Insight Networks: James Gleeson, University of Limerick, and the mathematics of opinion

Submitted on Friday, 17/02/2023

Data science is playing an increasingly important role in the social sciences. Sociophysics is a field that studies social behaviour using statistical theory. A key focus of sociophysics study is polling and public opinion. Making predictions based on public opinion data is a valuable mechanism for driving positive change in public health behaviours or attitudes to climate action, for example. Data models of opinion dynamics can include variables for how often people communicate with others who hold different opinions and so the study of echo chamber effects on social media is also a potential beneficiary.

The Deffuant model  is a popular mathematical model in sociophysics. Each individual holds an opinion and the opinion distribution of the population evolves with encounters between individuals. Social interactions perform an important function in the process of opinion formation. Discussions among friends, co-workers and family can lead people to change their views. How likely is this to happen? Mathematical modelling can give us an insight.

The Deffuant model is based on the principle that a pair of interacting individuals update their opinions towards a compromise only if their opinions differ by less than a given threshold, called the ‘confidence bound’. In other words, if two individuals are too far apart and confident in their thinking  it is unlikely that a compromise, and an evolution of opinion, will take place. The Deffuant model provides a mathematical equation to predict the evolution of opinion based on a number of variables.

Professor James Gleeson holds the Chair in Industrial and Applied Mathematics at the University of Limerick and is a Principal Investigator with the Insight SFI Research Centre for Data Analytics. He studies mean-field equations that have been developed recently to approximate the dynamics of the Deffuant model of opinion formation.

These equations can describe both fully-mixed populations and the case where individuals interact only along edges of a network. In each case, interactions only occur between individuals whose opinions differ by less than a given parameter; the confidence bound. The size of the confidence bound parameter is known to strongly affect both the dynamics and the number and location of opinion clusters. In this work Prof Gleeson and his collaborators carry out a mathematical analysis of the mean-field equations to investigate the role of the confidence bound and boundaries on these important observables of the model. They consider the limit in which the confidence bound interval is small and identify the key mechanisms driving opinion evolution.

This is fundamental mathematical research about the properties of certain types of models but it has the potential to aid understanding in opinion dynamics that could help in efforts to encourage populations to adopt healthier or more environmentally-friendly practices or to understand social phenomena like polarisation or vaccine hesitancy.

Read the full abstract here