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.
After revision:  More in detail, we prove that for every k \geq 3 \geq3 there exists a critical value p_{k,q 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.