In the theory of judgment aggregation on connected propositions, an important question remains open: Which aggregation rules are manipulable and which are strategy-proof? We define manipulability and strategy-proofness in judgment aggregation, characterize all strategyproof aggregation rules, and prove an impossibility theorem similar to the classic Gibbard-Satterthwaite theorem. Among other ways to avoid the impossibility, we discuss weakening strategy-proofness itself. Comparing two prominent aggregation rules in the literature, we show that "conclusion-based voting" is strategy-proof, but generates incomplete judgments, while "premise-based voting" is only strategy-proof for "reason-oriented" individuals. Surprisingly, for "outcome-oriented" individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy.
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