  We study a \emph{Plurality-Consensus} process in which each of $n$ anonymous
agents of a communication network initially supports an opinion (a color chosen
from a finite set $[k]$). Then, in every (synchronous) round, each agent can
revise his color according to the opinions currently held by a random sample of
his neighbors. It is assumed that the initial color configuration exhibits a
sufficiently large \emph{bias} $s$ towards a fixed plurality color, that is,
the number of nodes supporting the plurality color exceeds the number of nodes
supporting any other color by $s$ additional nodes. The goal is having the
process to converge to the \emph{stable} configuration in which all nodes
support the initial plurality. We consider a basic model in which the network
is a clique and the update rule (called here the \emph{3-majority dynamics}) of
the process is the following: each agent looks at the colors of three random
neighbors and then applies the majority rule (breaking ties uniformly).
  We prove that the process converges in time $\mathcal{O}( \min\{ k, (n/\log
n)^{1/3} \} \, \log n )$ with high probability, provided that $s \geqslant c
\sqrt{ \min\{ 2k, (n/\log n)^{1/3} \}\, n \log n}$.
  We then prove that our upper bound above is tight as long as $k \leqslant
(n/\log n)^{1/4}$. This fact implies an exponential time-gap between the
plurality-consensus process and the \emph{median} process studied by Doerr et
al. in [ACM SPAA'11].
  A natural question is whether looking at more (than three) random neighbors
can significantly speed up the process. We provide a negative answer to this
question: In particular, we show that samples of polylogarithmic size can speed
up the process by a polylogarithmic factor only.
