Weighted Electoral Control

TL;DR

This paper explores the computational complexity of controlling weighted elections by adding or removing voters, providing polynomial algorithms, NP-completeness results, and approximation methods for various voting rules.

Contribution

It offers a comprehensive analysis of weighted voter control, including complexity classifications and algorithms, filling a gap in election manipulation research.

Findings

Polynomial-time algorithms for some control problems

NP-completeness results for others

Approximation algorithms for many NP-complete cases

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. In particular, for scoring rules we completely characterize the complexity of weighted voter control. Our work shows that for quite a few important cases, either polynomial-time exact algorithms or polynomial-time approximation algorithms exist.