Majority-vote model on continuous networks

The dynamics of opinion formation in societies is a complex phenomenon where collective herd behavior and personal ideas drive essential grouping mechanics. This work investigates the evolutionary dynamics of opinion formation on a continuous network of social interactions. We use the two-state majority-vote model with noise, where an individual adopts the opinion of the majority of its neighbors with probability 1 − q, and a different opinion with chance q, where q stands for the noise parameter. This model presents three collective social opinion states: consensus, polarization, and fragmentation. In the continuous network framework, the interacting population consists of N individuals randomly positioned in a continuous square area of side L = 1, with periodic boundary conditions. The position of every individual assumes real-valued coordinates constrained to the square area, and we relate the average connectivity of each individual with their social interaction radius. We employ Monte Carlo simulations and finite-size scaling analysis to estimate the critical noise parameter as a function of the average connectivity and obtain the phase diagram and its critical exponents β/ν, γ/ν and 1/ν. We observe that the critical noise is an increasing function of the interaction radius R and that a higher R-value favors consensus.