Coalition Tactics: Bribery and Control in Parliamentary Elections

TL;DR

This paper explores how strategic manipulation through bribery and control can influence parliamentary elections, focusing on coalition seat counts and providing algorithms and complexity results for various manipulation types.

Contribution

It introduces new models for manipulating parliamentary elections with coalition goals, analyzing bribery and control, and offers polynomial algorithms and complexity proofs for these problems.

Findings

Polynomial algorithms for some bribery types.

NP-hardness results for other bribery variants.

Polynomial algorithms for control by adding/deleting voters.

Abstract

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.