  The construction of most supervised learning datasets revolves around
collecting multiple labels for each instance, then aggregating the labels to
form a type of "gold-standard". We question the wisdom of this pipeline by
developing a (stylized) theoretical model of this process and analyzing its
statistical consequences, showing how access to non-aggregated label
information can make training well-calibrated models more feasible than it is
with gold-standard labels. The entire story, however, is subtle, and the
contrasts between aggregated and fuller label information depend on the
particulars of the problem, where estimators that use aggregated information
exhibit robust but slower rates of convergence, while estimators that can
effectively leverage all labels converge more quickly if they have fidelity to
(or can learn) the true labeling process. The theory makes several predictions
for real-world datasets, including when non-aggregate labels should improve
learning performance, which we test to corroborate the validity of our
predictions.
