Manipulation of Nanson's and Baldwin's Rules

TL;DR

This paper investigates the computational complexity of manipulating Nanson's and Baldwin's voting rules, showing they are generally resistant to manipulation and proposing approximation methods with practical effectiveness.

Contribution

It demonstrates that Nanson's and Baldwin's rules are NP-hard to manipulate, both with unweighted and weighted votes, and introduces approximation techniques for manipulation.

Findings

NP-hard to manipulate with one manipulator (unweighted votes)

NP-hard to manipulate with small coalitions (weighted votes)

Manipulation is often difficult in practice

Abstract

Nanson's and Baldwin's voting rules select a winner by successively eliminating candidates with low Borda scores. We show that these rules have a number of desirable computational properties. In particular, with unweighted votes, it is NP-hard to manipulate either rule with one manipulator, whilst with weighted votes, it is NP-hard to manipulate either rule with a small number of candidates and a coalition of manipulators. As only a couple of other voting rules are known to be NP-hard to manipulate with a single manipulator, Nanson's and Baldwin's rules appear to be particularly resistant to manipulation from a theoretical perspective. We also propose a number of approximation methods for manipulating these two rules. Experiments demonstrate that both rules are often difficult to manipulate in practice. These results suggest that elimination style voting rules deserve further study.