Abstract
In this paper we present simulation results comparing the risk, stopping probability, and number of ballots required over multiple rounds of ballot polling risk-limiting audits (RLAs) Minerva, Selection-Ordered (SO) Bravo, and End-of-Round (EoR) Bravo . Bravo is the most commonly used ballot polling RLA and requires the smallest expected number of ballots when ballots are drawn one at a time and the (true) underlying election is as announced. In real audits, multiple ballots are drawn at a time, and Bravo is implemented as SO Bravo or EoR Bravo . Minerva is a recently proposed ballot polling RLA that requires fewer ballots than either implementation of Bravo in a first round with stopping probability 0.9 but requires a predetermined round schedule. It is an open question how these audits compare over multiple rounds and for lower stopping probabilities. Our simulations use stopping probabilities of 0.9 and 0.25. The results are consistent with predictions of the R2B2 open-source library for ballot polling audits. We observe that both Bravo audits are more conservative than Minerva, which stops with fewer ballots, for both first round stopping probabilities. However, the advantage of using Minerva decreases considerably for the smaller first round stopping probability, as one would expect.
O. Broadrick, S. Morin, G. McClearn and P. L. Vora—Supported in part by NSF Award 2015253.
F. Zagórski—Author was partially supported by Polish National Science Centre contract number DEC-2013/09/D/ST6/03927.
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Notes
- 1.
Their proof assumes that the number of relevant ballots drawn in each round is know beforehand. In MINERVA, the number of ballots drawn in each round is determined before any ballots are drawn. Because invalid ballots and ballots that are inconsequential for the contest being audited would be drawn in addition to relevant ballots, the assumption used by the proof is not true in general. (We are grateful to Philip Stark for drawing our attention to this.) However, any variation in number of relevant ballots drawn for a fixed round size would be random and not chosen by an adversary; the proof showing the risk-limiting property of MINERVA could hence be extended.
- 2.
or the announced winner lost by one vote, and the number of ballots is large enough that the probability of drawing a ballot for the winner is that of drawing one for the loser.
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Broadrick, O., Morin, S., McClearn, G., McBurnett, N., Vora, P.L., Zagórski, F. (2023). Simulations of Ballot Polling Risk-Limiting Audits. In: Matsuo, S., et al. Financial Cryptography and Data Security. FC 2022 International Workshops. FC 2022. Lecture Notes in Computer Science, vol 13412. Springer, Cham. https://doi.org/10.1007/978-3-031-32415-4_24
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