skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Improving the Computational Efficiency of Adaptive Audits of IRV Elections
Abstract AWAIRE is one of two extant methods for conducting risk-limiting audits of instant-runoff voting (IRV) elections. In principle AWAIRE can audit IRV contests with any number of candidates, but the original implementation incurred memory and computation costs that grew superexponentially with the number of candidates. This paper improves the algorithmic implementation of AWAIRE in three ways that make it practical to audit IRV contests with 55 candidates, compared to the previous 6 candidates. First, rather than trying from the start to rule out all candidate elimination orders that produce a different winner, the algorithm starts by considering only the final round, testing statistically whether each candidate could have won that round. For those candidates who cannot be ruled out at that stage, it expands to consider earlier and earlier rounds until either it provides strong evidence that the reported winner really won or a full hand count is conducted, revealing who really won. Second, it tests a richer collection of conditions, some of which can rule out many elimination orders at once. Third, it exploits relationships among those conditions, allowing it to abandon testing those that are unlikely to help. We provide real-world examples with up to 36 candidates and synthetic examples with up to 55 candidates, showing how audit sample size depends on the margins and on the tuning parameters. An open-source Python implementation is publicly available.  more » « less
Award ID(s):
2228884
PAR ID:
10656292
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
Springer Nature Switzerland
Date Published:
Page Range / eLocation ID:
37 to 53
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. The U.S. state of Georgia was central to e!orts to overturn the results of the 2020 Presidential election, including a phone call from then-president Donald Trump to Georgia Secretary of State Brad Ra!ensperger asking Ra!ensperger to ‘find’ 11,780 votes. Ra!ensperger has maintained that a ‘100% full-count risk-limiting audit’ and a machine recount agreed with the initial machine-count results, which proved that the reported election results were accurate and that ‘no votes were flipped.’ While there is no evidence that the reported outcome is wrong, neither is there evidence that it is correct: the two machine counts and the manual ‘audit’ tallies disagree substantially, even about the number of ballots cast. Some ballots in Fulton County, Georgia, were included in the original count at least twice; some were included in the machine recount at least thrice. Audit handcount results for some tally batches were omitted from the reported audit totals: reported audit results do not include all the votes the auditors counted. In short, the two machine counts and the audit were not probative of who won because of poor processes and controls: a lack of secure physical chain of custody, ballot accounting, pollbook reconciliation, and accounting for other election materials such as memory cards. Moreover, most voters used demonstrably untrustworthy ballot-marking devices; as a result, even a perfect handcount or audit would not necessarily reveal who really won. True risk-limiting audits (RLAs) and rigorous recounts can limit the risk that an incorrect electoral outcome will be certified rather than being corrected. But no procedure can limit that risk without a trustworthy record of the vote. And even a properly conducted RLA of some contests in an election does not show that any other contests in that election were decided correctly. The 2020 U.S. Presidential election in Georgia illustrates unrecoverable errors that can render recounts and audits ‘security theater’ that distract from the more serious problems rather than justifying trust. 
    more » « less
  2. The study of fairness in multiwinner elections focuses on settings where candidates have attributes. However, voters may also be divided into predefined populations under one or more attributes. The models that focus on candidate attributes alone may systematically under-represent smaller voter populations. Hence, we develop a model, DiRe Committee Winner Determination (DRCWD), which delineates candidate and voter attributes to select a committee by specifying diversity and representation constraints and a voting rule. We analyze its computational complexity and develop a heuristic algorithm, which finds the winning DiRe committee in under two minutes on 63% of the instances of synthetic datasets and on 100% of instances of real-world datasets. We also present an empirical analysis of feasibility and utility traded-off. Moreover, even when the attributes of candidates and voters coincide, it is important to treat them separately as diversity does not imply representation and vice versa. This is to say that having a female candidate on the committee, for example, is different from having a candidate on the committee who is preferred by the female voters, and who themselves may or may not be female. 
    more » « less
  3. 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, then 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 RLAs 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 reduce the expected number of draws needed to audit a single countywide contest on a 4-card ballot by 75%. Similarly, CSD reduce 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. 
    more » « less
  4. We consider the problem of finding, through adaptive sampling, which of n populations (arms) has the largest mean. Our objective is to determine a rule which identifies the best arm with a fixed minimum confidence using as few observations as possible.We study such problems when the population distributions are either Bernoulli or normal. We take a Bayesian approach that assumes that the unknown means are the values of independent random variables having a common specified distribution. We propose to use the classical vector at a time rule, which samples each remaining arm once in each round, eliminating arms whose cumulative sum falls k below that of another arm. We show how this rule can be implemented and analyzed in our Bayesian setting and how it can be improved by early elimination. We also propose and analyze a variant of the classical play the winner algorithm. Numerical results show that these rules perform quite well, even when considering cases where the set of means do not look like they come from the specified prior. 
    more » « less
  5. It remains an open question how to determine the winner of an election when voter preferences are incomplete or uncertain. One option is to assume some probability space over the voting profile and select the Most Probable Winner (MPW) -- the candidate or candidates with the best chance of winning. In this paper, we propose an alternative winner interpretation, selecting the Most Expected Winner (MEW) according to the expected performance of the candidates. We separate the uncertainty in voter preferences into the generation step and the observation step, which gives rise to a unified voting profile combining both incomplete and probabilistic voting profiles. We use this framework to establish the theoretical hardness of MEW over incomplete voter preferences, and then identify a collection of tractable cases for a variety of voting profiles, including those based on the popular Repeated Insertion Model (RIM) and its special case, the Mallows model. We develop solvers customized for various voter preference types to quantify the candidate performance for the individual voters, and propose a pruning strategy that optimizes computation. The performance of the proposed solvers and pruning strategy is evaluated extensively on real and synthetic benchmarks, showing that our methods are practical. 
    more » « less