Conference Paper

A Risk-Limiting Audit in Denmark: A Pilot

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Abstract

The theory of risk-limiting audits is well-understood, at least mathematically. Such audits serve to create confidence in the reported election outcome by checking the evidence created during the election. When election officials introduce election technologies into the voting process, it is best to do this after the appropriate auditing framework has been implemented. In this paper, we describe our experiences with piloting a risk-limiting audit of a referendum that was held in Denmark on December 3, 2015. At the time of the publication of this paper, Denmark’s election law did not permit electronic voting technologies to be used during voting allowing us to study auditing in isolation. Our findings are that (1) risk-limiting audits also apply to paper and pencil elections; (2) election officials usually support risk-limiting audits even if no voting technologies are used because these audits can improve the efficiency of the manual count; (3) that practical and organizational challenges must be overcome to keep audits repeatable, in particular it must be possible to identify individual ballots repeatedly and reliably; (4) it is possible to arrange an audit for the result of an earlier stage in a count during a later stage, for example, an audit of the rough count results fine count; and (5) that whenever the electronic voting technologies are considered, auditing should be considered as part of feasibility study.

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... It will automatically trigger a full recount if enough statistical evidence is not found to support the election outcome, and it can be adopted to several electoral systems, including first-past the post [6], d'Hondt based systems [15], and instant runoff elections [1]. One would expect RLAs to strengthen public confidence in the election, first, because they can be integrated into existing election processes, for example, in Denmark, where the result of the first (rough) count can be verified during the second (fine) count [10]. Second, some of the ceremonies surrounding RLAs can be turned into public events, such as the dice-rolling ceremony used to create entropy to select a random sample (see the public notice of the Colorado Secretary of State [5]). ...
... The statutory pilot programs are run in Georgia, Indiana, and Nevada whereas the use of RLAs is optional in California, Ohio, Oregon and Washington. In contrast, Michigan and New Jersey are running only administrative pilot programs, similar to the one, we conducted in Denmark [10]. For a detailed description of risk-limiting audits and its application in other countries, see [11]. ...
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Risk-limiting audits (RLAs) are expected to strengthen the public confidence in the correctness of an election outcome. We hypothesize that this is not always the case, in part because for large margins between the winner and the runner-up, the number of ballots to be drawn can be so small that voters lose confidence. We conduct a user study with 105 participants resident in the US. Our findings confirm the hypothesis, showing that our study participants felt less confident when they were told the number of ballots audited for RLAs. We elaborate on our findings and propose recommendations for future use of RLAs.
... While the full information assumption is not entirely realistic, we note that in a district-based model both parties only need to know the vote counts in each district rather than individual votes, and one can get fairly accurate district-level information from independent polls. Also, verifying whether the votes in a district have been tampered with is possible using risk-limiting audits Lindeman and Stark [2012]; Schürmann [2016]. ...
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Article
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Chapter
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Risk-limiting audits provide statistical assurance that election outcomes are correct by manually examining portions of the audit trail-paper ballots or voter-verifiable paper records. This article sketches two types of risk-limiting audits, ballot-polling audits and comparison audits, and gives example computations. These audits do not require in-house statistical expertise.
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The MACRO method of Stark (9) can be used to derive an ex- tremely simple risk-limiting audit procedure based on sampling individual ballots at random. There is an easy rule to determine how many ballots must be audited at random to confirm, at a given risk limit, the outcomes of all the contests on those ballots for which the reported margin in votes is suciently large—provided the percentage of ballots the audit finds to have overstated any margin is suciently low. For instance, suppose there is a collection of contests we wish to audit at simultaneous risk limit no larger than 10%: If any of the outcomes is wrong, we want there to be at least a 90% chance of a full hand count to set the record straight. Suppose that the smallest margin among the contests is V votes, and that N ballots were cast in those contests combined. We would like to be able to stop the audit if the percentage of ballots in the sample with errors that overstated the margin of some winner over some loser by one vote is at most M/2V (half the smallest margin, as a percentage of the total number of ballots), and no ballot in the sample has an error that overstated the margin of a winner over a loser by two votes. Then we may start by auditing a random sample of n = 15.2N/V ballots. Concretely, suppose that 100,000 ballots were cast in all and that the smallest margin among the contests was 2,000 ballots. We draw a random sample of 15.2/2% = 761 ballots. If at most 7 of those ballots (1% of the sample, half the diluted margin of 2%) shows one or more errors that overstated a margin by one vote and none shows an error that overstated any margin by 2 votes, the audit can stop: All contests can be certified at a risk limit of 6.7% (< 10%). If the audit reveals more errors, the sample might need to be expanded; in that case, the MACRO computations of Stark (9) determine when sampling can stop. This paper gives general rules for selecting the initial sample size as a function of the risk limit, the smallest margin, and the percentage of one-vote margin over- statements we would like to tolerate among ballots in the sample without having to expand the initial sample.
State of colorado, risk-limiting audit final report, post-election audit initiative grant no. eac110150e
  • N Mcburnett