Aggregation theory and the relevance of some issues to others

I propose a new axiom on the aggregation of individual yes/no judgments on propositions into collective judgments: each collective judgment depends only on people's judgments on 'relevant' propositions. This contrasts with classical independence: each collective judgment depends only on people's judgments on the 'current' proposition. I generalize the premise-based and sequential-priority rules to an arbitrary priority structure over propositions, instead of a dichotomous premise/conclusion structure or a linear order of priority. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow's Theorem (in its general and indifference-free versions) and the Arrow-type theorem in judgment aggregation.