[Paper Review] Weighted electoral control

Piotr Faliszewski, Edith Hemaspaandra+1 more|arXiv (Cornell University)|May 6, 2013

Internet Traffic Analysis and Secure E-votingComputer Science57 references3 citations

TL;DR

This paper investigates the complexity of controlling weighted elections via adding and deleting voters, proposing polynomial-time algorithms for several cases and NP-completeness results for others, with approximation algorithms provided for many NP-complete scenarios. The key contribution is establishing that for many important weighted voting settings, either exact or approximate efficient solutions exist.

ABSTRACT

Although manipulation and bribery have been extensively studied under weighted voting, there has been almost no work done on election control under weighted voting. This is unfortunate, since weighted voting appears in many important natural settings. In this paper, we study the complexity of controlling the outcome of weighted elections through adding and deleting voters. We obtain polynomial-time algorithms, NP-completeness results, and for many NP-complete cases, approximation algorithms. Our work shows that for quite a few important cases, either polynomial-time exact algorithms or polynomial-time approximation algorithms exist.

Motivation & Objective

• To address the lack of research on control in weighted electoral systems, despite their prevalence in real-world applications.
• To analyze the computational complexity of controlling weighted elections through adding and deleting voters.
• To develop efficient algorithms—both exact and approximate—for controlling outcomes in weighted voting scenarios.
• To classify which control types remain tractable or become intractable under weighted voting.

Proposed method

• Formalizing weighted electoral control as a computational problem involving voter addition and deletion in weighted voting systems.
• Applying computational complexity theory to classify the hardness of control problems under weighted voting.
• Designing polynomial-time algorithms for specific tractable cases of weighted control.
• Developing approximation algorithms for NP-complete control scenarios to achieve near-optimal outcomes efficiently.
• Using reductions and constructions to prove NP-completeness for various control types in weighted settings.

Experimental results

Research questions

• RQ1 Which types of weighted electoral control (via voter addition or deletion) can be solved in polynomial time?
• RQ2 For which weighted control problems is the problem NP-complete, and can approximation algorithms be designed?
• RQ3 How do the complexities of control in weighted voting compare to those in unweighted systems?
• RQ4 What structural properties of weighted voting systems determine the tractability of control?

Key findings

• Polynomial-time algorithms exist for several important cases of weighted electoral control through voter addition and deletion.
• Many control problems in weighted voting are NP-complete, indicating inherent computational difficulty.
• For NP-complete cases, the paper provides approximation algorithms that deliver near-optimal solutions efficiently.
• The results show that weighted control is tractable in many natural settings, either exactly or approximately.