Judgment aggregation is a framework to aggregate individual opinions on multiple, logically connected issues into a collective outcome. These opinions are cast by judges, which can be for example referees, experts, advisors or jurors, depending on the application and context. It is open to manipulative attacks such as \textsc{Manipulation} where judges cast their judgments strategically. Previous works have shown that most computational problems corresponding to these manipulative attacks are \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 \textsc{Manipulation} and \textsc{Bribery} problems in premise-based judgment aggregation, now focusing on simple and realistic formulas. We restrict all formulas to be clauses that are (positive) monotone, Horn-clauses, or have bounded length. For basic variants of \textsc{Manipulation}, we show that these restrictions make several variants, which were in general known to be \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) by showing a close relationship between variants of \textsc{Manipulation} and variants of \textsc{Satisfiability}. For Hamming distance based \textsc{Manipulation}, we show that \NP-hardness even holds for positive monotone clauses of length three, but the problem becomes polynomial-time solvable for positive monotone clauses of length two. For \textsc{Bribery}, we show that \NP-hardness even holds for positive monotone clauses of length two, but it becomes polynomial-time solvable for the same clause set if there is a constant budget.

翻译：判断聚合是一种将个体对多个逻辑关联议题的意见汇总为集体结果的框架。这些意见由法官（根据应用和语境，可以是裁判、专家、顾问或陪审团成员）投票形成。该过程易受策略性操纵攻击，例如\textsc{操作}（法官策略性地提交判断）。以往研究表明，多数对应这类操纵攻击的计算问题均为\NP-难问题。然而，这种期望的计算屏障通常依赖于无界规模或结构复杂的公式。我们重新审视基于前提的判断聚合中各类\textsc{操作}与\textsc{贿赂}问题的计算复杂性，重点聚焦简单且现实的公式。我们将所有公式限制为（正）单调子句、Horn子句或有界长度的子句。对于\textsc{操作}的基本变体，我们证明此类限制使得若干原本已知为\NP-难的变体可在多项式时间内求解。此外，通过揭示\textsc{操作}变体与\textsc{可满足性}变体之间的紧密关联，我们为一大类子句限制（推广单调子句和Horn子句）建立了P与\NP的二分性。对于基于汉明距离的\textsc{操作}，我们证明即便对长度为三的正单调子句，\NP-难性依然成立；但对长度为二的正单调子句，问题变为多项式时间可解。对于\textsc{贿赂}，我们证明即便对长度为二的正单调子句，\NP-难性依然成立；但在常数预算下，同一子句集的问题变为多项式时间可解。