Abstract
Accurately determining the outcome of an election is a complex task with many potential sources of error, ranging from software glitches in voting machines to procedural lapses to outright fraud. Risk-limiting audits (RLA) are statistically principled “incremental” hand counts that provide statistical assurance that reported outcomes accurately reflect the validly cast votes. We present a suite of tools for conducting RLAs using confidence sequences—sequences of confidence sets which uniformly capture an electoral parameter of interest from the start of an audit to the point of an exhaustive recount with high probability. Adopting the SHANGRLA [13] framework, we design nonnegative martingales which yield computationally and statistically efficient confidence sequences and RLAs for a wide variety of election types.
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Notes
- 1.
Code to reproduce all plots can be found at github.com/wannabesmith/RiLACS.
- 2.
At any point during the sampling, an election official can choose to abort the sampling and perform a full hand count for any reason. This cannot increase the risk limit: the chance of failing to correct an incorrect reported outcome does not increase.
- 3.
Notice that it is not always feasible to compute the set of all \(\mu \in [0, 1]\) such that \(\phi _t^\mu = 0\) since [0, 1] is uncountably infinite. However, all confidence sequences we will derive in this section are intervals (i.e. convex), and thus we can find the endpoints using a simple grid search or standard root-finding algorithms.
- 4.
- 5.
The use of the word “prior” here should not be interpreted in a Bayesian sense. No matter what values of \((\theta _1, \dots , \theta _D)\) are chosen, the resulting tests and confidence sequences have frequentist risk-limiting guarantees.
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Waudby-Smith, I., Stark, P.B., Ramdas, A. (2021). RiLACS: Risk Limiting Audits via Confidence Sequences. In: Krimmer, R., et al. Electronic Voting. E-Vote-ID 2021. Lecture Notes in Computer Science(), vol 12900. Springer, Cham. https://doi.org/10.1007/978-3-030-86942-7_9
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