基于前提的简单公式判断聚合中操纵与贿赂的复杂性
Complexity of Manipulation and Bribery in Premise-Based Judgment Aggregation with Simple Formulas
AI总结：
本文研究基于前提的判断聚合中操纵与贿赂问题的计算复杂性，通过将公式限制为单调子句、Horn子句或有界长度子句，揭示了若干NP难问题在简单公式下变为多项式时间可解，并给出了P与NP的二分性结果。
摘要：
判断聚合是一个将个体对多个逻辑相关议题的意见聚合为集体结果的框架。这些意见由法官给出，根据应用和上下文，法官可以是裁判、专家、顾问或陪审员。该框架容易受到操纵性攻击，例如法官策略性地表达判断的操纵问题。先前的研究表明，与这些操纵性攻击相对应的大多数计算问题都是NP难的。然而，这种期望的计算障碍通常依赖于规模无界或结构复杂的公式。我们重新审视基于前提的判断聚合中各种操纵与贿赂问题的计算复杂性，重点关注简单且现实的公式。我们将所有公式限制为（正）单调子句、Horn子句或长度有界的子句。对于操纵问题的基本变体，我们证明这些限制使得若干原本已知为NP难的变体变为多项式时间可解。此外，通过展示操纵问题的变体与可满足性问题的变体之间的密切关系，我们为一大类子句限制（推广单调子句和Horn子句）提供了P与NP的二分性结果。对于基于汉明距离的操纵问题，我们证明即使对于长度为三的正单调子句，NP难性仍然成立，但对于长度为二的正单调子句，该问题变为多项式时间可解。对于贿赂问题，我们证明即使对于长度为二的正单调子句，NP难性仍然成立，但在存在常数预算的情况下，同一子句集合上的问题变为多项式时间可解。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
