RLAs for 2-Seat STV Elections: Revisited
Michelle Blom, Peter J. Stuckey, Vanessa Teague, Damjan Vukcevic
TL;DR
This work tackles the problem of risk-limiting audits for 2-seat US-style STV elections, where ballot values change dynamically via transfer values $\tau_c$ across rounds. It advances prior approaches by introducing lower-bound reasoning on the first winner's transfer value, incorporating upper/lower bound assertions $ extsf{AG}^*$ and $ extsf{NL}^*$, and reframing the general method into a five-stage process that supports partial RLAs when a full audit is not possible. Empirical results show substantial reductions in expected sample sizes—between 15% and 19%—across diverse real-world contest sets, including NSW IRV mappings and Minneapolis BoE elections, and demonstrate effective handling of batch elimination alongside partial auditing. The framework systematically stages verification into batch-elimination checks, winner verifications, alternate-winner elimination, and optional summary steps, moving risk-limiting auditing closer to practical deployment for larger STV elections. Overall, the paper delivers refined assertion techniques and transfer-value bounding methods that reduce audit costs and expand the set of auditable 2-seat STV contests, while enabling partial assurances when a full audit is infeasible.
Abstract
Single Transferable Vote (STV) elections are a principled approach to electing multiple candidates in a single election. Each ballot has a starting value of 1, and a candidate is elected if they gather a total vote value more than a defined quota. Votes over the quota have their value reduced by a transfer value so as to remove the quota, and are passed to the next candidate on the ballot. Risk-limiting audits (RLAs) are a statistically sound approach to election auditing which guarantees that failure to detect an error in the result is bounded by a limit. A first approach to RLAs for 2-seat STV elections has been defined. In this paper we show how we can improve this approach by reasoning about lower bounds on transfer values, and how we can extend the approach to partially audit an election, if the method does not support a full audit.