Biased Opinion Dynamics: When the Devil Is in the Details

TL;DR

This paper models opinion dynamics in multi-agent networks with bias, analyzing how different update rules and network structures influence convergence to a superior opinion, revealing distinct effects of topology under different rules.

Contribution

It introduces a modular framework for biased opinion dynamics, analyzing convergence under majority and voter rules with insights into topology's role.

Findings

Voter rule convergence speed is topology-independent.

Majority rule convergence slows with increased network density.

The model captures complex interactions between bias, dynamics, and social structure.

Abstract

We investigate opinion dynamics in multi-agent networks when a bias toward one of two possible opinions exists; for example, reflecting a status quo vs a superior alternative. Starting with all agents sharing an initial opinion representing the status quo, the system evolves in steps. In each step, one agent selected uniformly at random adopts the superior opinion with some probability $\alpha$, and with probability $1 - \alpha$ it follows an underlying update rule to revise its opinion on the basis of those held by its neighbors. We analyze convergence of the resulting process under two well-known update rules, namely majority and voter. The framework we propose exhibits a rich structure, with a non-obvious interplay between topology and underlying update rule. For example, for the voter rule we show that the speed of convergence bears no significant dependence on the underlying topology, whereas the picture changes completely under the majority rule, where network density negatively affects convergence. We believe that the model we propose is at the same time simple, rich, and modular, affording mathematical characterization of the interplay between bias, underlying opinion dynamics, and social structure in a unified setting.