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

TL;DR

This paper analyzes the computational complexity of manipulation, bribery, and control in the Kemeny judgment aggregation procedure, proving these problems are complete for the second level of the Polynomial Hierarchy.

Contribution

It establishes the $ ext{Σ}_2^p$-completeness of strategic behavior problems in the Kemeny judgment aggregation, providing a complexity classification for these scenarios.

Findings

Manipulation, bribery, and control problems are $ ext{Σ}_2^p$-complete.

Determining the possibility of strategic behavior is computationally hard.

The results apply to the Kemeny judgment aggregation procedure.

Abstract

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 $\Sigma^p_2$-complete.