The process of polarisation as a loss of dimensionality: measuring changes in polarisation using Singular Value Decomposition of network graphs (2403.18191v2)

Abstract: In this paper we present new methods that extend Baldassari and Gelman's theory of polarisation. They show that it is useful to define polarisation as increasing correlation between positions in an ideological field, which reduces political pluralism. We also draw from post-structuralist work which argues that deliberate development of these correlations is a feature of polarised regimes such as apartheid. To measure polarisation in social networks, we use Random Dot Product Graphs to embed social networks in metric spaces. Singular Value Decomposition of a social network provides an embedded dimensionality which corresponds to the number of uncorrelated dimensions in the network. Each uncorrelated dimension in a social network represents a part of that society which allows two people from different groups to form a social connection, such as living in a racially integrated neighbourhood. A decrease in the optimal dimensionality for the embedding of the network graph means that the dimensions in the network are becoming more correlated, and therefore the network is becoming more polarised. We apply this method to the communication interactions among New Zealand Twitter users discussing climate change issues from 2017 to 2023. We find that the discussion is more polarised after 2020 than before, as shown by a decrease in the dimensionality of the communication network. Second, we apply this method to discussions of the COP climate change conferences, showing that our methods agree with other researchers' detections of polarisation in this space. Finally, we use networks generated by stochastic block models to explore how an increase of the isolation between distinct communities, or the increase of the predominance of one community over the other, in the social networks decrease the embedded dimensionality and are therefore identifiable as polarisation processes.