Advances in STV Margin Computation

2026-07-23

AI Summary

This study addresses the problem of efficiently computing the minimum number of ballot manipulations required to alter the outcome of a Single Transferable Vote (STV) election—referred to as the election margin—to support risk-limiting audits and assess the impact of tallying errors. To this end, we propose an optimized combinatorial search algorithm enhanced with tighter lower-bound estimation techniques for the margin, which we integrate into a risk-limiting audit framework. Experimental evaluation on multiple real-world STV election datasets demonstrates that our approach substantially improves both the computational efficiency and accuracy of margin lower-bound computation, yielding higher and tighter bounds. These advances enhance the practicality and reliability of verifying outcomes in large-scale STV elections.

Abstract

Single transferable vote (STV) is a multi-winner preferential proportional electoral system. The margin is the smallest number of ballots that need to be manipulated to alter the set of winners. If we can compute the margin of an STV election, or a reasonable lower bound on the margin, we can use recent advances in auditing research to conduct a risk-limiting audit of the election's winners. Knowledge of the margin also provides insight into whether uncovered mistakes, or a known error rate in ballot interpretation, could have influenced the outcome. This paper presents substantial improvements on an existing algorithm for computing lower bounds on the margin of an STV election. These improvements allow us to compute higher lower bounds for real STV elections, making mismatch-based risk-limiting audits more practical.

Problem

• STV
• margin computation
• risk-limiting audit
• election integrity
• multi-winner election

Innovation

• STV margin computation
• risk-limiting audit
• preference voting
• election integrity
• algorithmic improvement