Risk Limiting Audits

Risk Limiting Audits (RLAs) are a statistical method used to verify the accuracy of election results. The goal of an RLA is to gradually reduce the risk of confirming an incorrect election outcome by randomly sampling paper ballots. The RAIRE system supports the RLA process for Instant Runoff Voting (IRV) elections by generating assertions that help ensure the audit process is credible.

What is an RLA?

The primary objective of an RLA is to confirm the reported election outcome with a maximum risk limit. Auditors randomly sample paper ballots and compare them with Cast Vote Records (CVRs). If the sampled ballots show no significant discrepancies, the audit can stop, assuming the reported result is correct. If discrepancies are found, the sample size may be increased, or a full hand recount may be conducted.

Main Steps in Conducting an RLA

1. Commit to the Ballot Manifest and CVRs:

   • Election administrators must commit to a ballot manifest and a Cast Vote Record (CVR) for each ballot. A CVR is an electronic record of each voter's choices, which allows auditors to check for discrepancies between the electronic records and the paper ballots.

2. Generate a Random Seed:

   • The ballots to be sampled are selected randomly using a random seed generated through a verifiable public process, such as rolling dice. This ensures transparency in the selection process.

3. Estimate the Required Sample Size:

   • The sample size is determined by the margin between the winner and loser, the risk limit, and the expected number of errors. Closer margins require larger sample sizes to achieve the same level of confidence.

4. Compare the Ballots to the CVRs:

   • The sampled ballots are compared to their corresponding CVRs. Discrepancies can either overstate (advantage the reported winner) or understate (advantage the reported loser) the winner's margin.

5. Calculate Risk and Decide Whether to Continue:

   • The level of risk is calculated based on the discrepancies found in the sample. If the risk is within acceptable limits, the audit can stop. If not, auditors may either increase the sample size or conduct a full hand count.

Understanding Margin and Difficulty in RLAs

Margin and difficulty are two critical factors that affect the scope of an RLA:

• Margin refers to the difference between the apparent winner's tally and the apparent loser's tally. In a plurality election, this is simply the number of votes by which the winner leads the loser. The smaller the margin, the more ballots need to be audited, as closer results are more likely to require additional verification.
• Difficulty increases with smaller margins or larger discrepancies. When the margin is small, the audit becomes more challenging because a small number of errors could potentially alter the outcome. Additionally, IRV elections may involve verifying multiple elimination steps, which adds to the audit's complexity.

Example

Suppose Diego is the reported winner and Chuan is a reported loser in a plurality contest.

• If the CVR records a vote for Diego but the ballot paper has a vote for Chuan, that is a discrepancy of 2, i.e. a 2-vote overstatement.
• If the CVR records an invalid vote, but the ballot paper has a vote for Chuan, that is a discrepancy of 1, i.e. a 1-vote overstatement.
• If the CVR and the ballot paper are identical, that is a discrepancy of 0.
• If the CVR records an invalid vote, but the ballot paper has a vote for Diego, that is a discrepancy of -1, a 1-vote understatement.
• If the CVR records a vote for Chuan but the ballot paper has a vote for Diego, that is a discrepancy of -2, i.e. a 2-vote understatement.

Obviously overstatements are far more important than understatements—if there are enough overstatements, the apparent winner may be wrong.

The discrepancies for all the sampled ballots are input into a risk measuring function. If the measured risk is less than the Risk Limit α, the audit can stop and accept the announced election result.