Modeling Opinion Dynamics: Theoretical analysis and continuous approximation

TL;DR

This paper presents a theoretical analysis of opinion dynamics, providing exact solutions for a persuasion model with local and non-local interactions, validated by simulations.

Contribution

It introduces a novel theoretical approach to solve master equations in opinion formation models with non-local kernels.

Findings

Exact analytical solutions for opinion dynamics models

Excellent agreement between simulations and theoretical predictions

Insights into long and short range interaction effects

Abstract

Frequently we revise our first opinions after talking over with other individuals because we get convinced. Argumentation is a verbal and social process aimed at convincing. It includes conversation and persuasion. In this case, the agreement is reached because the new arguments are incorporated. In this paper we deal with a simple model of opinion formation with such persuasion dynamics, and we find the exact analytical solutions for both, long and short range interactions. A novel theoretical approach has been used in order to solve the master equations of the model with non-local kernels. Simulation results demonstrate an excellent agreement with results obtained by the theoretical estimation.