Electoral manipulation via influence: probabilistic model

We consider a natural generalization of the fundamental electoral manipulation problem, where a briber can change the opinion or preference of voters through influence. This is motivated by modern political campaigns where candidates try to convince voters through media such as TV, newspaper, Internet. Compared with the classical bribery problem, we do not assume the briber will directly exchange money for votes from individual voters, but rather assume that the briber has a set of potential campaign strategies. Each campaign strategy represents some way of casting influence on voters. A campaign strategy has some cost and can influence a subset of voters. If a voter belongs to the audience of a campaign strategy, then he/she will be influenced. A voter will be more likely to change his/her opinion/preference if he/she has received influence from a larger number of campaign strategies. We model this through an independent activation model which is widely adopted in social science research and study the computational complexity. In this paper, we give a full characterization by showing NP-hardness results and establishing a near-optimal fixed-parameter tractable algorithm that gives a solution arbitrarily close to the optimal solution.