Before revision:  We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT} p , k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k}  .
After revision:  We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT} p \SUBSCRIPT k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k} .