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.

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