Stochastic Opinion Dynamics under Social Pressure in Arbitrary Networks

TL;DR

This paper analyzes a stochastic opinion dynamics model where social pressure influences agents' declared opinions, revealing conditions for consensus and insights into inferring true beliefs under social influence.

Contribution

It introduces a comprehensive analysis of the Polya urn-based opinion model under social pressure, providing convergence and consensus conditions using Lyapunov and stochastic approximation methods.

Findings

Agents' declaration probabilities converge to equilibrium points.

Conditions for reaching consensus on declared opinions are established.

The model offers insights into inferring true beliefs under social pressure.

Abstract

Social pressure is a key factor affecting the evolution of opinions on networks in many types of settings, pushing people to conform to their neighbors' opinions. To study this, the interacting Polya urn model was introduced by Jadbabaie et al., in which each agent has two kinds of opinion: inherent beliefs, which are hidden from the other agents and fixed; and declared opinions, which are randomly sampled at each step from a distribution which depends on the agent's inherent belief and her neighbors' past declared opinions (the social pressure component), and which is then communicated to her neighbors. Each agent also has a bias parameter denoting her level of resistance to social pressure. At every step, each agent updates her declared opinion (simultaneously with all other agents) according to her neighbors' aggregate past declared opinions, her inherent belief, and her bias parameter. We study the asymptotic behavior of this opinion dynamics model and show that the agents' declaration probabilities approaches a set of equilibrium points of the expected dynamics using Lyapunov theory and stochastic approximation techniques. We also derive necessary and sufficient conditions for the agents to approach consensus on their declared opinions. Our work provides further insight into the difficulty of inferring the inherent beliefs of agents when they are under social pressure.