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We study the joint evolution of worldviews by proposing a model of opinion dynamics, which is inspired in notions from evolutionary ecology. Agents update their opinion on a specific issue based on their propensity to change -- asserted by the social neighbours -- weighted by their mutual similarity on other issues. Agents are, therefore, more influenced by neighbours with similar worldviews (set of opinions on various issues), resulting in a complex co-evolution of each opinion. Simulations show that the worldview evolution exhibits events of intermittent polarization when the social network is scale-free. This, in turn, trigger extreme crashes and surges in the popularity of various opinions. Using the proposed model, we highlight the role of network structure, bounded rationality of agents, and the role of key influential agents in causing polarization and intermittent reformation of worldviews on scale-free networks.
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It is known that individual opinions on different policy issues often align to a dominant ideological dimension (e.g. left vs. right) and become increasingly polarized. We provide an agent-based model that reproduces these two stylized facts as emergent properties of an opinion dynamics in a multi-dimensional space of continuous opinions. The mechanisms for the change of agents opinions in this multi-dimensional space are derived from cognitive dissonance theory and structural balance theory. We test assumptions from proximity voting and from directional voting regarding their ability to reproduce the expected emerging properties. We further study how the emotional involvement of agents, i.e. their individual resistance to change opinions, impacts the dynamics. We identify two regimes for the global and the individual alignment of opinions. If the affective involvement is high and shows a large variance across agents, this fosters the emergence of a dominant ideological dimension. Agents align their opinions along this dimension in opposite directions, i.e. create a state of polarization.
In this paper, we propose a Boltzmann-type kinetic description of opinion formation on social networks, which takes into account a general connectivity distribution of the individuals. We consider opinion exchange processes inspired by the Sznajd model and related simplifications but we do not assume that individuals interact on a regular lattice. Instead, we describe the structure of the social network statistically, assuming that the number of contacts of a given individual determines the probability that their opinion reaches and influences the opinion of another individual. From the kinetic description of the system, we study the evolution of the mean opinion, whence we find precise analytical conditions under which phase transitions, i.e. changes of sign between the initial and the asymptotic mean opinions, occur. Furthermore, we show that a non-zero correlation between the initial opinions and the connectivity of the individuals is necessary to observe phase transitions. Finally, we validate our analytical results through Monte Carlo simulations of the stochastic opinion exchange processes on the social network.
In this work we study the opinion evolution in a community-based population with intergroup interactions. We address two issues. First, we consider that such intergroup interactions can be negative with some probability $p$. We develop a coupled mean-field approximation that still preserves the community structure and it is able to capture the richness of the results arising from our Monte Carlo simulations: continuous and discontinuous order-disorder transitions as well as nonmonotonic ordering for an intermediate community strength. In the second part, we consider only positive interactions, but with the presence of inflexible agents holding a minority opinion. We also consider an indecision noise: a probability $q$ that allows the spontaneous change of opinions to the neutral state. Our results show that the modular structure leads to a nonmonotonic global ordering as $q$ increases. This inclination toward neutrality plays a dual role: a moderated propensity to neutrality helps the initial minority to become a majority, but this noise-driven opinion switching becomes less pronounced if the agents are too susceptible to become neutral.
The electoral college of voting system for the US presidential election is analogous to a coarse graining procedure commonly used to study phase transitions in physical systems. In a recent paper, opinion dynamics models manifesting a phase transition, were shown to be able to explain the cases when a candidate winning more number of popular votes could still lose the general election on the basis of the electoral college system. We explore the dependence of such possibilities on various factors like the number of states and total population (i.e., system sizes) and get an interesting scaling behavior. In comparison with the real data, it is shown that the probability of the minority win, calculated within the model assumptions, is indeed near the highest possible value. In addition, we also implement a two step coarse graining procedure, relevant for both opinion dynamics and information theory.
We show using scaling arguments and Monte Carlo simulations that a class of binary interacting models of opinion evolution belong to the Ising universality class in presence of an annealed noise term of finite amplitude. While the zero noise limit is known to show an active-absorbing transition, addition of annealed noise induces a continuous order-disorder transition with Ising universality class in the infinite-range (mean field) limit of the models.
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