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Mathematical measures of societal polarisation
In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in society. This paper presents four mathematical measures of polarisation derived from graph and network representations of societies an...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9531819/ https://www.ncbi.nlm.nih.gov/pubmed/36194573 http://dx.doi.org/10.1371/journal.pone.0275283 |
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author | Adams, Johnathan A. White, Gentry Araujo, Robyn P. |
author_facet | Adams, Johnathan A. White, Gentry Araujo, Robyn P. |
author_sort | Adams, Johnathan A. |
collection | PubMed |
description | In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in society. This paper presents four mathematical measures of polarisation derived from graph and network representations of societies and information-theoretic divergences or distance metrics. Two of the methods, min-max flow and spectral radius, rely on graph theory and define polarisation in terms of the structural characteristics of networks. The other two methods represent opinions as probability density functions and use the Kullback–Leibler divergence and the Hellinger distance as polarisation measures. We present a series of opinion dynamics simulations from two common models to test the effectiveness of the methods. Results show that the four measures provide insight into the different aspects of polarisation and allow real-time monitoring of social networks for indicators of polarisation. The three measures, the spectral radius, Kullback–Leibler divergence and Hellinger distance, smoothly delineated between different amounts of polarisation, i.e. how many cluster there were in the simulation, while also measuring with more granularity how close simulations were to consensus. Min-max flow failed to accomplish such nuance. |
format | Online Article Text |
id | pubmed-9531819 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-95318192022-10-05 Mathematical measures of societal polarisation Adams, Johnathan A. White, Gentry Araujo, Robyn P. PLoS One Research Article In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in society. This paper presents four mathematical measures of polarisation derived from graph and network representations of societies and information-theoretic divergences or distance metrics. Two of the methods, min-max flow and spectral radius, rely on graph theory and define polarisation in terms of the structural characteristics of networks. The other two methods represent opinions as probability density functions and use the Kullback–Leibler divergence and the Hellinger distance as polarisation measures. We present a series of opinion dynamics simulations from two common models to test the effectiveness of the methods. Results show that the four measures provide insight into the different aspects of polarisation and allow real-time monitoring of social networks for indicators of polarisation. The three measures, the spectral radius, Kullback–Leibler divergence and Hellinger distance, smoothly delineated between different amounts of polarisation, i.e. how many cluster there were in the simulation, while also measuring with more granularity how close simulations were to consensus. Min-max flow failed to accomplish such nuance. Public Library of Science 2022-10-04 /pmc/articles/PMC9531819/ /pubmed/36194573 http://dx.doi.org/10.1371/journal.pone.0275283 Text en © 2022 Adams et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
spellingShingle | Research Article Adams, Johnathan A. White, Gentry Araujo, Robyn P. Mathematical measures of societal polarisation |
title | Mathematical measures of societal polarisation |
title_full | Mathematical measures of societal polarisation |
title_fullStr | Mathematical measures of societal polarisation |
title_full_unstemmed | Mathematical measures of societal polarisation |
title_short | Mathematical measures of societal polarisation |
title_sort | mathematical measures of societal polarisation |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9531819/ https://www.ncbi.nlm.nih.gov/pubmed/36194573 http://dx.doi.org/10.1371/journal.pone.0275283 |
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