Consistency of weighted majority votes

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 precise necessary and sufficient conditions for consistency. When the competence levels are unknown, they must be empirically estimated. We provide frequentist and Bayesian analyses for this situation and discuss open problems presented by both approaches. Some of our proof techniques are non-standard and may be of independent interest. Experimental results are provided.