Abstract
Risk-limiting audits (RLAs) can provide routine, affirmative evidence that reported election outcomes are correct by checking a random sample of cast ballots. An efficient RLA requires checking relatively few ballots. Here we construct highly efficient RLAs by optimizing supermartingale tuning parameters—bets—for ballot-level comparison audits. The exactly optimal bets depend on the true rate of errors in cast-vote records (CVRs)—digital receipts detailing how machines tabulated each ballot. We evaluate theoretical and simulated workloads for audits of contests with a range of diluted margins and CVR error rates. Compared to bets recommended in past work, using these optimal bets can dramatically reduce expected workloads—by 93% on average over our simulated audits. Because the exactly optimal bets are unknown in practice, we offer some strategies for approximating them. As with the ballot-polling RLAs described in ALPHA and RiLACs, adapting bets to previously sampled data or diversifying them over a range of suspected error rates can lead to substantially more efficient audits than fixing bets to a priori values, especially when those values are far from correct. We sketch extensions to other designs and social choice functions, and conclude with some recommendations for real-world comparison audits.
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Notes
- 1.
\(\lambda ^{{\text {apK}}}\) implies a bet of \(\eta _i := \bar{x}\) in the ALPHA parameterization.
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Acknowledgements
Philip Stark and Amanda Glazer provided helpful feedback on an earlier draft of this paper. Jacob Spertus’ research is supported by NSF grant 2228884.
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Code implementing our simulations and generating our figures and tables is available on Github at https://github.com/spertus/comparison-RLA-betting.
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Spertus, J.V. (2024). COBRA: Comparison-Optimal Betting for Risk-Limiting Audits. In: Essex, A., et al. Financial Cryptography and Data Security. FC 2023 International Workshops. FC 2023. Lecture Notes in Computer Science, vol 13953. Springer, Cham. https://doi.org/10.1007/978-3-031-48806-1_7
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