Binary Collective Choice with Multiple Premises

Imagine a group of individuals facing with a complicated yes-no question whose truth value is logically driven from multiple premises. Their purpose is to make a correct group judgment on the question based on their individual judgments. There are two types of ways to aggregate individual judgments: "the premise driven way" (PDW) and "the conclusion driven way" (CDW). We analyze which way is superior to the other to find a correct answer. In our analysis, we introduce a Boolean algebraic approach to formulate a general class of such judgment aggregation problems. We find that if a decision problem is conjunctive, then PDW is more likely to avoid "false acquittance," while CDW is more likely to avoid "false conviction". If a decision problem is disjunctive, the converse of this result holds. These conditions are sufficient to characterize intrinsic biases of aggregation procedures when an aggregation rule possesses no veto power. We also study the asymptotic properties of aggregation procedures, and find that, as the size of a group goes to infinity, PDW ensures the probability that the voting outcome is correct converges to one, while this holds for CDW only if an additional condition is satisfied.