State-dependent opinion dynamics

We study the simultaneous evolution of the opinion profile and network topology of a system of N agents. Based on the opinion profile at any given time, agents probabilistically decide which other agents to form links with. The probability of a link being formed with another agent depends on both similarity of their opinions and the popularity of that agent. Agents then average their opinion with the opinions of the agents they have formed links with, giving rise to a new opinion profile that determines-in a probabilistic fashion- the network topology for the next time step. Thus both opinions and network structure exhibit a strong correlation over time. Despite this correlation, we show that this system converges to a consensus in opinion. We provide simulations of convergence times and the limiting opinion profile as a function of the parameters of the system.