"Bounded-Confidence Models of Opinion Dynamics with Adaptive Confidence Bounds"

Another of my papers just came out in final form. Here are some details.

Title: Bounded-Confidence Models of Opinion Dynamics with Adaptive Confidence Bounds

Authors: Grace J. Li, Jiajie Luo, and Mason A. Porter

Abstract: People's opinions change with time as they interact with each other. In a bounded-confidence model (BCM) of opinion dynamics, individuals (which are represented by the nodes of a network) have continuous-valued opinions and are influenced by neighboring nodes whose opinions are sufficiently similar to theirs (i.e., are within a confidence bound). In this paper, we formulate and analyze discrete-time BCMs with heterogeneous and adaptive confidence bounds. We introduce two new models: (1) a BCM with synchronous opinion updates that generalizes the Hegselmann–Krause model; and (2) a BCM with asynchronous opinion updates that generalizes the Deffuant–Weisbuch model. We analytically and numerically explore our adaptive-confidence BCMs' limiting behaviors, including the confidence-bound dynamics, the formation of clusters of nodes with similar opinions, and the time evolution of ``effective graphs,"" which are time-dependent subgraphs of networks with edges only between nodes that are receptive to each other. For a variety of networks and a wide range of values of the parameters that control the increase and decrease of confidence bounds, we demonstrate numerically that our adaptive-confidence BCMs result in fewer major opinion clusters and longer convergence times than the baseline (i.e., nonadaptive) BCMs. In our numerical simulations, we also observe that our adaptive-confidence BCMs can have adjacent nodes that converge to the same opinion but are not receptive to each other. This qualitative behavior does not occur in the associated baseline BCMs.