Before revision:  We consider a biased communication model: whenever nodes sample a neighbor they see state \sigma with some probability p, regardless of the state of the sampled node, and its true state with probability 1-p. Differently from previous works where specific graph topologies are considered, our analysis only requires the graphs to be sufficiently dense, i.e., to have minimum degree \omega(\log n), without any further topological assumption. In this setting we prove two phase transition phenomena, both occurring with high probability, depending on the bias p and on the initial unbalance toward state \sigma.
After revision:  We consider an external agent that wants to subvert the initial majority and, in each round, either tries to alter the communication between each pair of nodes transmitting state \mathcal{B and on the initial unbalance toward state \sigma.