Shift Bribery over Social Networks

2025-10-24

AI Summary

This paper introduces social network propagation effects into the shift bribery model for the first time: voters are modeled as nodes in a directed weighted graph, and bribing a voter not only alters their own preference but also influences neighbors via directed edges, inducing a cascade of persuasive effects. Given a budget and individual conversion cost functions, the goal is to decide whether a budget-feasible bribery strategy exists such that the target candidate wins under combined direct bribery and social influence. Method: We establish computational hardness results and design algorithms parameterized by structural graph measures—including treewidth and cluster vertex deletion number—as well as pseudo-polynomial-time algorithms. Contribution/Results: We prove the problem is NP-complete and W[2]-hard on general digraphs. For special graph classes—complete graphs, paths, transitive tournaments, and cluster graphs—we provide efficient exact algorithms. Our work systematically characterizes the problem’s complexity landscape and significantly enhances the model’s realism for capturing strategic manipulation in real-world elections.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Humans and AI: Voting
• Multiagent Systems: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In shift bribery, a briber seeks to promote his preferred candidate by paying voters to raise their ranking. Classical models of shift bribery assume voters act independently, overlooking the role of social influence. However, in reality, individuals are social beings and are often represented as part of a social network, where bribed voters may influence their neighbors, thereby amplifying the effect of persuasion. We study Shift bribery over Networks, where voters are modeled as nodes in a directed weighted graph, and arcs represent social influence between them. In this setting, bribery is not confined to directly targeted voters its effects can propagate through the network, influencing neighbors and amplifying persuasion. Given a budget and individual cost functions for shifting each voter's preference toward a designated candidate, the goal is to determine whether a shift strategy exists within budget that ensures the preferred candidate wins after both direct and network-propagated influence takes effect. We show that the problem is NP-Complete even with two candidates and unit costs, and W[2]-hard when parameterized by budget or maximum degree. On the positive side, we design polynomial-time algorithms for complete graphs under plurality and majority rules and path graphs for uniform edge weights, linear-time algorithms for transitive tournaments for two candidates, linear cost functions and uniform arc weights, and pseudo-polynomial algorithms for cluster graphs. We further prove the existence of fixed-parameter tractable algorithms with treewidth as parameter for two candidates, linear cost functions and uniform arc weights and pseudo-FPT with cluster vertex deletion number for two candidates and uniform arc weights. Together, these results give a detailed complexity landscape for shift bribery in social networks.

Problem

• Modeling bribery propagation through social network influence
• Determining budget-constrained shift strategies for candidate victory
• Analyzing computational complexity of network-based bribery problems

Innovation

• Modeling voters as nodes in directed weighted graphs
• Considering network-propagated influence in bribery effects
• Designing algorithms for various graph structures and voting rules