Local interaction scale controls the existence of a non-trivial optimal critical mass in opinion spreading

TL;DR

This paper investigates how local interaction scales influence the existence of an optimal critical mass in opinion spreading, revealing a unique critical mass that maximizes convergence efficiency and complex relaxation dynamics.

Contribution

It introduces a model showing the impact of local interaction scales on critical mass and identifies a non-trivial optimal critical mass for opinion consensus.

Findings

Existence of a unique, non-trivial critical mass for optimal consensus

Presence of two distinct relaxation time scales depending on critical mass

Metastable states influence the relaxation dynamics

Abstract

We study a model of opinion formation where the collective decision of group is said to happen if the fraction of agents having the most common opinion exceeds a threshold value, a \textit{critical mass}. We find that there exists a unique, non-trivial critical mass giving the most efficient convergence to consensus. In addition, we observe that for small critical masses, the characteristic time scale for the relaxation to consensus splits into two. The shorter time scale corresponds to a direct relaxation and the longer can be explained by the existence of intermediate, metastable states similar to those found in [P.\ Chen and S.\ Redner, Phys.\ Rev.\ E \textbf{71}, 036101 (2005)]. This longer time-scale is dependent on the precise condition for consensus---with a modification of the condition it can go away.