Noise-synchronizability of opinion dynamics

TL;DR

This paper investigates how noise can induce synchronization in opinion dynamics models that combine bounded confidence and local discourse topology, establishing that connectivity of the discourse graph is key for noise-induced consensus.

Contribution

It introduces a new opinion model combining bounded confidence and local discourse topology, and proves the equivalence between discourse graph connectivity and noise-induced synchronization.

Findings

Noise-synchronizability occurs if and only if the discourse graph is uniformly jointly connected.

Connectivity of the discourse graph is essential for noise to facilitate opinion consensus.

The model generalizes classical heterogeneous HK model with time-varying discourse topology.

Abstract

With the analysis of noise-induced synchronization of opinion dynamics with bounded confidence (BC), a natural and fundamental question is what opinion structures can be synchronized by noise. In the traditional Hegselmann-Krause (HK) model, each agent examines the opinion values of all the other ones and then choose neighbors to update its own opinion according to the BC scheme. In reality, people are more likely to interchange opinions with only some individuals, resulting in a predetermined local discourse relationship as introduced by the DeGroot model. In this paper, we consider an opinion dynamics that combines the schemes of BC and local discourse topology and investigate its synchronization induced by noise. The new model endows the heterogeneous HK model with a time-varying discourse topology. With the proposed definition of noise-synchronizability, it is shown that the compound noisy model is almost surely noise-synchronizable if and only if the time-varying discourse graph is uniformly jointly connected, taking the noise-induced synchronization of the classical heterogeneous HK model as a special case. As a natural implication, the result for the first time builds the equivalence between the connectivity of discourse graph and the beneficial effect of noise for opinion consensus.