Complexity of Judgment Aggregation: Safety of the Agenda

Aggregating the judgments of a group of agents regarding a set of interdependent propositions can lead to inconsistent outcomes. One of the parameters involved is the agenda, the set of propositions on which agents are asked to express an opinion. We introduce the problem of checking the safety of the agenda: for a given agenda, can we guarantee that judgment aggregation will never produce an inconsistent outcome for any aggregation procedure satisfying a given set of axioms? We prove several characterisation results, establishing necessary and sufficient conditions for the safety of the agenda for different combinations of the most important axioms proposed in the literature, and we analyse the computational complexity of checking whether a given agenda satisfies these conditions.