Strategic manipulation of elections is typically studied in the context of promoting individual candidates. In parliamentary elections, however, the focus shifts: voters may care more about the overall governing coalition than the individual parties' seat counts. This paper studies this new problem: manipulating parliamentary elections with the goal of promoting the collective seat count of a coalition of parties. We focus on proportional representation elections, and consider two variants of the problem; one in which the sole goal is to maximize the total number of seats held by the desired coalition, and the other with a dual objective of both promoting the coalition and promoting the relative power of some favorite party within the coalition. We examine two types of strategic manipulations: \emph{bribery}, which allows modifying voters' preferences, and \emph{control}, which allows changing the sets of voters and parties. We consider multiple bribery types, presenting polynomial-time algorithms for some, while proving NP-hardness for others. For control, we provide polynomial-time algorithms for control by adding and deleting voters. In contrast, control by adding and deleting parties, we show, is either impossible (i.e., the problem is immune to control) or computationally hard, in particular, W[1]-hard when parameterized by the number of parties that can be added or deleted.

翻译：选举的策略性操纵通常是在提升个体候选人的背景下进行研究的。然而，在议会选举中，关注点发生了转移：选民可能更关心整体的执政联盟，而非单个政党的席位数量。本文研究了这一新问题：以提升政党联盟集体席位数量为目标的议会选举操纵。我们聚焦于比例代表制选举，并考虑该问题的两种变体：一种其唯一目标是最大化期望联盟所持有的总席位数量；另一种则具有双重目标，既要提升联盟的整体实力，又要提升联盟内某个偏好政党的相对权力。我们考察了两种类型的策略性操纵：\emph{贿赂}（允许修改选民的偏好）和\emph{操控}（允许改变选民和政党的集合）。针对多种贿赂类型，我们为其中一些提出了多项式时间算法，同时证明了其他类型的NP难解性。对于操控，我们为通过添加和删除选民进行的操控提供了多项式时间算法。相比之下，通过添加和删除政党进行的操控，我们证明要么是不可能的（即该问题对操控具有免疫性），要么在计算上是困难的，特别是当以可添加或删除的政党数量作为参数时，该问题是W[1]-难的。