Before revision:  More in detail,  we prove that for every k \geq 3 \geq3 there exists a p_k^\star such that if p>p _k^\star the process reaches in O(1) rounds a \sigma-almost-consensus, i.e., a configuration where a fraction 1-o(1) of the volume is in state \sigma. On the other hand, if p < p_k^\star, we look at random initial configurations in which every node is in state \sigma with probability 1-q independently of the others.
After revision:  More in detail, we prove that for every k \geq 3 \geq3 there exists a p_k^\star such that if p>p _{k,q < p_k^\star, we look at random initial configurations in which every node is in state \sigma with probability 1-q independently of the others.