UCLA

In experiments that date back to at least the 1930s, psychologists have observed the tendency of subjects to change their beliefs to match those of others. From this observation, researchers have hypothesized that the beliefs of populations should move towards consensus. However, despite marked similarities between the beliefs of individuals in social groups, large-scale consensus is often not observed. This disparity between psychological and sociological observations, called the ``community-cleavage problem'', is one of many problems that have been examined by researchers through the development and analysis of mathematical models of belief changes. These mathematical models, often in the form of models for opinion dynamics or social influence, attract much interest from researchers for explaining how the behaviors of individuals combine to produce sociological phenomena.

In this dissertation, we draw from psychological studies to develop a consensus model of social influence. Our model is distinct from most previous models in that (1) it includes both direct and indirect social influence and (2) it incorporates group interactions of any number of individuals. We study the convergence time to consensus of our model under various assumptions on how groups form. In doing so, we make some hypotheses about how the size and composition of groups of interacting individuals affect the speed of convergence to consensus.

In various applications---such as optimizing both marketing and political campaigns and disrupting the formation of echo chambers in online social networks---researchers have used mathematical models to develop strategies for influencing opinions. These strategies prescribe how to modify factors like individuals' opinions, susceptibilities to influence, and social connections. In this dissertation, we apply our model of opinion dynamics to conflict resolution, and we propose group-selection strategies for choosing groups of individuals to meet for the purpose of accelerating convergence to consensus. We show through analytical estimates, simulations, and examples that our strategies generate an improvement in convergence time over random choices of groups.