# Towards Computing Victory Margins in STV Elections

## TL;DR

This paper introduces algorithms to compute bounds on the victory margin in STV elections, aiding election auditing and integrity assessment by estimating how much vote manipulation could change the outcome.

## Contribution

It presents the first algorithms for calculating lower and upper bounds on the MOV in STV elections, including exact margins for small instances.

## Key findings

- Algorithms can compute exact margins in small elections.
- Bounds provide insight into election robustness.
- Method enhances election auditing processes.

## Abstract

The Single Transferable Vote (STV) is a system of preferential voting employed in multi-seat elections. Each vote cast by a voter is a (potentially partial) ranking over a set of candidates. No techniques currently exist for computing the margin of victory (MOV) in STV elections. The MOV is the smallest number of vote manipulations (changes, additions, and deletions) required to bring about a change in the set of elected candidates. Knowledge of the MOV of an election gives greater insight into both how much time and money should be spent on the auditing of the election, and whether uncovered mistakes (such as ballot box losses) throw the election result into doubt---requiring a costly repeat election---or can be safely ignored. In this paper, we present algorithms for computing lower and upper bounds on the MOV in STV elections. In small instances, these algorithms are able to compute exact margins.