UCLA

Bounded-confidence models (BCMs) are a type of model of opinion dynamics with continuous-valued opinions. The two most popular BCMs are the Deffuant--Weisbuch (DW) model [DNA00] and the Hegselmann--Krause (HK) model [HK02]. In a BCM, interacting pairs of agents only influence each other if their opinions differ by less than some “confidence bound” between them.One major challenge in the study of opinion dynamics is making models more realistic and applicable to real-world data and situations. In this dissertation, we develop and study three generalizations of BCMs. They each incorporate some mechanism to make them more realistic, while maintaining tractability.

We first develop and study a generalization of the DW model that uses node weights to model heterogeneous agent-activity levels. The node weights in this BCM allow us to consider individuals in a social network that share their ideas and opinions more frequently than others. Using numerical simulations, we systematically investigate the effects of node weights, which we assign uniformly at random to the nodes. We demonstrate that introducing heterogeneous node weights results in longer convergence times and more opinion fragmentation than in an associated baseline DW model.

We then investigate BCMs in which each pair of agents has a distinct confidence bound that changes when the pair interacts. The confidence bounds in these BCMs encode the mutual willingness of agents to consider each other's opinions. We demonstrate numerically that our adaptive BCMs tend to promote consensus and yield longer convergence times than the associated baseline BCMs. We also show that these adaptive BCMs can have neighboring agents that converge to the same opinion but are not receptive to each other. This qualitative behavior does not occur in the associated baseline BCMs.

Finally, we study BCMs that have multi-dimensional opinions that consist of multiple interdependent topics. When a pair of agents interact on a topic, whether or not they compromise their opinions depends on the differences in their opinions on all topics. Using numerical simulations, we demonstrate for these BCMs that the choice of initial opinion distribution has a large effect on the amount of opinion fragmentation.