Abstract
Post-election audits can provide convincing evidence that election outcomes are correct—that the reported winner(s) really won—by manually inspecting ballots selected at random from a trustworthy paper trail of votes. Risk-limiting audits (RLAs) control the probability that, if the reported outcome is wrong, it is not corrected before the outcome becomes official. RLAs keep this probability below the specified “risk limit.” Bayesian audits (BAs) control the probability that the reported outcome is wrong, the “upset probability.” The upset probability does not exist unless one invents a prior probability distribution for cast votes. RLAs ensure that if this election’s reported outcome is wrong, the procedure has a large chance of correcting it. BAs control a weighted average probability of correcting wrong outcomes over a hypothetical collection of elections; the weights come from the prior. In general, BAs do not ensure a large chance of correcting the outcome of an election when the reported outcome is wrong. “Nonpartisan” priors, i.e., priors that are invariant under relabeling the candidates, lead to upset probabilities that can be far smaller than the chance of correcting wrong reported outcomes. We demonstrate the difference using simulations based on several real contests .
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Notes
- 1.
The law is a bit more complicated, including provisions to ensure that every contest gets some scrutiny and options for sampling vote-by-mail ballots (including not sampling them if they arrive after election day).
- 2.
Organized by J. Morrell; one of us (PBS) provided software and support.
- 3.
J. Morrell, personal communication, 2020.
- 4.
This is related to the problem of constructing least-favorable priors in statistical decision problems. There is a deep duality between Bayesian and frequentist procedures: under mild regularity conditions the Bayes risk for a least-favorable prior is equal to the minimax risk [5]. (Here, risk is a term of art, a measure of the performance of the procedure.) That is to say, for a particular choice of prior, the Bayesian procedure is in fact the frequentist procedure that does best in the worst case. The least-favorable prior is generally not “flat” or “uninformative.”
- 5.
The final-round margin of an IRV contest is an upper bound on the true margin.
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Glazer, A.K., Spertus, J.V., Stark, P.B. (2020). Bayesian Audits Are Average But Risk-Limiting Audits are Above Average. In: Krimmer, R., et al. Electronic Voting. E-Vote-ID 2020. Lecture Notes in Computer Science(), vol 12455. Springer, Cham. https://doi.org/10.1007/978-3-030-60347-2_6
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