Consistency of weighted majority votes
This work addresses the problem of improving decision-making accuracy in expert voting systems, though it is incremental as it builds on classical decision-theoretic foundations.
The paper examines the consistency of optimal weighted majority voting rules, providing sharp error estimates for known expert competence levels and analyzing frequentist and Bayesian approaches when competence levels are unknown, with nearly optimal bounds and experimental validation.
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.