Comparison of Mathematical Models of Opinion Dynamics

Abstract

Sociophysics is an emerging interdisciplinary research field that uses theories and methods developed by physicists as a modelling framework for various social science phenomena. This paper presents the Sznajd model, which is the basis of one of the simplest yet most efficient methods to predict the collective human behaviour in a binary opinion society. This model is a variation of the Ising model – a mathematical model used in statistical mechanics when studying the ferromagnetic phase transitions for the magnetization of a system based on the interaction between the neighbouring atomic spins of the system. In both the Ising model and the Sznajd model, individuals are only allowed to have a binary opinion – yes (spin up) or no (spin down).  The Sznajd model is mostly based around the idea of social validation -  the model requires that two neighbours share the same opinion to be able to convince individuals around them of their opinion.  Using MATLAB, this paper applies a two dimensional simplified version of the Sznajd model to track the opinion movement over many time steps in a lattice of individuals with an initial randomly generated distribution of opinions. The results of this simplified model are then analyzed using psychological principals to examine the validity of the outcomes