Distilling the wisdom of crowds: weighted aggregation of decisions on multiple issues

Given the judgments of multiple voters regarding some issue, it is generally assumed that the best way to arrive at some collective judgment is by following the majority. We consider here the now common case in which each voter expresses some (binary) judgment regarding each of a multiplicity of independent issues and assume that each voter has some fixed (unknown) probability of making a correct judgment for any given issue. We leverage the fact that multiple votes by each voter are known in order to demonstrate, both analytically and empirically, that a method based on maximum likelihood estimation is superior to the simple majority rule for arriving at true collective judgments.