Control for Coalitions in Parliamentary Elections

2025-03-06

AI Summary

This paper initiates the study of the *coalition control problem* in parliamentary elections: manipulating the total seat count of a ruling coalition—rather than optimizing seats for a single party—via adding or deleting parties. Methodologically, it introduces single-peaked preference modeling and voter type aggregation, distinguishes between *compact* and *expanded* problem instances, and conducts a parameterized complexity analysis. Its main contributions are threefold: (1) It is the first work to generalize election control from the party level to the coalition level; (2) It establishes the tractability boundary: the problem is W[1]-hard or immune when preferences are unrestricted, yet becomes polynomial-time solvable for certain variants under symmetric single-peaked preferences; (3) It reveals a critical representation effect: several variants are NP-hard under compact representation but polynomial-time solvable under expanded representation.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Knowledge Representation and Reasoning: Preferences
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

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

Abstract

The traditional election control problem focuses on the use of control to promote a single candidate. In parliamentary elections, however, the focus shifts: voters care no less about the overall governing coalition than the individual parties' seat count. This paper introduces a new problem: controlling parliamentary elections, where the goal extends beyond promoting a single party to influencing the collective seat count of coalitions of parties. We focus on plurality rule and control through the addition or deletion of parties. Our analysis reveals that, without restrictions on voters' preferences, these control problems are W[1]-hard. In some cases, the problems are immune to control, making such efforts ineffective. We then study the special case where preferences are symmetric single-peaked. We show that in the single-peaked setting, aggregation of voters into types allows for a compact representation of the problem. Our findings show that for the single-peaked setting, some cases are solvable in polynomial time, while others are NP-hard for the compact representation - but admit a polynomial algorithm for the extensive representation.

Problem

• Extends election control to influence coalition seat counts.
• Analyzes control via party addition or deletion under plurality rule.
• Explores solvability in polynomial time for symmetric single-peaked preferences.

Innovation

• Introduces coalition control in parliamentary elections
• Analyzes control via party addition or deletion
• Explores polynomial solutions for single-peaked preferences