Premise-based versus outcome-based information aggregation

A group of rational individuals with common interest need to select one of two outcomes. The optimal decision depends on whether certain premises or pieces of evidence are established as being true, and each member receives a noisy signal of the truth value of the relevant premises. Should the group reach a decision by voting whether each premise is true or false, or should they simply vote on the outcome? We show that for any finite number of individuals, the premise-based voting rule is more efficient in aggregating information than the outcome-based rule. However, generically, the gain from using the premise-based over the outcome-based rule can only be marginal when numerous individuals express independent opinions. Indeed, the outcome-based game is almost always asymptotically efficient.