Abstract
We present a method and software for ballot-polling risk-limiting audits (RLAs) based on Bernoulli sampling: ballots are included in the sample with probability p, independently. Bernoulli sampling has several advantages: (1) it does not require a ballot manifest; (2) it can be conducted independently at different locations, rather than requiring a central authority to select the sample from the whole population of cast ballots or requiring stratified sampling; (3) it can start in polling places on election night, before margins are known. If the reported margins for the 2016 U.S. Presidential election are correct, a Bernoulli ballot-polling audit with a risk limit of 5% and a sampling rate of \(p_0=1\%\) would have had at least a 99% probability of confirming the outcome in 42 states. (The other states were more likely to have needed to examine additional ballots). Logistical and security advantages that auditing in the polling place affords may outweigh the cost of examining more ballots than some other methods might require.
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Notes
- 1.
The current method uses the reported results to construct the alternative hypothesis. A variant of the method does not require the reported results. We do not present that method here; it is related to ClipAudit (Rivest 2017).
- 2.
The same general approach works for some preferential voting schemes, such as Borda count and range voting, and for proportional representation schemes such as D’Hondt (Stark and Teague 2014). We do not consider instant-runoff voting (IRV).
- 3.
For instance, for a majority contest, one simply pools the votes for all the reported losers into a single “pseudo-candidate” who reportedly lost.
- 4.
The alternative hypothesis is that the reported results are correct; as mentioned above, there are other approaches one could use that do not involve the reported results, but we do not present them here.
- 5.
Once ballots are aggregated in a precinct or scanned centrally, it is unlikely that they will stay in the same order.
- 6.
The distribution of the sample size is skewed to the right: the expected sample size is generally larger than the median sample size.
- 7.
http://openelections.net/, last visited 8/5/19.
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Ottoboni, K., Bernhard, M., Halderman, J.A., Rivest, R.L., Stark, P.B. (2020). Bernoulli Ballot Polling: A Manifest Improvement for Risk-Limiting Audits. In: Bracciali, A., Clark, J., Pintore, F., Rønne, P., Sala, M. (eds) Financial Cryptography and Data Security. FC 2019. Lecture Notes in Computer Science(), vol 11599. Springer, Cham. https://doi.org/10.1007/978-3-030-43725-1_16
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