Bounded-Confidence Models of Opinion Dynamics with Adaptive Confidence Bounds

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Publication date: 13 March 2023

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 only by neighboring nodes whose opinions are within their 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 (HK) and (2) a BCM with asynchronous opinion updates that generalizes the Deffuant--Weisbuch (DW) model. We analytically and numerically explore our adaptive BCMs' limiting behaviors, including the confidence-bound dynamics, the formation of clusters of nodes with similar opinions, and the time evolution of an ``effective graph, which is a time-dependent subgraph of a network with edges between nodes that can currently influence each other. For a wide range of parameters that control the increase and decrease of confidence bounds, we demonstrate for a variety of networks that our adaptive BCMs result in fewer major opinion clusters and longer convergence times than the baseline (i.e., nonadaptive) BCMs. We also show that our adaptive BCMs can have pairs of adjacent nodes that converge to the same opinion but are not able to influence each other. This qualitative behavior does not occur in the associated baseline BCMs.

Has companion code repository: https://gitlab.com/graceli1/adaptive-confidence-bcm

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