Brief Announcement: Phase Transitions of the k-Majority Dynamics in a Biased Communication Model.

We analyze the binary-state (either $R$ or $B$ ) $k$-majority dynamics in a biased communication model where nodes have some fixed probability $p$, independent of the dynamics, of being seen in state $B$ by their neighbors. In this setting we study how $p$, as well as the initial unbalance between the two states, impact on the speed of convergence of the process, identifying sharp phase transitions.