Optimization of consensus time by combining the voter and the majority voter models on scale-free networks

We introduce a spin model combining the majority voter model with probability p and the voter model with probability 1- p and then measure its consensus time on scale-free networks with various degree exponents γ. We find that consensus time depends on both p and γ. When all spins follow either the voter model or the majority voter model, it takes much greater time to reach consensus. On the other hand, when spins may alternate between the majority voter model and the voter model, consensus time is shortened. We find via numerical calculation that the optimized ratio to minimize consensus time is around p =0.72.