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Counting votes is complex and error-prone. Several statistical methods have been developed to assess election accuracy by manually inspecting randomly selected physical ballots. Two 'principled' methods are risk-limiting audits (RLAs) and…

Applications · Statistics 2021-05-13 Zhuoqun Huang , Ronald L. Rivest , Philip B. Stark , Vanessa Teague , Damjan Vukcevic

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…

Computers and Society · Computer Science 2021-10-05 Michelle Blom , Jurlind Budurushi , Ronald L. Rivest , Philip B. Stark , Peter J. Stuckey , Vanessa Teague , Damjan Vukcevic

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…

Cryptography and Security · Computer Science 2020-12-08 Amanda K. Glazer , Jacob V. Spertus , Philip B. Stark

Criteria for a good voting system have been given particularly careful scrutiny in recent years, with general agreement that the core values are fair results, voter power and choice, and local representation. This paper reexamines the basic…

Physics and Society · Physics 2023-03-29 Denis Mollison

One approach to risk-limiting audits (RLAs) compares randomly selected cast vote records (CVRs) to votes read by human auditors from the corresponding ballot cards. Historically, such methods reduce audit sample sizes by considering how…

Computers and Society · Computer Science 2026-03-27 Alexander Ek , Michelle Blom , Philip B. Stark , Peter J. Stuckey , Vanessa J. Teague , Damjan Vukcevic

We describe the vote package in R, which implements the plurality (or first-past-the-post), two-round runoff, score, approval and single transferable vote (STV) electoral systems, as well as methods for selecting the Condorcet winner and…

Computation · Statistics 2021-02-12 Adrian E. Raftery , Hana Ševčíková , Bernard W. Silverman

Risk-limiting audits (RLAs) guarantee a high probability of correcting incorrect reported outcomes before the outcomes are certified. The most efficient use ballot-level comparison, comparing the voting system's interpretation of individual…

Cryptography and Security · Computer Science 2023-09-01 Philip B. Stark

Single Transferable Vote (STV) counting, used in several jurisdictions in Australia, is a system for choosing multiple election winners given voters' preferences among candidates. The system is complex and it is not always obvious how an…

Computers and Society · Computer Science 2025-09-18 Andrew Conway , Michelle Blom , Alexander Ek , Peter Stuckey , Vanessa Teague , Damjan Vukcevic

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

Proportional representation plays a crucial role in electoral systems. In ordinal elections, where voters rank candidates based on their preferences, the Single Transferable Vote (STV) is the most widely used proportional voting method. STV…

Computer Science and Game Theory · Computer Science 2025-05-02 Tuva Bardal , Markus Brill , David McCune , Jannik Peters

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

An election audit is risk-limiting if the audit limits (to a pre-specified threshold) the chance that an erroneous electoral outcome will be certified. Extant methods for auditing instant-runoff voting (IRV) elections are either not…

Applications · Statistics 2023-10-06 Alexander Ek , Philip B. Stark , Peter J. Stuckey , Damjan Vukcevic

The voting systems known as Alternative Vote (AV) and Single Transferable Vote (STV) are extensively used for elections in Australia, possibly more than in any other jurisdiction. Often proposed as superior alternatives to Plurality and…

Physics and Society · Physics 2025-07-22 Anthony B. Morton

Errors are inevitable in the implementation of any complex process. Here we examine the effect of random errors on Single Transferable Vote (STV) elections, a common approach to deciding multi-seat elections. It is usually expected that…

Computers and Society · Computer Science 2020-11-10 Michelle Blom , Andrew Conway , Peter J. Stuckey , Vanessa Teague , Damjan Vukcevic

We study ballot exhaustion in multiwinner single transferable vote (STV) elections using a dataset of 1,070 Scottish local government elections comprising over 5.4 million ballots. While ballot exhaustion has been studied extensively in…

General Economics · Economics 2026-05-14 David McCune , E. E. Naber

Risk-limiting audits (RLAs) for many social choice functions can be reduced to testing sets of null hypotheses of the form "the average of this list is not greater than 1/2" for a collection of finite lists of nonnegative numbers. Such…

Applications · Statistics 2020-03-26 Philip B. Stark

The methods of single transferable vote (STV) and sequential ranked-choice voting (RCV) are different methods for electing a set of winners in multiwinner elections. STV is a classical voting method that has been widely used internationally…

General Economics · Economics 2023-07-03 David McCune , Erin Martin , Grant Latina , Kaitlyn Simms

Limited Voting (LV) is an approval-based method for multi-winner elections where all ballots are required to have a same fixed size. While it appears to be used as voting method in corporate governance and has some political applications,…

Computer Science and Game Theory · Computer Science 2024-07-26 Maaike Venema-Los , Zoé Christoff , Davide Grossi

We analyze a type of voting paradox which we term an involvement paradox, in which a candidate who loses an election could be made into a winner if more of the candidate's non-supporters participated in the election, or a winner could be…

General Economics · Economics 2024-11-26 David McCune

Single Transferable Vote (STV) counting, used in several jurisdictions in Australia, is a system for choosing multiple election winners given voters' preferences over candidates. There are a variety of different versions of STV legislated…

Computers and Society · Computer Science 2024-09-19 Andrew Conway , Michelle Blom , Alexander Ek , Peter J. Stuckey , Vanessa J. Teague , Damjan Vukcevic