  Multiclass extensions of the support vector machine (SVM) have been
formulated in a variety of ways. A recent empirical comparison of nine such
formulations [Do\v{g}an et al. 2016] recommends the variant proposed by Weston
and Watkins (WW), despite the fact that the WW-hinge loss is not calibrated
with respect to the 0-1 loss. In this work we introduce a novel discrete loss
function for multiclass classification, the ordered partition loss, and prove
that the WW-hinge loss is calibrated with respect to this loss. We also argue
that the ordered partition loss is maximally informative among discrete losses
satisfying this property. Finally, we apply our theory to justify the empirical
observation made by Do\v{g}an et al. that the WW-SVM can work well even under
massive label noise, a challenging setting for multiclass SVMs.
