Judgment aggregation and agenda manipulation

When individual judgments ('yes' or 'no') on some propositions are aggregated into collective judgments, outcomes may be sensitive to the choice of propositions under consideration (the agenda). Such agenda-sensitivity opens the door to manipulation by agenda setters. I define three types of agenda-insensitivity ('basic', 'full', and 'focal') and for each type axiomatically characterize the aggregation procedures satisfying it. Two axioms turn out to be central for agenda-insensitivity: the familiar independence axiom, requiring propositionwise aggregation, and the axiom of implicit consensus preservation, requiring the respect of any (possibly implicit) consensus. As the paper's second contribution, I prove a new impossibility theorem whereby these two axioms imply dictatorial aggregation for almost all agendas.

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