Asymmetric coevolutionary voter dynamics

TL;DR

This paper introduces an asymmetric coevolutionary voter model where different opinion groups use distinct strategies for spreading opinions and rewiring, analyzing its phase diagram, metastability, and consensus dynamics through simulations and pair approximation.

Contribution

It provides a comprehensive phase diagram of the asymmetric model and compares analytical predictions with stochastic simulations, highlighting how asymmetry influences consensus and active phases.

Findings

Global consensus is more likely than in the symmetric case.

Rewiring accelerates convergence to consensus.

Final states depend on system parameters, not initial conditions, in large networks.

Abstract

We consider a modification of the adaptive contact process which, interpreted in the context of opinion dynamics, breaks the symmetry of the coevolutionary voter model by assigning to each node type a different strategy to promote consensus: orthodox opinion holders spread their opinion via social pressure and rewire their connections following a segregationist strategy; heterodox opinion holders adopt a proselytic strategy, converting their neighbors through personal interactions, and relax to the orthodox opinion according to its representation in the population. We give a full description of the phase diagram of this asymmetric model, using the standard pair approximation equations and assessing their performance by comparison with stochastic simulations. We find that although global consensus is favored with regard to the symmetric case, the asymmetric model also features an active phase. We study the stochastic properties of the corresponding metastable state in finite-size networks, discussing the applicability of the analytic approximations developed for the coevolutionary voter model. We find that, in contrast to the symmetric case, the final consensus state is predetermined by the system's parameters and independent of initial conditions for sufficiently large system sizes. We also find that rewiring always favors consensus, both by significantly reducing convergence times and by changing their scaling with system size.