Autonomous Agents and Multi-Agent Systems (2023) 37:18 https://doi.org/10.1007/s10458-023-09602-z Electoral manipulation via inﬂuence: probabilistic model Liangde Tao 1 · Lin Chen 2 · Lei Xu 3 · Shouhuai Xu 4 · Zhimin Gao 5 · Weidong Shi 5 Accepted: 4 February 2023 / Published online: 8 March 2023 © Springer Science+Business Media, LLC, part of Springer Nature 2023 Abstract 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. Keywords Computational social choice · Approximation algorithms B Lin Chen chenlin198662@gmail.com Liangde Tao vast.tld@gmail.com Lei Xu xuleimath@gmail.com Shouhuai Xu sxu@uccs.edu Zhimin Gao gao@kell.vin Weidong Shi larryshi@ymail.com 1 Zhejiang University, Hangzhou, China 2 Texas Tech University, Lubbock, USA 3 Kent State University, Kent, USA 4 University of Colorado Colorado Springs, Colorado Springs, USA 5 University of Houston, Houston, USA 123