Before revision:  Herein, we analyze the synchronous k-Majority dynamics, where nodes sample k neighbors uniformly at random with replacement and adopt the majority state among the nodes in the sample ( potential ties are broken uniformly at random).
After revision:  Herein, we analyze the synchronous k-Majority dynamics, where in each discrete-time round nodes simultaneously sample k neighbors uniformly at random with replacement and adopt the majority state among the nodes in the sample ( potential ties are broken uniformly at random).