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A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs

Hickok, Abigail and Kureh, Yacoub and Brooks, Heather Z. and Feng, Michelle and Porter, Mason A. (2022) A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs. SIAM Journal on Applied Dynamical Systems, 21 (1). pp. 1-32. ISSN 1536-0040. doi:10.1137/21m1399427. https://resolver.caltech.edu/CaltechAUTHORS:20220322-742527000

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Abstract

People's opinions evolve with time as they interact with their friends, family, colleagues, and others. In the study of opinion dynamics on networks, one often encodes interactions between people in the form of dyadic relationships, but many social interactions in real life are polyadic (i.e., they involve three or more people). In this paper, we extend an asynchronous bounded-confidence model (BCM) on graphs, in which nodes are connected pairwise by edges, to an asynchronous BCM on hypergraphs, in which arbitrarily many nodes can be connected by a single hyperedge. We show that our hypergraph BCM converges to consensus for a wide range of initial conditions for the opinions of the nodes, including for nonuniform and asymmetric initial opinion distributions. We also show that, under suitable conditions, echo chambers can form on hypergraphs with community structure. We demonstrate that the opinions of nodes can sometimes jump from one opinion cluster to another in a single time step; this phenomenon (which we call “opinion jumping'') is not possible in standard dyadic BCMs. Additionally, we observe a phase transition in the convergence time of our BCM on a complete hypergraph when the variance σ² of the initial opinion distribution equals the confidence bound c. We prove that the convergence time grows at least exponentially fast with the number of nodes when σ² > c and the initial opinions are normally distributed. Therefore, to determine the convergence properties of our hypergraph BCM when the variance and the number of hyperedges are both large, it is necessary to use analytical methods instead of relying only on Monte Carlo simulations.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1137/21M1399427DOIArticle
https://doi.org/10.1137/22M147267XDOIErratum
https://arxiv.org/abs/2102.06825arXivDiscussion Paper
ORCID:
AuthorORCID
Brooks, Heather Z.0000-0003-4274-107X
Porter, Mason A.0000-0002-5166-0717
Additional Information:© 2022 Society for Industrial and Applied Mathematics. Received by the editors February 17, 2021; accepted for publication (in revised form) by J. Moehlis August 24, 2021; published electronically January 4, 2022. The work of the first, second, fourth, and fifth authors was supported by National Science Foundation grant 1922952 through the Algorithms for Threat Detection (ATD) program. We thank Phil Chodrow and Ryan Wilkinson for helpful discussions and comments.
Errata:Erratum: A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs Abigail Hickok, Yacoub Kureh, Heather Zinn Brooks, Michelle Feng, and Mason A. Porter SIAM Journal on Applied Dynamical Systems 2022 21:2, 1660-1661; DOI: 10.1137/22M147267X
Funders:
Funding AgencyGrant Number
NSFDMS-1922952
Subject Keywords:opinion models, hypergraphs, bounded-confidence models, polyadic interactions
Issue or Number:1
Classification Code:AMS subject classifications. 91D30, 05C65, 05C82
DOI:10.1137/21m1399427
Record Number:CaltechAUTHORS:20220322-742527000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220322-742527000
Official Citation:A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs Abigail Hickok, Yacoub Kureh, Heather Z. Brooks, Michelle Feng, and Mason A. Porter SIAM Journal on Applied Dynamical Systems 2022 21:1, 1-32 https://doi.org/10.1137/21M1399427
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114013
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:23 Mar 2022 14:12
Last Modified:15 Aug 2022 20:27

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