Many-valued judgment aggregation: characteriing the possibility/impossibility boundary for an important class of agendas

A general model of judgment aggregation is presented in which judgments on propositions are not binary but come in degrees. The primitives of the model are a set of propositions, an entailment relation, and a “triangular norm” which establishes a lower bound on the degree to which a proposition is true whenever it is entailed by a set of propositions. For an important class of agendas, we identify a necessary and sufficient condition for judgment aggregation to be free from veto power. This condition says that the triangular norm used to establish the lower bound must contain a zero divisor.