Ballot-Polling Risk Limiting Audits for IRV Elections

Blom, Michelle L.; Stuckey, Peter J.; Teague, Vanessa

doi:10.1007/978-3-030-00419-4_2

Cited by 20 publications

(16 citation statements)

References 8 publications

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“…For more complex social choice functions, constructing sufficient sets of assertions may be much less obvious. Blom et al [2] use a heuristic method, RAIRE, to derive assertions for Instant Runoff Voting (IRV) from the CVRs. RAIRE allows the RLA to test an IRV outcome-the claim that Alice won-without checking the entire IRV elimination.…”

Section: Assertion-based Auditing: Properties and Challengesmentioning

confidence: 99%

Assertion-Based Approaches to Auditing Complex Elections, with Application to Party-List Proportional Elections

Blom,

Budurushi,

Rivest

et al. 2021

Preprint

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Risk-limiting audits (RLAs), an ingredient in evidence-based elections, are increasingly common. They are a rigorous statistical means of ensuring that electoral results are correct, usually without having to perform an expensive full recount-at the cost of some controlled probability of error. A recently developed approach for conducting RLAs, SHANGRLA, provides a flexible framework that can encompass a wide variety of social choice functions and audit strategies. Its flexibility comes from reducing sufficient conditions for outcomes to be correct to canonical 'assertions' that have a simple mathematical form. Assertions have been developed for auditing various social choice functions including plurality, multi-winner plurality, super-majority, Hamiltonian methods, and instant runoff voting. However, there is no systematic approach to building assertions. Here, we show that assertions with linear dependence on transformations of the votes can easily be transformed to canonical form for SHANGRLA. We illustrate the approach by constructing assertions for party-list elections such as Hamiltonian free list elections and elections using the D'Hondt method, expanding the set of social choice functions to which SHANGRLA applies directly.

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Section: Assertion-based Auditing: Properties and Challengesmentioning

confidence: 99%

Assertion-Based Approaches to Auditing Complex Elections, with Application to Party-List Proportional Elections

Blom,

Budurushi,

Rivest

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…There is some flexibility in selecting a set of assertions to confirm IRV contests [1], so the set can be chosen to minimize a measure of the anticipated workload. We will estimate the workload on the assumption that the assertion is true but the reported tallies are not exactly correct.…”

Section: Estimating Sample Size and Riskmentioning

confidence: 99%

“…Efficient RLAs for IRV have been devised only recently [1]. To audit the first stage of an IRV Hamiltonian election we must eliminate the possibility that a different set of candidates is viable.…”

Section: Viability: Instant-runoff Hamiltonian Electionsmentioning

confidence: 99%

Auditing Hamiltonian Elections

Blom,

Stark,

Stuckey

et al. 2021

Preprint

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Presidential primaries are a critical part of the United States Presidential electoral process, since they are used to select the candidates in the Presidential election. While methods differ by state and party, many primaries involve proportional delegate allocation using the so-called Hamilton method. In this paper we show how to conduct risklimiting audits for delegate allocation elections using variants of the Hamilton method where the viability of candidates is determined either by a plurality vote or using instant runoff voting. Experiments on real-world elections show that we can audit primary elections to high confidence (small risk limits) usually at low cost.8 There are more complicated alternate rules for the case where no candidate reaches T ; we do not consider this case here.

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“…[21] showed how BRAVO can be used to audit proportional representation schemes such as D'Hondt. [5] showed how BRAVO can be used to audit ranked-choice voting as well. BRAVO is based on Wald's [25] sequential probability ratio test (SPRT) of the simple hypothesis θ = µ against a simple alternative θ = η from IID Bernoulli(θ) observations.…”

Section: Introductionmentioning

confidence: 99%

ALPHA: Audit that Learns from Previously Hand-Audited Ballots

Stark¹

2022

Preprint

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A risk-limiting election audit (RLA) offers a statistical guarantee: if the reported electoral outcome is incorrect, the audit has at most a known maximum chance (the risk limit) of not correcting it before it becomes final. BRAVO [10], based on Wald's sequential probability ratio test for the Bernoulli distribution, is the most widely tried method for RLAs. It has limitations. It cannot accommodate sampling without replacement or stratified sampling, which can improve efficiency and are sometimes required by law. It applies only to ballot-polling audits, which are less efficient than comparison audits. It applies to plurality, majority, super-majority, proportional representation, and ranked-choice voting contests, but not to many other social choice functions for which there are RLA methods, such as approval voting, STAR-voting, Borda count, and general scoring rules. And while BRAVO has the smallest expected sample size among sequentially valid ballot-polling-with-replacement methods when the reported vote shares are exactly correct, BRAVO can require arbitrarily large samples when the reported reported winner(s) really won but the reported vote shares are incorrect. ALPHA is a simple generalization of BRAVO that (i) works for sampling with and without replacement; (ii) can be used with stratified sampling; (iii) works not only for ballot-polling but also for ballot-level comparison, batch-polling, and batch-level comparison audits, sampling with or without replacement, uniformly or with weights proportional to a measure of size; (iv) works for all social choice functions covered by SHANGRLA [19], including approval voting, Borda count, and all scoring rules; and (v) in situations where both ALPHA and BRAVO apply, requires smaller samples than BRAVO when the reported vote shares are wrong but the outcome is correct-five orders of magnitude in some examples. AL-PHA includes the family of betting martingale tests in RiLACS [27], with a different betting strategy parametrized as an estimator of the population mean and the flexibility to accommodate sampling weights and population bounds that change with each draw. A Python implementation is provided.

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Ballot-Polling Risk Limiting Audits for IRV Elections

Cited by 20 publications

References 8 publications

Assertion-Based Approaches to Auditing Complex Elections, with Application to Party-List Proportional Elections

Assertion-Based Approaches to Auditing Complex Elections, with Application to Party-List Proportional Elections

Auditing Hamiltonian Elections

ALPHA: Audit that Learns from Previously Hand-Audited Ballots

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