Manipulation Can Be Hard in Tractable Voting Systems Even for Constant-Sized Coalitions

TL;DR

This paper explores the complexity of manipulating certain voting systems, showing that even with small coalitions, manipulation can be computationally hard despite easy winner determination.

Contribution

It surveys voting systems where manipulation is NP-hard for constant-sized coalitions, despite having polynomial-time winner determination.

Findings

Manipulation can be computationally hard even for small coalitions.

Some voting systems have NP-hard manipulation problems despite easy winner determination.

The paper provides a survey of such voting systems and their complexity results.

Abstract

Voting theory has become increasingly integrated with computational social choice and multiagent systems. Computational complexity has been extensively used as a shield against manipulation of voting systems, however for several voting schemes this complexity may cause calculating the winner to be computationally difficult. Of the many voting systems that have been studied with regard to election manipulation, a few have been found to have an unweighted coalitional manipulation problem that is NP-hard for a constant number of manipulators despite having a winner problem that is in P. We survey this interesting class of voting systems and the work that has analyzed their complexity.