Approximation and Hardness of Shift-Bribery

TL;DR

This paper introduces a polynomial-time approximation scheme for the Shift-Bribery problem under positional scoring rules and demonstrates strong inapproximability results for the Copeland rule, advancing understanding of election manipulation complexity.

Contribution

It provides the first approximation scheme for Shift-Bribery with positional scoring rules and establishes hardness results for Copeland, highlighting differences in computational complexity.

Findings

Polynomial-time approximation scheme for positional scoring rules

Strong inapproximability results for Copeland rule

Enhanced understanding of election manipulation complexity

Abstract

In the Shift-Bribery problem we are given an election, a preferred candidate, and the costs of shifting this preferred candidate up the voters' preference orders. The goal is to find such a set of shifts that ensures that the preferred candidate wins the election. We give the first polynomial-time approximation scheme for the Shift-Bribery problem for the case of positional scoring rules, and for the Copeland rule we show strong inapproximability results.