Large-Scale Election Campaigns: Combinatorial Shift Bribery

Robert Bredereck, Piotr Faliszewski, Rolf Niedermeier, Nimrod Talmon
2016 The Journal of Artificial Intelligence Research  
We study the complexity of a combinatorial variant of the Shift Bribery problem in elections. In the standard Shift Bribery problem, we are given an election where each voter has a preference order over the set of candidates and where an outside agent, the briber, can pay each voter to rank the briber's favorite candidate a given number of positions higher. The goal is to ensure the victory of the briber's preferred candidate. The combinatorial variant of the problem, introduced in this paper,
more » ... ced in this paper, models settings where it is possible to affect the position of the preferred candidate in multiple votes, either positively or negatively, with a single bribery action. This variant of the problem is particularly interesting in the context of large-scale campaign management problems (which, from the technical side, are modeled as bribery problems). We show that, in general, the combinatorial variant of the problem is highly intractable; specifically, NP-hard, hard in the parameterized sense, and hard to approximate. Nevertheless, we provide parameterized algorithms and approximation algorithms for natural restricted cases.
doi:10.1613/jair.4927 fatcat:gcwvxkudgrgnvju24k67jgocxi