Approximation Algorithms for Campaign Management

TL;DR

This paper develops approximation algorithms for campaign management problems where an external party aims to ensure its preferred candidate wins by minimizing costs, applicable to various voting rules including scoring, Copeland, and maximin.

Contribution

It introduces a 2-approximation algorithm for vote-buying under scoring rules and extends approximation methods to Copeland and maximin voting systems.

Findings

2-approximation algorithm for scoring rules

Algorithms applicable to weighted voters

Extensions to Copeland and maximin rules

Abstract

We study electoral campaign management scenarios in which an external party can buy votes, i.e., pay the voters to promote its preferred candidate in their preference rankings. The external party's goal is to make its preferred candidate a winner while paying as little as possible. We describe a 2-approximation algorithm for this problem for a large class of electoral systems known as scoring rules. Our result holds even for weighted voters, and has applications for campaign management in commercial settings. We also give approximation algorithms for our problem for two Condorcet-consistent rules, namely, the Copeland rule and maximin.