Effect of multiple degrees of ambivalence on the Naming Game

TL;DR

This paper studies a modified Naming Game with multiple ambivalence levels, analyzing how zealots influence consensus stability and the emergence of multiple steady states in opinion dynamics.

Contribution

It introduces a multi-ambivalence model in the Naming Game and characterizes the stability of various steady states under different zealot configurations.

Findings

Consensus states are stable in the absence of zealots.

Zealots induce multiple steady states depending on their proportion.

Adding zealots on both sides enlarges the region with multiple steady states.

Abstract

We examine a modified Naming Game in the mean field where there are multiple degrees of ambivalence. Once an agent in one state fears an opinion one way or another, he or she moves one step in the appropriate direction. In the absence of zealots, the two consensus states are stable steady states and the uniform distribution is an unstable steady state. With zealots for one opinion only, there is a critical value below which there are three steady states and above which there is only one. Consensus in favor of the zealots' opinion is the steady state that always exists, and is stable. The second steady state is the uniform distribution in the absence of zealots, and moves away from the zealots' opinion as the number of zealots increases. This state is unstable. The last steady state starts at consensus against the zealots, and moves toward the zealots' opinion as the number of zealots increases. This state is stable. When zealots are added on both sides, the "beak" pattern observed for the Naming Game remains, with the region of multiple steady states growing with the addition of more intermediate states.