Optimizing Influence Campaigns: Nudging under Bounded Confidence

TL;DR

The paper tackles persuading audiences in networks governed by bounded confidence, showing direct messaging is often ineffective and proposing a control-theoretic nudging framework that evolves content over time to gradually shift opinions. It introduces a two-phase process—greedy targeting to select agents’ targets and a dynamic content policy to generate nudging content—validated through simulations on real Twitter networks and synthetic topologies. The results show nudging outperforms DeGroot-style direct persuasion and that multiple agents can enhance impact, though gains depend on network activity and targeting strategy; the authors also bridge theory with practice by outlining LLM prompt designs to operationalize nudging content. This work highlights the practical feasibility and risks of nudging under bounded confidence, suggesting a path from mathematical policy design to real-world content generation, with implications for influence operations and policy design.

Abstract

Influence campaigns in online social networks are often run by organizations, political parties, and nation states to influence large audiences. These campaigns are employed through the use of agents in the network that share persuasive content. Yet, their impact might be minimal if the audiences remain unswayed, often due to the bounded confidence phenomenon, where only a narrow spectrum of viewpoints can influence them. Here we show that to persuade under bounded confidence, an agent must nudge its targets to gradually shift their opinions. Using a control theory approach, we show how to construct an agent's nudging policy under the bounded confidence opinion dynamics model and also how to select targets for multiple agents in an influence campaign on a social network. Simulations on real Twitter networks show that a multi-agent nudging policy can shift the mean opinion, decrease opinion polarization, or even increase it. We find that our nudging based policies outperform other common techniques that do not consider the bounded confidence effect. Finally, we show how to craft prompts for large language models, such as ChatGPT, to generate text-based content for real nudging policies. This illustrates the practical feasibility of our approach, allowing one to go from mathematical nudging policies to real social media content.

Figures (18)

• Figure 1: Top: The two-node network with the agent targeting node 1 (left) or node 0 (right). Bottom: The opinions of agent and nodes, obtained by the collocation method for the two-node network with agent targeting node 1 (left) or node 0 (right). The objective is to maximize the opinion mean.
• Figure 2: Agent opinions under the greedy content policy for a two-node network, where the agent targets node 1 (left) or node 0 (right) to maximize the mean opinion. Under our greedy targeting policy, the agent will select node 0 as its target.
• Figure 3: Targets of the three agents to persuade a ten-node path network, for the objectives of maximizing the mean (left), maximizing the variance (middle), and minimizing the variance (right).
• Figure 4: Opinion time series (top row) and density plots (bottom row) for different objectives under three nudging agents on a ten-node path network. The time series depicts opinion distributions (shaded regions) and agent opinions (dashed lines). The purple region represents the 25th to 75th quantiles, while the pink region represents the 5th to 95th quantiles. Opinion densities are plotted for initial (blue) and final (orange) opinions. The objectives are to maximize mean (left), maximize variance (middle), and minimize variance (right).
• Figure 5: Bar plots comparing the change in final objective values for different Twitter network datasets relative to no agent under DeGroot (blue) and nudging (orange) policies. The objectives are maximizing mean (left), maximizing variance (middle), and minimizing variance (right). The y-axis "Objective Delta" measures the percentage change relative to the objective without an agent.

Theorems & Definitions (3)

• Theorem 1: Non-Submodular Targeting
• Theorem 2: Optimality of Adding Agents
• Proposition 1: Limitations of Adding Agents Under a Suboptimal Policy