  We consider the \emph{exact plurality consensus} problem for \emph{population
protocols}. Here, $n$ anonymous agents start each with one of $k$ opinions.
Their goal is to agree on the initially most frequent opinion (the
\emph{plurality opinion}) via random, pairwise interactions. The case of $k =
2$ opinions is known as the \emph{majority problem}. Recent breakthroughs led
to an always correct, exact majority population protocol that is both time- and
space-optimal, needing $O(\log n)$ states per agent and, with high probability,
$O(\log n)$ time~[Doty, Eftekhari, Gasieniec, Severson, Stachowiak, and
Uznanski; 2021]. We know that any always correct protocol requires
$\Omega(k^2)$ states, while the currently best protocol needs $O(k^{11})$
states~[Natale and Ramezani; 2019]. For ordered opinions, this can be improved
to $O(k^6)$~[Gasieniec, Hamilton, Martin, Spirakis, and Stachowiak; 2016]. We
design protocols for plurality consensus that beat the quadratic lower bound by
allowing a negligible failure probability. While our protocols might fail, they
identify the plurality opinion with high probability even if the bias is $1$.
Our first protocol achieves this via $k-1$ tournaments in time $O(k \cdot \log
n)$ using $O(k + \log n)$ states. While it assumes an ordering on the opinions,
we remove this restriction in our second protocol, at the cost of a slightly
increased time $O(k \cdot \log n + \log^2 n)$. By efficiently pruning
insignificant opinions, our final protocol reduces the number of tournaments at
the cost of a slightly increased state complexity $O(k \cdot \log\log n + \log
n)$. This improves the time to $O(n / x_{\max} \cdot \log n + \log^2 n)$, where
$x_{\max}$ is the initial size of the plurality. Note that $n/x_{\max}$ is at
most $k$ and can be much smaller (e.g., in case of a large bias or if there are
many small opinions).
