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In this paper, we study numerically the dynamics of opinion formation under the influence of mass media using the q-voter model on a Barabasi–Albert network. We investigate the scenario where a voter adopts the mass media's opinion with a probability p when there is no unanimity among a group of q agents. Through numerical simulation, we identify a critical probability threshold, p t , at which the system consistently reaches complete consensus. This threshold probability p t decreases as the group size q increases, following a power-law relation p t ∝ q γ with γ ≈ − 1. 1 8 7. Additionally, we analyze the system's relaxation time, the time required to reach a complete consensus state. This relaxation time increases with the population size N, following a power-law τ ∝ N ν , where ν ≈ 1. 0 9 3. Conversely, an increase in the probability p results in a decrease in relaxation time following a power-law relationship τ ∝ p δ , with δ ≈ − 0. 5 9 6. The value of the exponent ν is similar to the exponents obtained in the voter and q-voter models across various network topologies. [ABSTRACT FROM AUTHOR]

A unifying setup for opinion models originating in statistical physics and stochastic opinion dynamics are developed and used to analyze election data. The results are interpreted in the light of political theory. We investigate the connection between Potts (Curie–Weiss) models and stochastic opinion models in the view of the Boltzmann distribution and stochastic Glauber dynamics. We particularly find that the q-voter model can be considered as a natural extension of the Zealot model, which is adapted by Lagrangian parameters. We also discuss weak and strong effects (also called extensive and nonextensive) continuum limits for the models. The results are used to compare the Curie–Weiss model, two q-voter models (weak and strong effects), and a reinforcement model (weak effects) in explaining electoral outcomes in four western democracies (United States, Great Britain, France, and Germany). We find that particularly the weak effects models are able to fit the data (Kolmogorov–Smirnov test) where the weak effects reinforcement model performs best (AIC). Additionally, we show how the institutional structure shapes the process of opinion formation. By focusing on the dynamics of opinion formation preceding the act of voting, the models discussed in this paper give insights both into the empirical explanation of elections as such, as well as important aspects of the theory of democracy. Therefore, this paper shows the usefulness of an interdisciplinary approach in studying real world political outcomes by using mathematical models. [ABSTRACT FROM AUTHOR]

During the COVID-19 pandemic, it became evident that the effectiveness of applying intervention measures is significantly influenced by societal acceptance, which, in turn, is affected by the processes of opinion formation. This article explores one among the many possibilities of coupled opinion–epidemic systems. The findings reveal either intricate periodic patterns or chaotic dynamics, leading to substantial fluctuations in opinion distribution and, consequently, significant variations in the total number of infections over time. Interestingly, the model exhibits a protective pattern.

Despite ample research devoted to the non-linear q-voter model and its extensions, little or no attention has been paid to the relationship between the composition of the influence group and the resulting dynamics of opinions. In this paper, we investigate two variants of the q-voter model with independence. Following the original q-voter model, in the first one, among the q members of the influence group, each given agent can be selected more than once. In the other variant, the repetitions of agents are explicitly forbidden. The models are analyzed by means of Monte Carlo simulations and via analytical approximations. The impact of repetitions on the dynamics of the model for different parameter ranges is discussed.