  We study the evolution of majority dynamics with more than two states on the
binomial random graph $G(n,p)$. In this process, each vertex has a state in
$\{1,\ldots, k\}$, with $k\geq 3$, and at each round every vertex adopts state
$i$ if it has more neighbours in state $i$ that in any other state. Ties are
resolved randomly. We show that with high probability the process reaches
unanimity in at most three rounds, if $np\gg n^{2/3}$.
