The concern of this thesis is the modelling of opinion polarisation. There is increasing worry that the political debate of today has levels of polarisation that result in hostility between groups and the obstruction of collective decision making. One research approach to studying polarisation is opinion dynamics; it consists of the formal mathematical modelling and simulation of the opinions of a population to understand how they might reach consensus, polarisation, or somewhere in between. Simulating opinions and understanding population dynamics through scenarios, as well as identifying tipping points between consensus and polarisation, avoids the difficulty and complexity of observing a population's opinions change over time. However, a drawback is the limited empirical validation of current opinion dynamics research, which raises questions as to its relevancy in real-world application. A further shortcoming of the current literature is that the impacts of social identity and attitudes towards groups are rarely considered, despite the importance placed on these concepts in the social science literature. These two research gaps -- empirical validation and group identification -- are the subjects addressed in the following work in order to place opinion dynamics in an improved real-world context.
To answer this research aim, two contributions in the form of two modelling extensions are proposed. First, the perception of groups is incorporated into an existing opinion dynamics model such that the convergence or divergence of opinions is directly impacted by an individual's understanding of others as either in-group or out-group. The second extension seeks to enable the empirical validation of models by providing a framework that finds plausible model parameters for simulation. This is achieved by a mean-field approximation of the same model and subsequent numerical simulation, which allows for the modelling of opinion distributions of populations rather than the agent-based approach which focuses on an individual's opinion change. A set of criteria is then established in order to find simulated distributions that match behaviour displayed by empirical distributions and so may be considered plausible.
The findings from the group identification extension reveal that treatment of out-group is a central part of understanding the eventual polarisation of a population, while the influence of in-group interactions can temper extreme opinion shifts or, conversely, fragment groups from within. While the results of the mean-field extension identify a set of model parameters for which a given model can plausibly simulate an opinion distribution, which is a step towards closing the gap between theoretical opinion dynamics and empirical validation. Together, these findings contribute to ongoing debates surrounding the development of polarisation in public and private spheres, as well as enhancing the relevance of opinion dynamics through connection to social science theory and empirical validation.