Eliminating the Weakest Link: Making Manipulation Intractable?

TL;DR

This paper investigates whether candidate elimination in voting rules always makes manipulation computationally harder, finding that for many practical rules, it indeed increases complexity, making manipulation NP-hard.

Contribution

It proves that elimination does not always increase manipulation complexity, but for several common voting rules, it makes manipulation NP-hard, extending previous results.

Findings

Manipulation complexity increases for elimination versions of certain voting rules.

NP-hardness of manipulation is established for elimination versions of veto, Coombs', and scoring rules.

Candidate elimination does not universally make manipulation computationally intractable.

Abstract

Successive elimination of candidates is often a route to making manipulation intractable to compute. We prove that eliminating candidates does not necessarily increase the computational complexity of manipulation. However, for many voting rules used in practice, the computational complexity increases. For example, it is already known that it is NP-hard to compute how a single voter can manipulate the result of single transferable voting (the elimination version of plurality voting). We show here that it is NP-hard to compute how a single voter can manipulate the result of the elimination version of veto voting, of the closely related Coombs' rule, and of the elimination versions of a general class of scoring rules.