Consistent Judgement Aggregation : The Truth-Functional Case

Generalizing the celebrated “discursive dilemma,” we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions (the “conclusions”) and on a set of “premises” by which the conclusions are truth-functionally determined. We show that for conclusion- and premise-based aggregation rules to be mutually consistent, the aggregation must always be “oligarchic,” that is: unanimous within a subset of agents, and typically even be dictatorial. We characterize exactly when consistent non-dictatorial (or anonymous) aggregation rules exist, allowing for arbitrary conclusions and arbitrary interdependencies among premises