Manipulability of Single Transferable Vote

TL;DR

This paper empirically investigates the difficulty of manipulating the single transferable vote (STV) rule, finding that it is generally easy for a single agent to manipulate or determine the impossibility of manipulation, despite its theoretical NP-hardness.

Contribution

The study provides empirical evidence that manipulating STV is often computationally easy in practice, contrasting with its theoretical NP-hardness.

Findings

Manipulation by a single agent is usually easy to compute or prove impossible.

STV manipulation remains computationally feasible in most tested elections.

Open question: coalition manipulation complexity in practice is still unknown.

Abstract

For many voting rules, it is NP-hard to compute a successful manipulation. However, NP-hardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. We study empirically the cost of manipulating the single transferable vote (STV) rule. This was one of the first rules shown to be NP-hard to manipulate. It also appears to be one of the harder rules to manipulate since it involves multiple rounds and since, unlike many other rules, it is NP-hard for a single agent to manipulate without weights on the votes or uncertainty about how the other agents have voted. In almost every election in our experiments, it was easy to compute how a single agent could manipulate the election or to prove that manipulation by a single agent was impossible. It remains an interesting open question if manipulation by a coalition of agents is hard to compute in practice.