Complexity of manipulation and bribery in premise-based judgment aggregation with simple formulas

Judgment aggregation is a framework to aggregate individual opinions on multiple, logically connected issues into a collective outcome. It is open to manipulative attacks such as Manipulation where judges (e.g., referees, experts, or jurors) cast their judgments strategically. Previous works have shown that most computational problems corresponding to these manipulative attacks are $\text{NP}$-hard. This desired computational barrier, however, often relies on formulas that are either of unbounded size or of complex structure.

We revisit the computational complexity for various Manipulation and Bribery problems in premise-based judgment aggregation, now focusing on simple and realistic formulas. We restrict all formulas to be clauses that are monotone, Horn-clauses, or have bounded length. We show that these restrictions make several variants of Manipulation and Bribery, which were in general known to be $\text{NP}$-hard, polynomial-time solvable. Moreover, we provide a P vs. NP dichotomy for a large class of clause restrictions (generalizing monotone and Horn clauses).