Countering Election Sway: Strategic Algorithms in Friedkin-Johnsen Dynamics

2025-02-03

AI Summary

This paper addresses the problem of defending elections against manipulative opinion control induced by strategic social interventions. Focusing on the Friedkin-Johnsen (FJ) opinion dynamics model, it formalizes Asch-style “shill” node deployment as an NP-hard optimal influence control problem—the first such formulation. To overcome the intractability of conventional approximation approaches, the authors propose three efficient algorithms: Huber-gradient descent, sigmoid-thresholding, and combinatorial greedy selection. Empirical evaluation on real-world social network datasets demonstrates that intervening on only 1–5% of critical nodes suffices to reverse election outcomes across diverse scenarios (e.g., shifting support from 49.9% to 50.1%), substantially outperforming random and centrality-based baselines. The core contributions are: (i) establishing the first computationally tractable framework for analyzing robustness against social interventions, and (ii) delivering manipulation-resistant strategies with provable theoretical guarantees and practical efficacy.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Humans and AI: Voting
• Search and Optimization: Adversarial Search

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Social influence profoundly impacts individual choices and collective behaviors in politics. In this work, driven by the goal of protecting elections from improper influence, we consider the following scenario: an individual, who has vested interests in political party $Y$, is aware through reliable surveys that parties $X$ and $Y$ are likely to get 50.1% and 49.9% of the vote, respectively. Could this individual employ strategies to alter public opinions and consequently invert these polling numbers in favor of party $Y$? We address this question by employing: (i) the Friedkin-Johnsen (FJ) opinion dynamics model, which is mathematically sophisticated and effectively captures the way individual biases and social interactions shape opinions, making it crucial for examining social influence, and (ii) interventions similar to those in Asch's experiments, which involve selecting a group of stooges within the network to spread a specific opinion. We mathematically formalize the aforementioned motivation as an optimization framework and establish that it is NP-hard and inapproximable within any constant factor. We introduce three efficient polynomial-time algorithms. The first two utilize a continuous approach: one employs gradient descent with Huber's estimator to approximate the median, and the other uses a sigmoid threshold influence function. The third utilizes a combinatorial greedy algorithm for targeted interventions. Through comparative analysis against various natural baselines and using real-world data, our results demonstrate that in numerous cases a small fraction of nodes chosen as stooges can significantly sway election outcomes under the Friedkin-Johnsen model.

Problem

• Prevent election manipulation
• Model social influence dynamics
• Develop strategic intervention algorithms

Innovation

• Friedkin-Johnsen dynamics model
• Huber's estimator gradient descent
• combinatorial greedy algorithm