Cooperative and affinity effects on majority-vote opinion dynamics

Abstract

This work investigates how social collaborative behavior and connectivity influence con- sensus formation of the majority-vote model with noise q. Collaborative agents experience a reduced e!ective social noise μq, where 0 <μ< 1 is the noise sensibility parameter that enhances social validation. Using Monte Carlo simulations, we find second-order dissensus- consensus phase transitions and the cooperative majority-vote model belongs to the same universality class as the 2D equilibrium Ising model. We investigate social entropy produc- tion in the majority-vote model on regular square networks and conjecture the heterogeneity between cooperative and non-cooperative individuals could be a potential natural manifesta- tion of the Maximum Entropy Production Principle, where the most probable non-equilibrium steady states have the highest entropy production rate. Our results highlight the e!ects of a social anxiety attenuation level in improving group consensus. Inspired by social media, such as X and Facebook, we also propose and examine the e!ects of a"nity-based scale-free networks on opinion formation dynamics. In this context, we define a continuous substrate and modify the Barabási-Albert algorithm by introducing a connection probability based on distance and power law exponent ω, defined as the a"nity parameter. These a"nity-based networks display the scale-free property, feature a higher clustering coe"cient, and generate concave power law distributions, aligning with real-world data of popular social media. We find that local a"nitypromotes the emergence of opinion polarization and phase transitions in the majority-vote model, introducing a new universality class. Our work exhibits how the connections between cooperation, a"nity, and opinion dynamics shape consensus formation in social networks, pro-viding essential perspectives on societal behavior and the underlying mechanisms of complex systems.