Judgment aggregation with consistency alone

All existing impossibility theorems on judgment aggregation require individ- ual and collective judgment sets to be consistent and complete (in some recent results with completeness relaxed to deductive closure), arguably a demand- ing rationality requirement. They do not carry over to aggregation functions mapping pro…les of (merely) consistent individual judgment sets to (merely) consistent collective ones. We prove that, whenever the agenda of propositions under consideration exhibits mild interconnections, any such aggregation func- tion that is "neutral" between the acceptance and rejection of each proposition is dictatorial. We relate this theorem to the literature.