Efficient Computation of Exact IRV Margins

TL;DR

This paper introduces a practical branch-and-bound algorithm for accurately computing the margin of victory in Instant Runoff Voting elections, addressing a key challenge in election integrity and auditing.

Contribution

It presents a novel, efficient algorithm that significantly improves the ability to compute exact IRV margins compared to previous methods.

Findings

Algorithm runs efficiently on real-world examples

Able to compute margins for cases unsolvable by prior methods

Improves reliability of election audits and outcome verification

Abstract

The margin of victory is easy to compute for many election schemes but difficult for Instant Runoff Voting (IRV). This is important because arguments about the correctness of an election outcome usually rely on the size of the electoral margin. For example, risk-limiting audits require a knowledge of the margin of victory in order to determine how much auditing is necessary. This paper presents a practical branch-and-bound algorithm for exact IRV margin computation that substantially improves on the current best-known approach. Although exponential in the worst case, our algorithm runs efficiently in practice on all the real examples we could find. We can efficiently discover exact margins on election instances that cannot be solved by the current state-of-the-art.