Social Networks and Opinion Dynamics

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Daniel Simonson (University of California, Irvine, USA), Samuel Lopez (University of California, Irvine, USA)


Social Networks and Opinion Dynamics is a thriving field at the intersection of mathematical biology and social sciences, where methods of mathematical biology are used to investigate the structural properties of communities, to gain understanding of patterns of group dynamics, faction formation, convergence, and stability. Studies of networks plays a central role in the mathematical and computational work performed in this area. This field of investigation is important to understand the dynamics of human opinion, including such new important topics as opinion spread on social media, the role of social media influencers, and the spread of false information/misinformation. The advance of communication platforms such as Twitter, Facebook, and others, has provided additional channels for information spread, that allow for higher level of self-organization and community formation. Studying these and related processes requires methods of mathematical biology, ecology, and population dynamics. Methodologically, it has applications areas of more traditional biology, including community structure in bacterial biofilms.

Maxi San Miguel

( Institute for Cross-Disciplinary Physics and Complex Systems - Campus Universitat de les Illes Balears, Spain)
"Coevolution dynamics of opinion and social network"
Modeling opinion dynamics of a set of interacting agents requires specifying the social network of interactions and the state (opinion) of the agents, represented as nodes of the network. The links of the network can also have a state, representing for instance attractive or repulsive interactions. In addition, the network might not be fixed, but adaptive with a time dependent topology in which agents can choose and change their neighbors. We introduce such a general dynamical model for binary opinions including the coupled dynamics of the states of the nodes, the states of the links and the topology of the network. We find a transition from a dynamical state of coexisting opinions to a consensus state showing network fragmentation at the transition line. Our results contribute to the description of processes of emergence of social fragmentation and polarization.

Tomasz Raducha

( IFISC, Institute for Cross-disciplinary Physics and Complex Systems (UIB-CSIC), Spain)
"Vulnerabilities of democratic electoral systems: zealot and media-susceptibility"
The vulnerability of democratic processes is under scrutiny after scandals related to Cambrige Analytica (2016 U.S. elections, the Brexit referendum, and elections in Kenya). The deceptive use of social media in the US, the European Union and several Asian countries, increased social and political polarization across world regions. Finally, there are straightforward frauds like Crimea referendum and Belarus elections. These challenges are eroding democracy, the most frequent source of governmental power, and raises multiple questions about its vulnerabilities. Democratic systems have countless ways of performing elections, which create different electoral systems (ES). It is therefore in citizens' interest to study and understand how different ESs relate to different vulnerabilities and contemporary challenges. These systems can be analyzed using network science in various layers -- they involve a network of voters in the first place, a network of electoral districts connected by commuting flow for instance, or a network of political parties to give a few examples. It is essential to provide new tools and arguments to the discussion on the evaluation of electoral systems. We aim at comparing different ESs in a dynamical framework. Our novel approach of analyzing electoral systems in such way with all its aspects included, from opinion dynamics in the population of voters to inter-district commuting patterns to seat appointment methods, will help answering questions like: Which electoral systems are more predictable/stable under fluctuations? Which electoral systems are the most robust (or vulnerable) under external and internal influences? Which features of electoral systems make them more (less) stable?

Daniel Simonson

(University of California, Irvine, USA)
" The effects of opinion weighting, (dis)agreement, and external influence on social group formation"
Opinion dynamics can be modeled by using agent-based simulations, where agents in a population are characterized by binary opinions on a number of different issues. They engage in pairwise interactions, whereby if the agreement level is high, the interlocutor is recognized as an ``ally' and the individual will flip one of their opinions to coincide with the interlocutor; if the agreement is low, they will switch away from the interlocutor. While it is usually assumed that all issues in the opinion vector are equally important, here we investigate how breaking this symmetry influences the dynamics. We find that the model outcomes can be predicted by a single Agreement-Disagreement Score (ADS) in [-1,1]. ADS characterizes how likely individuals in the population are to regard an interlocutor as an ally; low-ADS (very ``cautious') populations tend to converge to a two-faction system with exponentially high convergence times, while high-ADS (very ``trusting') populations tend to converge to a single-faction system relatively fast. In heterogeneous populations characterized by individual issue weighting, individuals that are more ``trusting' are more likely to join the majority group compared to those that are more ``cautious'. In the presence of an influencer, for ADS both near -1 and 1, a single faction tends to emerge, but in the former case it coincides with the influencer's opinions, while in the latter case it is the opposite. Time to fixation is also affected by the presence of an influencer, especially for negative-ADS populations, where it no longer experiences such a large increase near -1. One can say that an influencer unifies the population to align with the source of influence if ADS>1 and to disagree with it if ADS<1, and consensus is reached relatively fast for both extremely ``trusting' and extremely ``cautious' populations.

Gyorgy Korniss

( Rensselaer Polytechnic Institute, USA)
"The Impact of Heterogeneous Thresholds on Social Contagion and Influencing with Multiple Initiators"
The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We observe a non-monotonic change in the cascade size as we vary the standard deviation. Further, for a sufficiently large spread in the threshold distribution, the tipping-point behavior of the social influencing process disappears and is replaced by a smooth crossover governed by the size of initiator set. P.D. Karampourniotis, S. Sreenivasan, B.K. Szymanski, and G. Korniss, The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators', PLoS ONE 10(11): e0143020 (2015); http://dx.doi.org/10.1371/journal.pone.0143020. P. D. Karampourniotis, B.K. Szymanski, G. Korniss, 'Influence Maximization for Fixed Heterogeneous Thresholds', Scientific Reports 9, 5573 (2019); https://doi.org/10.1038/s41598-019-41822-w.

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