Complexity of Shift Bribery in Committee Elections

Robert Bredereck, Piotr Faliszewski, Rolf Niedermeier, Nimrod Talmon

Abstract: We study the (parameterized) complexity of SHIFT BRIBERY for multiwinner voting rules. We focus on the SNTV, Bloc, k-Borda, and Chamberlin–Courant rules, as well as on approximate variants of the Chamberlin–Courant rule, since the original rule is NP-hard to compute. We show that SHIFT BRIBERY tends to be significantly harder in the multiwinner setting than in the single-winner one by showing settings where SHIFT BRIBERY is easy in the single-winner cases, but is hard (and hard to approximate) in the multi-winner ones. We show that the non-monotonicity of those rules which are based on approximation algorithms for the Chamberlin–Courant rule sometimes affects the complexity of SHIFT BRIBERY.