Coalition Tactics: Bribery and Control in Parliamentary Elections

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 to promote 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 promoting both the coalition and the relative power of some favorite party within the coalition. We examine two types of strategic manipulations: bribery, which allows modifying voters’ preferences, and 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.