Opinion response functions are key to understanding tipping of social conventions

TL;DR

This paper introduces opinion response functions as a new analytical tool to understand how small committed minorities can overturn social conventions, providing a theoretical framework that complements previous simulation-based studies.

Contribution

It develops a mean-field ODE model using opinion response functions to analyze opinion dynamics and determine the minimum size of a committed minority needed to overturn social conventions.

Findings

Confirmed earlier numerical results on minority influence

Provided a precise formula for critical minority size

Offered a formal analysis of opinion coexistence and overturning

Abstract

The extent to which committed minorities can overturn social conventions is an active area of research in the mathematical modelling of opinion dynamics. Researchers generally use simulations of agent-based models (ABMs) to compute approximate values for the minimum committed minority size needed to overturn a social convention. In this manuscript, we expand on previous work by studying an ABM's mean-field behaviour using ordinary differential equation (ODE) models and a new tool, opinion response functions. Using these methods allows for formal analysis of the deterministic model which can provide a theoretical explanation for observed behaviours, e.g., coexistence or overturning of opinions. In particular, opinion response functions are a method of characterizing the equilibria in our social model. Our analysis confirms earlier numerical results and supplements them with a precise formula for computing the minimum committed minority size required to overturn a social convention.