@article{ba487b694eca424086da45cc573f97c0,
title = "Complexity of Shift Bribery in Committee Elections",
abstract = "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.",
keywords = "Approximation, Committee elections, Parameterized complexity, Shift-bribery",
author = "Robert Bredereck and Piotr Faliszewski and Rolf Niedermeier and Nimrod Talmon",
note = "Funding Information: The authors were supported in part by the DFG project PAWS (NI 369/10) and the NCN project DEC-2012/06/M/ST1/00358. Nimrod Talmon, while at TU Berlin, was supported by the DFG Research Training Group “Methods for Discrete Structures” (GRK 1408), and while at Ben-Gurion University, was supported by the Israeli Science Foundation (ISF; grant no. 630/19). Pi-otr Faliszewski{\textquoteright}s visits to TU Berlin were supported by the COST action IC1205 and by a Friedrich Wilhelm Bessel Research Award from the Alexander-von-Humboldt Foundation, Bonn, Germany. Robert Bredereck is now at Humboldt-Universit{\"a}t zu Berlin, Institut f{\"u}r Informatik. Work was done while Robert Bredereck was with TU Berlin. Authors{\textquoteright} addresses: R. Bredereck, Humboldt-Universit{\"a}t zu Berlin, Institut f{\"u}r Informatik, Algorithm Engineering, Rudower Chaussee 25, 12489 Berlin, Germany; email: robert.bredereck@hu-berlin.de; P. Faliszewski, AGH University, Krakow, Poland; email: faliszew@agh.edu.pl; R. Niedermeier, Technische Universit{\"a}t Berlin, Berlin, Germany; email: rolf.niedermeier@tu-berlin.de; N. Talmon, Ben-Gurion University, Be{\textquoteright}er Sheva, 1 Ben-Gurion Boulevard, Israel; email: talmonn@bgu.ac.il. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. {\textcopyright} 2021 Copyright held by the owner/author(s). Publication rights licensed to ACM. 1942-3454/2021/08-ART20 $15.00 https://doi.org/10.1145/3470647 Publisher Copyright: {\textcopyright} 2021 ACM.",
year = "2021",
month = sep,
day = "1",
doi = "10.1145/3470647",
language = "English",
volume = "13",
journal = "ACM Transactions on Computation Theory",
issn = "1942-3454",
publisher = "Association for Computing Machinery (ACM)",
number = "3",
}