Complexity Results for Manipulation, Bribery and Control of the Kemeny Procedure in Judgment Aggregation
This addresses theoretical security and fairness concerns in judgment aggregation systems, but it is incremental as it extends known complexity results to a specific procedure.
The paper tackles the computational complexity of strategic behaviors like manipulation, bribery, and control in the Kemeny procedure for judgment aggregation, showing that determining their feasibility and computing strategies is Σ^p_2-complete.
We study the computational complexity of several scenarios of strategic behavior for the Kemeny procedure in the setting of judgment aggregation. In particular, we investigate (1) manipulation, where an individual aims to achieve a better group outcome by reporting an insincere individual opinion, (2) bribery, where an external agent aims to achieve an outcome with certain properties by bribing a number of individuals, and (3) control (by adding or deleting issues), where an external agent aims to achieve an outcome with certain properties by influencing the set of issues in the judgment aggregation situation. We show that determining whether these types of strategic behavior are possible (and if so, computing a policy for successful strategic behavior) is complete for the second level of the Polynomial Hierarchy. That is, we show that these problems are $Σ^p_2$-complete.