Risk-Limiting Audits by Stratified Union-Intersection Tests of Elections (SUITE)

TL;DR

SUITE is a new stratified RLA method that efficiently combines stratum-level tests to provide a flexible, risk-limiting audit applicable to diverse voting systems and sampling strategies.

Contribution

It introduces a novel approach to stratified RLAs that maximizes combined P-values over all outcome-changing error partitions, enhancing efficiency and flexibility.

Findings

SUITE improves audit efficiency over traditional ballot polling.

It accommodates different voting systems within a single audit.

The method is applicable to real-world elections with mixed voting systems.

Abstract

Risk-limiting audits (RLAs) offer a statistical guarantee: if a full manual tally of the paper ballots would show that the reported election outcome is wrong, an RLA has a known minimum chance of leading to a full manual tally. RLAs generally rely on random samples. Stratified sampling--partitioning the population of ballots into disjoint strata and sampling independently from the strata--may simplify logistics or increase efficiency compared to simpler sampling designs, but makes risk calculations harder. We present SUITE, a new method for conducting RLAs using stratified samples. SUITE considers all possible partitions of outcome-changing error across strata. For each partition, it combines P-values from stratum-level tests into a combined P-value; there is no restriction on the tests used in different strata. SUITE maximizes the combined P-value over all partitions of outcome-changing error. The audit can stop if that maximum is less than the risk limit. Voting systems in some Colorado counties (comprising 98.2% of voters) allow auditors to check how the system interpreted each ballot, which allows ballot-level comparison RLAs. Other counties use ballot polling, which is less efficient. Extant approaches to conducting an RLA of a statewide contest would require major changes to Colorado's procedures and software, or would sacrifice the efficiency of ballot-level comparison. SUITE does not. It divides ballots into two strata: those cast in counties that can conduct ballot-level comparisons, and the rest. Stratum-level P-values are found by methods derived here. The resulting audit is substantially more efficient than statewide ballot polling. SUITE is useful in any state with a mix of voting systems or that uses stratified sampling for other reasons. We provide an open-source reference implementation and exemplar calculations in Jupyter notebooks.