Aggregating sets of judgments: an impossibility result

Abstract

The concern of this paper is the aggregation of sets of rationally connected judgments that the members of a group individually endorse into a corresponding, collectively endorsed set of judgments. After documenting the need for various groups to aggregate judgments, we explain how this task is challenged by the "doctrinal" or "discursive" paradox. We then show that this paradox is not just an artifact of certain specific situations, but that it actually illustrates a new impossibility theorem, according to which there exists no systematic mechanism for generally solving relevant types of aggregation problems in accordance with some undemanding conditions. This new result highlights a tension between two plausible demands: on the one hand, that a group be responsive to the judgments of individual members in forming collective judgments and, on the other, that it be rational in the judgments it collectively endorses. We consider at some length how groups can deal with this problem and evade our impossibility result, and we look at some established practices whereby they manage to do so. A formal proof of the new theorem is presented in an appendix.