  We revisit the classical decision-theoretic problem of weighted expert voting
from a statistical learning perspective. In particular, we examine the
consistency (both asymptotic and finitary) of the optimal Nitzan-Paroush
weighted majority and related rules. In the case of known expert competence
levels, we give sharp error estimates for the optimal rule. When the competence
levels are unknown, they must be empirically estimated. We provide frequentist
and Bayesian analyses for this situation. Some of our proof techniques are
non-standard and may be of independent interest. The bounds we derive are
nearly optimal, and several challenging open problems are posed. Experimental
results are provided to illustrate the theory.
