Premise Independence in Judgment Aggregation

Judgment aggregation studies how agent opinions on logically interconnected propositions can be mapped into a collective judgment on the same propositions, and is plagued by impossibility results. In this paper we study the central notion of independence in these impossibility results. First, we argue that the distinction between the premises and conclusions play an important role in the benchmark examples of judgment aggregation. Second, we consider the notion of independence in judgment aggregation frameworks, and we observe that the distinction between premises and conclusion is not taken into account. Third, based on our analysis, we introduce independence assumptions that distinguish premises from conclusion. We show that, by introducing new operators that satisfy our independence assumptions, the problematic impossibility results no longer hold.