Complexity of Shift Bribery in Committee Elections

Abstract

Given an election, a preferred candidate  p , and a budget, the S HIFT B RIBERY 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 S HIFT B RIBERY 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 S HIFT B RIBERY tends to be harder in the multiwinner setting than in the single-winner one by showing settings where S HIFT B RIBERY is computationally easy in the single-winner cases, but is hard (and hard to approximate) in the multiwinner ones.