Bayesian Audits Are Average But Risk-Limiting Audits are Above Average.

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.