberg (2009)

    MATH  CrossRef  Google Scholar 

  5. Betzler, N., Hemmann, S., Niedermeier, R.: A multivariate complexity analysis of determining possible winners given incomplete votes. In: Proceedings of IJCAI 2009, pp. 53–58 (2009)

    Google Scholar 

  6. Betzler, N., Slinko, A., Uhlmann, J.: On the computation of fully proportional representation. Journal of Artificial Intelligence Research (2013)

    Google Scholar 

  7. Brams, S., Fishburn, P.: Approval voting. American Political Review 72(3), 831–847 (1978)

    MATH  CrossRef  Google Scholar 

  8. Brams, S., Fishburn, P.: Approval Voting, 2nd edn. Birkhäuser (1987)

    Google Scholar 

  9. Brams, S., Sanver, R.: Critical strategies under approval voting: Who gets ruled in and ruled out. Electoral Studies 25(2), 287–305 (2006)

    CrossRef  Google Scholar 

  10. Chevaleyre, Y., Lang, J., Maudet, N., Monnot, J., Xia, L.: New candidates welcome! possible winners with respect to the addition of new candidates. Mathematical Social Sciences 64(1), 74–88 (2012)

    MathSciNet  MATH  CrossRef  Google Scholar 

  11. Darmann, A.: Popular committees. Mathematical Social Sciences (to appear, 2013)

    Google Scholar 

  12. Delort, C., Spanjaard, O., Weng, P.: Committee selection with a weight constraint based on a pairwise dominance relation. In: ADT, pp. 28–41 (2011)

    Google Scholar 

  13. Elkind, E., Lang, J., Saffidine, A.: Choosing collectively optimal sets of alternatives based on the condorcet criterion. In: IJCAI 2011, pp. 186–191 (2011)

    Google Scholar 

  14. Endriss, U.: Sincerity and manipulation under approval voting. Theory and Decision (2011)

    Google Scholar 

  15. Endriss, U., Pini, M.S., Rossi, F., Venable, K.B.: Preference aggregation over restricted ballot languages: Sincerity and strategy-proofness. In: Boutilier, C. (ed.) IJCAI 2009, pp. 122–127 (2009)

    Google Scholar 

  16. Erdélyi, G., Nowak, M., Rothe, J.: Sincere-strategy preference-based approval voting broadly resists control. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 311–322. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  17. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  18. Kalech, M., Kraus, S., Kaminka, G.A., Goldman, C.V.: Practical voting rules with partial information. Autonomous Agents and Multiagent Systems 22(1), 151–182 (2011)

    CrossRef  Google Scholar 

  19. Kilgour, M.: Approval balloting for multi-winner elections. In: Laslier, J.-F., Sanver, R. (eds.) Handbook of Approval Voting, pp. 105–124. Springer (2010)

    Google Scholar 

  20. Klamler, C., Pferschy, U., Ruzika, S.: Committee selection with a weight constraint based on lexicographic rankings of individuals. In: Rossi, F., Tsoukias, A. (eds.) ADT 2009. LNCS, vol. 5783, pp. 50–61. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  21. Konczak, K., Lang, J.: Voting procedures with incomplete preferences. In: IJCAI 2005 Multidisciplinary Workshop on Advances in Preference Handling (2005)

    Google Scholar 

  22. Lang, J., Pini, M.S., Rossi, F., Salvagnin, D., Venable, K.B., Walsh, T.: Winner determination in voting trees with incomplete preferences and weighted votes. In: Autonomous Agents and Multi-Agent Systems (2011)

    Google Scholar 

  23. Laslier, J.-F.: The leader rule – a model of strategic approval voting in a large electorate. Journal of Theoretical Politics 21, 113–136 (2009)

    CrossRef  Google Scholar 

  24. Laslier, J.-F., Sanver, R.: The basic approval voting game. In: Laslier, J.-F., Sanver, R. (eds.) Handbook of Approval Voting. Springer (2010)

    Google Scholar 

  25. Meir, R., Procaccia, A., Rosenschein, J., Zohar, A.: The complexity of strategic behavior in multi-winner elections. JAIR 33, 149–178 (2008)

    MathSciNet  MATH  CrossRef  Google Scholar 

  26. Nuñez, M.: Condorcet consistency of approval voting: a counter example in large Poisson games. Journal of Theoretical Politics 22, 64–84 (2010)

    CrossRef  Google Scholar 

  27. Procaccia, A., Rosenschein, J., Zohar, A.: On the complexity of achieving proportional representation. Social Choice and Welfare 30(3), 353–362 (2008)

    MathSciNet  MATH  CrossRef  Google Scholar 

  28. Saari, D.: Systematic analysis of multiple voting rules. Social Choice and Welfare 34(2), 217–247 (2010)

    MathSciNet  MATH  CrossRef  Google Scholar 

  29. Sertel, M., Yılmaz, B.: The majoritarian compromise is majoritarian-optimal and subgame-perfect implementable. Social Choice and Welfare 16(4), 615–627 (1999)

    MathSciNet  MATH  CrossRef  Google Scholar 

  30. De Sinopoli, F., Dutta, B., Laslier, J.-F.: Approval voting: three examples. International Journal of Game Theory 35(1), 27–38 (2006)

    MathSciNet  MATH  CrossRef  Google Scholar 

  31. Skowron, P., Faliszewski, P., Slinko, A.: Achieving fully proportional representation is easy in practice. In: AAMAS 2013, pp. 399–406 (2013)

    Google Scholar 

  32. Xia, L., Conitzer, V.: Determining possible and necessary winners under common voting rules given partial orders. In: Proceedings of AAAI 2008, pp. 196–201 (2008)

    Google Scholar 

  33. Xia, L., Lang, J., Monnot, J.: Possible winners when new alternatives join: new results coming up! In: Sonenberg, L., Stone, P., Tumer, K., Yolum, P. (eds.) AAMAS. IFAAMAS, pp. 829–836 (2011)

    Google Scholar 

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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

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