Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.01010 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910649754320896 |
|---|---|
| author | Spertus, Jacob |
| author_facet | Spertus, Jacob |
| contents | Risk-limiting audits (RLAs) can provide routine, affirmative evidence that reported election outcomes are correct by checking a random sample of cast ballots. An efficient RLA requires checking relatively few ballots. Here we construct highly efficient RLAs by optimizing supermartingale tuning parameters--$\textit{bets}$--for ballot-level comparison audits. The exactly optimal bets depend on the true rate of errors in cast-vote records (CVRs)--digital receipts detailing how machines tabulated each ballot. We evaluate theoretical and simulated workloads for audits of contests with a range of diluted margins and CVR error rates. Compared to bets recommended in past work, using these optimal bets can dramatically reduce expected workloads--by 93% on average over our simulated audits. Because the exactly optimal bets are unknown in practice, we offer some strategies for approximating them. As with the ballot-polling RLAs described in ALPHA and RiLACs, adapting bets to previously sampled data or diversifying them over a range of suspected error rates can lead to substantially more efficient audits than fixing bets to $\textit{a priori}$ values, especially when those values are far from correct. We sketch extensions to other designs and social choice functions, and conclude with some recommendations for real-world comparison audits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01010 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | COBRA: Comparison-Optimal Betting for Risk-limiting Audits Spertus, Jacob Applications Methodology Risk-limiting audits (RLAs) can provide routine, affirmative evidence that reported election outcomes are correct by checking a random sample of cast ballots. An efficient RLA requires checking relatively few ballots. Here we construct highly efficient RLAs by optimizing supermartingale tuning parameters--$\textit{bets}$--for ballot-level comparison audits. The exactly optimal bets depend on the true rate of errors in cast-vote records (CVRs)--digital receipts detailing how machines tabulated each ballot. We evaluate theoretical and simulated workloads for audits of contests with a range of diluted margins and CVR error rates. Compared to bets recommended in past work, using these optimal bets can dramatically reduce expected workloads--by 93% on average over our simulated audits. Because the exactly optimal bets are unknown in practice, we offer some strategies for approximating them. As with the ballot-polling RLAs described in ALPHA and RiLACs, adapting bets to previously sampled data or diversifying them over a range of suspected error rates can lead to substantially more efficient audits than fixing bets to $\textit{a priori}$ values, especially when those values are far from correct. We sketch extensions to other designs and social choice functions, and conclude with some recommendations for real-world comparison audits. |
| title | COBRA: Comparison-Optimal Betting for Risk-limiting Audits |
| topic | Applications Methodology |
| url | https://arxiv.org/abs/2304.01010 |