Modeling and analysis of continuous opinion dynamics using statistical mechanical methods

In the past two decades, the advance in computational power and the availability of social interaction data have opened the way for applying statistical physics such as Monte-Carlo simulations, mean-field approximations, and theories of non-linear dynamics and network topology to explain and predict social dynamics. Opinion dynamics is an important topic in the study of social dynamics. In particular, Social Judgment Theory (SJT) is a well-established theory which explains how an individual's opinion changes upon encountering a new idea. SJT is not limited to predicting individual behavior. It also provides a framework for us to exploit statistical mechanical methods to simulate the collective opinion dynamics. Therefore, we proposed a SJT-based model to study opinion dynamics by using both agent-based and density-based approaches. Our model can be regarded as an extension of the famous Deffuant model. Unlike the Deffuant model, our model exhibits opinion polarization, which is a crucial topic in the real world. Through in-depth investigation, we found that the boomerang effect suggested in SJT could be an origin of opinion polarization. In this thesis, I presented and compared the results obtained from agent-based and density-based approaches. I also applied mean-field analysis to explain the interesting observations in phase diagrams and collective opinion dynamics. Lastly, by further adapting our model to heterogeneous agents, I discovered that advocating open-mindedness to a small fraction of agents could reduce the total number of final opinion clusters and the degree of opinion polarization. Our findings might help us to search for feasible solutions towards the problem of opinion polarization.published_or_final_versionPhysicsMasterMaster of Philosoph