  We analyze the convergence of the $k$-opinion Undecided State Dynamics (USD)
in the population protocol model. For $k$=2 opinions it is well known that the
USD reaches consensus with high probability within $O(n \log n)$ interactions.
Proving that the process also quickly solves the consensus problem for $k>2$
opinions has remained open, despite analogous results for larger $k$ in the
related parallel gossip model. In this paper we prove such convergence: under
mild assumptions on $k$ and on the initial number of undecided agents we prove
that the USD achieves plurality consensus within $O(k n \log n)$ interactions
with high probability, regardless of the initial bias. Moreover, if there is an
initial additive bias of at least $\Omega(\sqrt{n} \log n)$ we prove that the
initial plurality opinion wins with high probability, and if there is a
multiplicative bias the convergence time is further improved. Note that this is
the first result for $k > 2$ for the USD in the population protocol model.
Furthermore, it is the first result for the unsynchronized variant of the USD
with $k>2$ which does not need any initial bias.
