Complexity of Shift Bribery in Committee Elections

Robert Bredereck, Piotr Faliszewski, Rolf Niedermeier, Nimrod Talmon

Research output: Contribution to journalArticlepeer-review


Given an election, a preferred candidate p, and a budget, the SHIFT BRIBERY problem asks whether p can win the election after shifting p higher in some voters' preference orders. Of course, shifting comes at a price (depending on the voter and on the extent of the shift) and one must not exceed the given budget. We study the (parameterized) computational complexity of SHIFT BRIBERY for multiwinner voting rules where winning the election means to be part of some winning committee. We focus on the well-established SNTV, Bloc, k-Borda, and Chamberlin-Courant rules, as well as on approximate variants of the Chamberlin-Courant rule. We show that SHIFT BRIBERY tends to be harder in the multiwinner setting than in the single-winner one by showing settings where SHIFT BRIBERY is computationally easy in the single-winner cases, but is hard (and hard to approximate) in the multiwinner ones.

Original languageEnglish
Article number20
JournalACM Transactions on Computation Theory
Issue number3
StatePublished - 1 Sep 2021


  • Approximation
  • Committee elections
  • Parameterized complexity
  • Shift-bribery

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics


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