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Exploring Three-State Opinion Dynamics: A Journey Through Single and Multilayer Network Topologies

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Universitat de Barcelona. Facultat de Física

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[eng] The word "emergence" refers to the formation of collective behaviors, actions not undertaken by the components of a system when isolated. On one hand, we have the components—particles or agents, ranging from water molecules to bees, birds, and humans. On the other hand, we see interactions, the capacity for these particles to perceive each other, through electrical energy, released and received substances, observation and movement coordination, or verbal communication.
Societies are intricate systems composed of multiple interacting layers. Grasping their mechanics enables us to enhance our analytical and strategic capabilities. A significant breakthrough in twentieth-century science was the development of statistical physics, which bridges microscopic and macroscopic phenomena and provides an ideal framework for examining a system's emergent properties. Consequently, much of the sociophysics literature relies on physico-statistical models, initially devised to describe physical entities like gases and magnetic materials.
This thesis adapts a physical model, originally used to describe helium isotope transitions to explore opinion dynamics. The aim is to underscore the influence of a central faction in opinion exchanges and examine how varying degrees of conviction between neutral and extremist viewpoints impact the overall dynamics. By applying the principle of homophily or peer pressure, the model implements individuals’ tendency to align their opinions with those they interact with. Additionally, the model integrates the possibility of deviations from this alignment, similar to thermal fluctuations in physical systems.
The implementation across diverse network topologies helps capture some fundamental aspects of human behavior, such as the phenomenon of cognitive dissonance and the reconfiguration of relationships following a preference for like-minded associations. Initial applications to straightforward networks provide a base for extending the study to more complex structures, integrating multi-level community structures and real networks extracted from platforms like Twitter.
The thesis is structured into two main sections: the first focuses on single-layer topologies, and the second expands into spatiotemporal and multilayer topologies. The foundational part of the thesis sets the stage for dynamic and equilibrium analyses using mean-field theory, then progresses to models that include complex topological features. This consists of the exploration of completely random networks as well as synthetic networks with multi-level community structures.
The second part of the thesis explores, on the one hand, the coevolution of topology and opinion dynamics, merging ideas from active matter and opinion models. On the other hand, it introduces a novel framework for depicting individual opinion states, moving away from a singular variable to a network of beliefs.

The goal is to deepen our understanding of topological nuances within a discrete opinion model, which has two extreme states and a neutral one — the latter not signifying indecision but a different option with various levels of engagement. When there is a dense connection pattern, with a homogeneous degree distribution, neutral agents can dominate the opinion dynamics, catalyzing neutral consensus, even when less committed than extremists. On the other hand, sparser topologies can prevent consensus and lead to echo chambers shaped by the network structure.


Finally, by using network descriptions to broaden the concept of opinion states, we facilitate the study of consensus formation at multiple scales. This framework allows us to explain the presence of zealots resulting from a star-like internal topology in an agent's belief system. Sparse belief systems can lead to cognitive dissonance which, in some cases, enhances global agreement.
Furthermore, the intermixing of agents with diverse internal structures significantly affects individual and collective behavior, especially near critical transition points, which could be useful in understanding system-wide shifts in consensus.

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[cat] La paraula emergència es refereix a l'existència o formació de comportaments col·lectius, allò que els constituents del conjunt no farien si estiguessin sols. Destaca la importància de la física estadística en l'enllaç entre fenòmens microscòpics i macroscòpics, oferint un marc per a l'estudi de propietats emergents.
La tesi adapta un model físic per analitzar la dinàmica d’opinions, emfatitzant l'existència d'una facció central que participa en l'intercanvi d'opinions de manera activa, i permet modular el seu grau de convicció respecte a les faccions extremistes per a estudiar-ne l'efecte. L'evolució del sistema està dominada pel principi d'homofília o pressió de grup, que assumeix la tendència a l'aliniament de les opinions pròpies amb les dels individus amb qui interaccionem. D'altra banda, es considera una certa probabilitat que aquesta tendència no es compleixi, per l'acumulació de diversos factors com ara tensions o conflictes socials. L'increment d'aquesta probabilitat es relaciona amb el concepte de temperatura en els sistemes físics.
Es proposa l'aplicació del model a diferents topologies, de més senzilles a més elaborades. Quan hi ha un patró de connexió dens i una distribució de graus homogènia, els agents neutres poden dominar la dinàmica, catalitzant un consens neutral, encara que estiguin menys compromesos que els extremistes. D'altra banda, les topologies més disperses poden impedir el consens i conduir a cambres de ressò conformades per l'estructura de la xarxa. També s’explora la coevolució de la topologia amb la dinàmica d'opinions, barrejant conecptes de matèria activa i models d'opinió.
Fnalment utilitzem les descripcions en forma de xarxes per ampliar el concepte d'estats d'opinió, facilitant l'estudi de la formació de consens a diverses escales. Aquest marc ens permet explicar la presència de fanàtics com a resultat d'una topologia interna en forma d'estrella en el sistema de creences d'un agent. Els sistemes de creences amb poques connexions internes poden conduir a la dissonància cognitiva, que en alguns casos pot millorar el grau de consens social. A més, la barreja d'agents amb estructures internes diverses afecta significativament el comportament individual i col·lectiu, especialment a prop de punts de transició crítics, el que podria ser útil a l'hora d'entendre canvis en el consens global del sistema.

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Exploring Three-State Opinion Dynamics: A Journey Through Single and Multilayer Network Topologies