Complexity of and Algorithms for Borda Manipulation

TL;DR

This paper proves that manipulating the Borda voting rule with two manipulators is NP-hard, introduces new approximation algorithms for manipulation, and demonstrates their effectiveness through experiments, suggesting computational difficulty may not strongly prevent manipulation.

Contribution

It establishes NP-hardness for two-manipulator Borda manipulation and proposes two novel approximation algorithms with superior performance.

Findings

NP-hardness of two-manipulator Borda manipulation

Proposed approximation algorithms outperform previous methods

Most random elections allow finding optimal manipulations

Abstract

We prove that it is NP-hard for a coalition of two manipulators to compute how to manipulate the Borda voting rule. This resolves one of the last open problems in the computational complexity of manipulating common voting rules. Because of this NP-hardness, we treat computing a manipulation as an approximation problem where we try to minimize the number of manipulators. Based on ideas from bin packing and multiprocessor scheduling, we propose two new approximation methods to compute manipulations of the Borda rule. Experiments show that these methods significantly outperform the previous best known %existing approximation method. We are able to find optimal manipulations in almost all the randomly generated elections tested. Our results suggest that, whilst computing a manipulation of the Borda rule by a coalition is NP-hard, computational complexity may provide only a weak barrier against manipulation in practice.