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BRAVO, the most widely tried method for risk-limiting election audits, cannot accommodate sampling without replacement or stratified sampling, which can improve efficiency and may be required by law. It applies only to ballot-polling…

Methodology · Statistics 2022-08-15 Philip B. Stark

Risk-limiting audits (RLAs) are expected to strengthen the public confidence in the correctness of an election outcome. We hypothesize that this is not always the case, in part because for large margins between the winner and the runner-up,…

Computers and Society · Computer Science 2021-09-17 Asmita Dalela , Oksana Kulyk , Carsten Schürmann

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…

Applications · Statistics 2023-09-19 Amanda K. Glazer , Jacob V. Spertus , Philip B. Stark

We present a method and software for ballot-polling risk-limiting audits (RLAs) based on Bernoulli sampling: ballots are included in the sample with probability $p$, independently. Bernoulli sampling has several advantages: (1) it does not…

Card-level comparison risk-limiting audits (CLCAs) heretofore required a CVR for each cast card and a "link" identifying which CVR is for which card -- which many voting systems cannot provide. Every set of CVRs that produces the same…

Applications · Statistics 2023-06-21 Philip B. Stark

Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains…

Machine Learning · Computer Science 2026-05-19 Jinglong Xiong , Xiaotian Liu , Ruoxin Wang , Zihang Liu , Yefan Zhou , Yujun Yan , Yaoqing Yang

Indian Electronic Voting Machines (EVMs) will be fitted with printers that produce Voter-Verifiable Paper Audit Trails (VVPATs) in time for the 2019 general election. VVPATs provide evidence that each vote was recorded as the voter…

Cryptography and Security · Computer Science 2019-01-28 Vishal Mohanty , Nicholas Akinyokun , Andrew Conway , Chris Culnane , Philip B. Stark , Vanessa Teague

We present an approximate sampling framework and discuss how risk-limiting audits can compensate for these approximations, while maintaining their "risk-limiting" properties. Our framework is general and can compensate for counting mistakes…

Data Structures and Algorithms · Computer Science 2019-01-04 Mayuri Sridhar , Ronald L. Rivest

Ranked Choice Voting (RCV) and Single Transferable Voting (STV) are widely valued; but are complex to understand due to intricate per-round vote transfers. Questions like determining how far a candidate is from winning or identifying…

Computer Science and Game Theory · Computer Science 2024-07-22 Sanyukta Deshpande , Nikhil Garg , Sheldon Jacobson

Colorado conducted risk-limiting tabulation audits (RLAs) across the state in 2017, including both ballot-level comparison audits and ballot-polling audits. Those audits only covered contests restricted to a single county; methods to…

Applications · Statistics 2018-03-05 Mark Lindeman , Neal McBurnett , Kellie Ottoboni , Philip B. Stark

SOBA is an approach to election verification that provides observers with justifiably high confidence that the reported results of an election are consistent with an audit trail ("ballots"), which can be paper or electronic. SOBA combines…

Applications · Statistics 2011-07-05 Josh Benaloh , Douglas Jones , Eric Lazarus , Mark Lindeman , Philip B. Stark

For more than a century, election officials across the United States have inspected voting machines before elections using a procedure called Logic and Accuracy Testing (LAT). This procedure consists of election officials casting a test…

Cryptography and Security · Computer Science 2024-10-01 Braden L. Crimmins , J. Alex Halderman , Bradley Sturt

We introduce the notion of a risk-limiting financial auditing (RLFA): given $N$ transactions, the goal is to estimate the total misstated monetary fraction~($m^*$) to a given accuracy $\epsilon$, with confidence $1-\delta$. We do this by…

Methodology · Statistics 2023-05-12 Shubhanshu Shekhar , Ziyu Xu , Zachary C. Lipton , Pierre J. Liang , Aaditya Ramdas

Studying distributed computing through the lens of algebraic topology has been the source of many significant breakthroughs during the last two decades, especially in the design of lower bounds or impossibility results for deterministic…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-05-26 Pierre Fraigniaud , Ran Gelles , Zvi Lotker

The main risk-limiting ballot polling audit in use today, BRAVO, is designed for use when single ballots are drawn at random and a decision regarding whether to stop the audit or draw another ballot is taken after each ballot draw…

Cryptography and Security · Computer Science 2021-02-23 Filip Zagórski , Grant McClearn , Sarah Morin , Neal McBurnett , Poorvi L. Vora

In many real world elections, agents are not required to rank all candidates. We study three of the most common methods used to modify voting rules to deal with such partial votes. These methods modify scoring rules (like the Borda count),…

Computer Science and Game Theory · Computer Science 2014-06-02 Nina Narodytska , Toby Walsh

The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that they unfairly favor a particular political party, often…

Data Structures and Algorithms · Computer Science 2024-02-22 Jin-Yi Cai , Jacob Kruse , Kenneth Mayer , Daniel P. Szabo

The single transferable vote (STV) is a system of preferential proportional voting employed in multi-seat elections. Each ballot cast by a voter is a (potentially partial) ranking over a set of candidates. The margin of victory, or simply…

Computer Science and Game Theory · Computer Science 2025-03-26 Michelle Blom , Alexander Ek , Peter J. Stuckey , Vanessa Teague , Damjan Vukcevic

Accurately predicting road networks from satellite images requires a global understanding of the network topology. We propose to capture such high-level information by introducing a graph-based framework that simulates the addition of…

Computer Vision and Pattern Recognition · Computer Science 2022-10-04 Sotiris Anagnostidis , Aurelien Lucchi , Thomas Hofmann

We propose a simple risk-limiting audit for elections, ClipAudit. To determine whether candidate A (the reported winner) actually beat candidate B in a plurality election, ClipAudit draws ballots at random, without replacement, until either…

Cryptography and Security · Computer Science 2017-01-31 Ronald L. Rivest