搜索与搜索：论可坍缩选举控制类型
Search versus Search for Collapsing Electoral Control Types
AI总结：
本文研究选举控制类型坍缩对的搜索版本复杂度关系，证明各坍缩对成员的搜索复杂度多项式相关并给出高效归约，同时完全确定了 plurality、veto 和 approval 系统中哪些坍缩搜索问题对是多项式时间可计算的，哪些是 NP 难的。
摘要：
选举控制类型是指通过改变选举的组成和结构来试图改变选举结果的方式 [BTT92]。我们称两个兼容的（即具有相同输入类型的）、关于同一选举系统 E 的控制类型构成一个坍缩对，如果对于每一个可能的输入（通常包括候选集、选票集、焦点候选者，以及有时与试图进行的改变的性质相关的其他参数），这两个试图实施的攻击要么都能成功执行，要么都不能成功执行。对于 Hemaspaandra、Hemaspaandra 和 Menton [HHM20] 发现的七个一般性（即对所有选举系统都成立）选举控制类型坍缩对中的每一个，以及 Carleton 等人 [CCH+24] 针对 veto 和 approval（并且根据该论文定理 3.6 和 3.9，还适用于许多其他选举系统）发现的每一个额外选举控制类型坍缩对，坍缩对的两个成员具有相同的复杂度，因为作为集合它们是同一个集合。然而，具有相同的复杂度（作为集合）不足以保证它们作为搜索问题也具有相同的复杂度。在本文中，我们探索了坍缩对的搜索版本之间的关系。对于 Hemaspaandra、Hemaspaandra 和 Menton [HHM20] 以及 Carleton 等人 [CCH+24] 的每一个坍缩对，我们证明了该对成员的搜索版本复杂度是多项式相关的（在获胜者问题本身不属于多项式时间的情况下，给定对获胜者问题的 oracle 访问）。除此之外，我们给出了高效的归约，可以从一个问题的解计算出另一个问题的解。对于具体系统 plurality、veto 和 approval，我们完全确定了它们（根据我们的结果）多项式相关的坍缩搜索问题对中哪些是多项式时间可计算的，哪些是 NP 难的。
英文摘要：
Electoral control types are ways of trying to change the outcome of elections by altering aspects of their composition and structure [BTT92]. We say two compatible (i.e., having the same input types) control types that are about the same election system E form a collapsing pair if for every possible input (which typically consists of a candidate set, a vote set, a focus candidate, and sometimes other parameters related to the nature of the attempted alteration), either both or neither of the attempted attacks can be successfully carried out. For each of the seven general (i.e., holding for all election systems) electoral control type collapsing pairs found by Hemaspaandra, Hemaspaandra, and Menton [HHM20] and for each of the additional electoral control type collapsing pairs of Carleton et al. [CCH+24] for veto and approval (and many other election systems in light of that paper's Theorems 3.6 and 3.9), both members of the collapsing pair have the same complexity since as sets they are the same set. However, having the same complexity (as sets) is not enough to guarantee that as search problems they have the same complexity. In this paper, we explore the relationships between the search versions of collapsing pairs. For each of the collapsing pairs of Hemaspaandra, Hemaspaandra, and Menton [HHM20] and Carleton et al. [CCH+24], we prove that the pair's members' search-version complexities are polynomially related (given access, for cases when the winner problem itself is not in polynomial time, to an oracle for the winner problem). Beyond that, we give efficient reductions that from a solution to one compute a solution to the other. For the concrete systems plurality, veto, and approval, we completely determine which of their (due to our results) polynomially-related collapsing search-problem pairs are polynomial-time computable and which are NP-hard.
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。
