The Premiss-Based Approach to Judgment Aggregation

We investigate judgment aggregation by assuming that some formulas of the agenda are singled out as premises, and the Independence condition (formula-wise aggregation) holds for them, though perhaps not for others. Whether premise-based aggregation thus defined is non-degenerate depends on how premises are logically connected, both among themselves and with other formulas. We identify necessary and sufficient conditions for dictatorship or oligarchy on the premisses, and investigate when these results extend to the whole agenda. Our theorems recover or strengthen several existing ones and are formulated for infinite populations, an innovation of this paper.