International Conference on Algorithmic DecisionTheory

ADT 2015: Algorithmic Decision Theory pp 414-431 | Cite as

Elections with Few Candidates: Prices, Weights, and Covering Problems

  • Robert Bredereck
  • Piotr Faliszewski
  • Rolf Niedermeier
  • Piotr Skowron
  • Nimrod Talmon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9346)

Abstract

We show that a number of election-related problems with prices (such as, for example, bribery) are fixed-parameter tractable (in \({\mathsf {FPT}}\)) when parameterized by the number of candidates. For bribery, this resolves a nearly 10-year old family of open problems. Our results follow by a general technique that formulates voting problems as covering problems and extends the classic approach of using integer linear programming and the algorithm of Lenstra [19]. In this context, our central result is that Weighted Set Multicover parameterized by the universe size is fixed-parameter tractable. Our approach is also applicable to weighted electoral control for Approval voting. We improve previously known \({\mathsf {XP}}\)-memberships to \({\mathsf {FPT}}\)-memberships. Our preliminary experiments on real-world-based data show the practical usefulness of our approach for instances with few candidates.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Robert Bredereck
    • 1
  • Piotr Faliszewski
    • 2
  • Rolf Niedermeier
    • 1
  • Piotr Skowron
    • 3
  • Nimrod Talmon
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany
  2. 2.AGH University of Science and TechnologyKrakowPoland
  3. 3.University of WarsawWarsawPoland

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