  In many machine learning applications, crowdsourcing has become the primary
means for label collection. In this paper, we study the optimal error rate for
aggregating labels provided by a set of non-expert workers. Under the classic
Dawid-Skene model, we establish matching upper and lower bounds with an exact
exponent $mI(\pi)$ in which $m$ is the number of workers and $I(\pi)$ the
average Chernoff information that characterizes the workers' collective
ability. Such an exact characterization of the error exponent allows us to
state a precise sample size requirement
$m>\frac{1}{I(\pi)}\log\frac{1}{\epsilon}$ in order to achieve an $\epsilon$
misclassification error. In addition, our results imply the optimality of
various EM algorithms for crowdsourcing initialized by consistent estimators.
