Coalition Tactics: Bribery and Control in Parliamentary Elections

2026-01-12

AI Summary

This study addresses electoral manipulation under proportional representation systems, focusing on strategic interventions—such as bribery (altering voter preferences) and control (adding or deleting voters or parties)—to enhance both the total seat allocation of a party coalition and the relative power of a specific party within it. Departing from prior work centered on individual candidates, this work introduces a novel bi-objective optimization model targeting coalitions and systematically delineates the computational feasibility boundaries of various manipulation strategies. Leveraging tools from computational social choice, the authors design polynomial-time algorithms for several voter-level bribery and control problems, while proving that party-level control is either infeasible or computationally intractable—specifically W[1]-hard or NP-hard under standard parameterizations—thereby revealing the inherent complexity of coalition-based electoral manipulation.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Search and Optimization: Combinatorial Optimization
• Humans and AI: Voting

Application Category

• Economics, Online Markets and Human Computation: Economics and fairness of platforms and recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• coalition manipulation
• parliamentary elections
• bribery
• control
• proportional representation

Innovation

• coalition manipulation
• proportional representation
• bribery
• control
• computational complexity