  The evaluation of noisy binary classifiers on unlabeled data is treated as a
streaming task: given a data sketch of the decisions by an ensemble, estimate
the true prevalence of the labels as well as each classifier's accuracy on
them. Two fully algebraic evaluators are constructed to do this. Both are based
on the assumption that the classifiers make independent errors. The first is
based on majority voting. The second, the main contribution of the paper, is
guaranteed to be correct. But how do we know the classifiers are independent on
any given test? This principal/agent monitoring paradox is ameliorated by
exploiting the failures of the independent evaluator to return sensible
estimates. A search for nearly error independent trios is empirically carried
out on the \texttt{adult}, \texttt{mushroom}, and \texttt{two-norm} datasets by
using the algebraic failure modes to reject evaluation ensembles as too
correlated. The searches are refined by constructing a surface in evaluation
space that contains the true value point. The algebra of arbitrarily correlated
classifiers permits the selection of a polynomial subset free of any
correlation variables. Candidate evaluation ensembles are rejected if their
data sketches produce independent estimates too far from the constructed
surface. The results produced by the surviving ensembles can sometimes be as
good as 1\%. But handling even small amounts of correlation remains a
challenge. A Taylor expansion of the estimates produced when independence is
assumed but the classifiers are, in fact, slightly correlated helps clarify how
the independent evaluator has algebraic `blind spots'.
