Strategic opinion manipulation can distort consensus in multiplex networks
Strategic Opinion Manipulation in Multiplex Networks
Computer Science and Game TheorySocial and Information Networks
Summary
People often share their opinions on multiple connected networks, but they might lie differently on each to push the overall result toward what they want. The authors study how this affects the final combined opinion when a platform pools information from several network layers. They find that some influential people can make the final consensus more extreme than the truth and that spreading attention across different networks can reduce or increase this distortion depending on conditions. Their work also suggests how platforms might adjust the importance they give to different networks to make opinion aggregation more reliable.
What this means in practice
- •For social media platform designers: Optimize the weighting of multiple social networks to reduce manipulated opinion distortions in aggregated user feedback.
- •For online polling service teams: Detect and mitigate strategic misreporting across interconnected polling sources to improve accuracy of combined survey results.
A theory result. No direct application yet.
Authors
Raman Ebrahimi, Massimo Franceschetti
Abstract
Models of opinion dynamics on networks, provide a framework to study how a network of agents aggregates dispersed opinions into a consensus. However, existing models assume that agents truthfully report their opinions, and do not account for environments in which a platform aggregates agents' reports across multiple networks, and agents can strategically report different opinions on each. In this paper, we propose a model of strategic opinion manipulation on multiplex networks, in which a platform merges L network layers with attention weights, and each agent, holding a private opinion, chooses (potentially different) reports on each layer, at a layer-specific misreporting cost, so as to pull the merged consensus toward their own opinion. We show that this game has a unique Nash equilibrium in closed form, that the resulting consensus is the truthful consensus under a centrality tilted toward a manipulability index of each agent, and that the resulting distortion is the (centrality-weighted) covariance of agents' manipulability and opinions. We further show that agents' reports on every layer are more extreme than their opinions, so that the polarization observed by the platform overestimates the true polarization. Notably, we highlight that merging layers is a double-edged sword: as manipulability depends on the square of an agent's influence on each layer, spreading attention across layers dilutes manipulation, while heterogeneous misreporting costs across layers and shifts in agents' centralities can amplify it. Finally, we characterize the platform's optimal choice of attention weights, in closed form when the layers share a stationary distribution, and through an exact gradient and a marginal test otherwise. Together, our findings shed light on when aggregating opinions across networks is (not) robust to strategic manipulation, and point out potential interventions to alleviate it.