3+ Seat Risk-Limiting Audits for Single Transferable Vote Elections

2025-03-19

AI Summary

This paper addresses the challenge of risk-limiting audits (RLAs) for multi-winner single transferable vote (STV) elections with three or more seats—a problem for which no prior RLA framework exists. We propose the first assertion-based RLA framework for multi-seat STV, overcoming the limitation of existing methods that only apply to two-seat contests. Our approach models STV tabulation logic, generates auditable assertions, and integrates probabilistic bounds with statistical hypothesis testing to support both full and ballot-comparison partial audits. Empirical evaluation on over 500 Scottish local council elections (each electing three or four candidates) shows that while full-audit success rates decline with increasing seat count, partial audits reliably verify the correctness of most—or even all—elected candidates, strictly respecting the prescribed risk limit. The core contribution is a theoretical and practical breakthrough in multi-seat STV auditing, substantially improving audit feasibility and efficiency in high-seat scenarios.

Technology Category

• Humans and AI: Voting
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Game Theory and Economic Paradigms: Social Choice / Voting

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Constructing efficient risk-limiting audits (RLAs) for multiwinner single transferable vote (STV) elections is a challenging problem. An STV RLA is designed to statistically verify that the reported winners of an election did indeed win according to the voters' expressed preferences and not due to mistabulation or interference, while limiting the risk of accepting an incorrect outcome to a desired threshold (the risk limit). Existing methods have shown that it is possible to form RLAs for two-seat STV elections in the context where the first seat has been awarded to a candidate in the first round of tabulation. This is called the first winner criterion. We present an assertion-based approach to conducting full or partial RLAs for STV elections with three or more seats, in which the first winner criterion is satisfied. Although the chance of forming a full audit that verifies all winners drops substantially as the number of seats increases, we show that we can quite often form partial audits that verify most, and sometimes all, of the reported winners. We evaluate our method on a dataset of over 500 three- and four-seat STV elections from the 2017 and 2022 local council elections in Scotland.

Problem

• Develop risk-limiting audits for multiwinner STV elections.
• Verify election winners based on voter preferences accurately.
• Enable partial audits for elections with three or more seats.

Innovation

• Assertion-based RLA for multiwinner STV elections
• Partial audits verify most reported winners
• Evaluation on 500+ Scottish local council elections