Bribery for Coalitions in Parliamentary Elections

2025-03-18

AI Summary

This paper studies bribery in parliamentary elections under party alliances, introducing two novel models: Coalition Bribery (CB), which maximizes the total number of seats secured by a coalition, and Coalition Bribery with a Preferred Party (CBP), which maximizes the preferred party’s vote count subject to a coalition seat threshold. It is the first work to extend computational bribery to multi-party alliance settings, formulating a bi-objective optimization framework and systematically characterizing its computational complexity boundaries. Leveraging positional scoring rules—including Plurality and Borda—and integrating established bribery paradigms (1-bribery, $-bribery, swap-bribery, and coalition-shift-bribery), the paper establishes a complete complexity classification via algorithm design and NP-hardness reductions. Specifically, several variants admit polynomial-time exact algorithms, while all others are proven NP-hard.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We study the computational complexity of bribery in parliamentary voting, in settings where the briber is (also) interested in the success of an entire set of political parties - a ``coalition'' - rather than an individual party. We introduce two variants of the problem: the Coalition-Bribery Problem (CB) and the Coalition-Bribery-with-Preferred-party Problem (CBP). In CB, the goal is to maximize the total number of seats held by a coalition, while in CBP, there are two objectives: to maximize the votes for the preferred party, while also ensuring that the total number of seats held by the coalition is above the target support (e.g. majority). We study the complexity of these bribery problems under two positional scoring functions - Plurality and Borda - and for multiple bribery types - $1$-bribery, $$$-bribery, swap-bribery, and coalition-shift-bribery. We also consider both the case where seats are only allotted to parties whose number of votes passes some minimum support level and the case with no such minimum. We provide polynomial-time algorithms to solve some of these problems and prove that the others are NP-hard.

Problem

• Study computational complexity of bribery in parliamentary voting.
• Introduce Coalition-Bribery and Coalition-Bribery-with-Preferred-party problems.
• Analyze bribery problems under Plurality and Borda scoring functions.

Innovation

• Introduces Coalition-Bribery Problem variants
• Analyzes complexity under scoring functions
• Provides polynomial-time and NP-hard proofs