Complexity Results for Manipulation, Bribery and Control of the Kemeny Judgment Aggregation Procedure

An important criterium for social choice methods is their resistance against various types of strategic behavior. Seminal results in the social choice literature indicate that absolute resistance is in many cases impossible. For this reason, it has often been argued that computational intractability could be used as an obstruction for strategic behavior for different procedures. In this paper, we study the computational complexity of strategic behavior for the Kemeny procedure in the setting of judgment aggregation. In particular, we investigate problems related to (1) strategic manipulation, (2) bribery, and (3) control (by adding or deleting issues). We show that these problems are complete for the second level of the Polynomial Hierarchy. Our results hold for two different judgment aggregation frameworks and for different notions of preference over judgment sets. The hardness results that we establish hold up even under various restrictions, such as unidimensional alignment of the profile.