arXiv subjects

Jacob V. Spertus

Publications and source records attributed to Jacob V. Spertus.

4 recordsLinked to original sources

arXiv2024

Sequential stratified inference for the mean

We develop conservative tests for the mean of a bounded population under stratified sampling and apply them to risk-limiting post-election audits. The tests are "anytime valid" under sequential sampling, allowing optional stopping in each stratum. Our core method expresses a global hypothesis about the population mean as a union of intersection hypotheses describing within-stratum means. It tests each intersection hypothesis using a test supermartingale (TSM) combined across strata by multiplication. A $P$-value for each intersection hypothesis is the reciprocal of that TSM, and the largest $P$-value in the union is a $P$-value for the global hypothesis. This approach has two primary moving parts: the rule selecting which stratum to draw from next, and the form of the TSM within each stratum. These rules may vary over intersection hypotheses. We construct intersection tests with the smallest expected sample size and propagate them to approximate an efficient global test. In instances that arise in auditing and other applications, its expected sample size is substantially smaller than that of previous methods.

stat.ME↗

arXiv2023

Stylish Risk-Limiting Audits in Practice

Risk-limiting audits (RLAs) can use information about which ballot cards contain which contests (card-style data, CSD) to ensure that each contest receives adequate scrutiny, without examining more cards than necessary. RLAs using CSD in this way can be substantially more efficient than RLAs that sample indiscriminately from all cast cards. We describe an open-source Python implementation of RLAs using CSD for the Hart InterCivic Verity voting system and the Dominion Democracy Suite(R) voting system. The software is demonstrated using all 181 contests in the 2020 general election and all 214 contests in the 2022 general election in Orange County, CA, USA, the fifth-largest election jurisdiction in the U.S., with over 1.8 million active voters. (Orange County uses the Hart Verity system.) To audit the 181 contests in 2020 to a risk limit of 5% without using CSD would have required a complete hand tally of all 3,094,308 cast ballot cards. With CSD, the estimated sample size is about 20,100 cards, 0.65% of the cards cast--including one tied contest that required a complete hand count. To audit the 214 contests in 2022 to a risk limit of 5% without using CSD would have required a complete hand tally of all 1,989,416 cast cards. With CSD, the estimated sample size is about 62,250 ballots, 3.1% of cards cast--including three contests with margins below 0.1% and 9 with margins below 0.5%.

stat.AP↗

arXiv2022

Sweeter than SUITE: Supermartingale Stratified Union-Intersection Tests of Elections

Stratified sampling can be useful in risk-limiting audits (RLAs), for instance, to accommodate heterogeneous voting equipment or laws that mandate jurisdictions draw their audit samples independently. We combine the union-intersection tests in SUITE, the reduction of RLAs to testing whether the means of a collection of lists are all $\leq 1/2$ of SHANGRLA, and the nonnegative supermartingale (NNSM) tests in ALPHA to improve the efficiency and flexibility of stratified RLAs. A simple, non-adaptive strategy for combining stratumwise NNSMs decreases the measured risk in the 2018 pilot hybrid audit in Kalamazoo, Michigan, USA by more than an order of magnitude, from 0.037 for SUITE to 0.003 for our method. We give a simple, computationally inexpensive, adaptive rule for deciding which stratum to sample next that reduces audit workload by as much as 74% in examples. We also present NNSM-based tests that are computationally tractable even when there are many strata, illustrated with a simulated audit stratified across California's 58 counties.

stat.ME↗

arXiv2020

More style, less work: card-style data decrease risk-limiting audit sample sizes

U.S. elections rely heavily on computers such as voter registration databases, electronic pollbooks, voting machines, scanners, tabulators, and results reporting websites. These introduce digital threats to election outcomes. Risk-limiting audits (RLAs) mitigate threats to some of these systems by manually inspecting random samples of ballot cards. RLAs have a large chance of correcting wrong outcomes (by conducting a full manual tabulation of a trustworthy record of the votes), but can save labor when reported outcomes are correct. This efficiency is eroded when sampling cannot be targeted to ballot cards that contain the contest(s) under audit. If the sample is drawn from all cast cards, RLA sample sizes scale like the reciprocal of the fraction of ballot cards that contain the contest(s) under audit. That fraction shrinks as the number of cards per ballot grows (i.e., when elections contain more contests) and as the fraction of ballots that contain the contest decreases (i.e., when a smaller percentage of voters are eligible to vote in the contest). States that conduct RLAs of contests on multi-card ballots or of small contests can dramatically reduce sample sizes by using information about which ballot cards contain which contests -- by keeping track of card-style data (CSD). For instance, CSD reduces the expected number of draws needed to audit a single countywide contest on a 4-card ballot by 75%. Similarly, CSD reduces the expected number of draws by 95% or more for an audit of two contests with the same margin on a 4-card ballot if one contest is on every ballot and the other is on 10% of ballots. In realistic examples, the savings can be several orders of magnitude.

cs.CR↗