Mathematical and statistical models for studying social interaction

Individuals’ opinions, beliefs and behaviours are formed through social interaction. In this thesis we are interested in the influence of social interaction on (i) how opinions spread and (ii) the emergence of social norms. In the first part of this thesis we derive a generalised mean-field ap proximation that accounts for the effect of network topology on Def fuant opinion dynamics through the degree distribution or community structure of the network. We examine the accuracy of the approxima tion by comparing with Monte Carlo simulations on both synthetic and real-world networks. We carry out a mathematical analysis of the mean-field equations to understand the early-time behaviour and to locate the clusters in steady state. We obtain analytic results on fully connected networks and networks with two degree classes. In the second part of this thesis we outline a modelling methodology for analysing social interaction data. We apply our method to data collected using the Virtual Interaction Application (VIAPPL) — a software platform for conducting experiments that reveal how social norms and identities emerge through social interaction. We apply our model to show that ingroup favouritism and reciprocity are present in the experiments, and to quantify the strengthening of these be haviours over time. Our method enables us to identify participants whose behaviour is markedly different from the norm. We use the method to provide a visualisation of the data that highlights the level of ingroup favouritism, the strong reciprocal relationships, and the different behaviour of participants in the game. While our method ology was developed with VIAPPL in mind, its usage extends to any type of social interaction data.