  We present a family of pairwise tournaments reducing $k$-class classification
to binary classification. These reductions are provably robust against a
constant fraction of binary errors. The results improve on the PECOC
construction \cite{SECOC} with an exponential improvement in computation, from
$O(k)$ to $O(\log_2 k)$, and the removal of a square root in the regret
dependence, matching the best possible computation and regret up to a constant.
