An Empirical Study of the Manipulability of Single Transferable Voting

TL;DR

This study empirically investigates whether computational complexity effectively prevents manipulation in single transferable voting (STV), finding that manipulation is often computationally easy in practice despite theoretical NP-hardness.

Contribution

The paper provides empirical evidence that manipulation of STV is generally computationally feasible, challenging the assumption that NP-hardness acts as a practical barrier.

Findings

Manipulation was easy to compute in most tested elections.

Proving the impossibility of manipulation was also computationally feasible.

Empirical results contrast with theoretical NP-hardness of manipulating STV.

Abstract

Voting is a simple mechanism to combine together the preferences of multiple agents. Agents may try to manipulate the result of voting by mis-reporting their preferences. One barrier that might exist to such manipulation is computational complexity. In particular, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. However, NP-hardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. In this paper, we study empirically the manipulability of single transferable voting (STV) to determine if computational complexity is really a barrier to manipulation. STV was one of the first voting rules shown to be NP-hard. It also appears one of the harder voting rules to manipulate. We sample a number of distributions of votes including uniform and real world elections. 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.