The Decisive Power of Indecision: Low-Variance Risk-Limiting Audits and Election Contestation via Marginal Mark Recording

TL;DR

This paper tackles the efficiency and robustness limitations of risk-limiting audits (RLAs) for large elections by rethinking cast-vote records (CVRs) to express marginal marks. It introduces two main frameworks: Bayesian CVR-based ballot-comparison RLAs that reduce variance and sample needs, and conservative CVRs that preserve interpretability while enabling efficient auditing; both are proven risk-limiting under an adaptive, game-based model. A striking contribution is the contested (competitive) audit, where multiple candidates submit CVRs and the audit achieves a constant, margin-independent sample size, enabling effective election contestation. The work also lays out deployment implications, formal definitions, and extensions to polling and batch settings, offering a practical path to stronger, more transparent post-election verification and contest resolution.

Abstract

Risk-limiting audits (RLAs) are techniques for verifying the outcomes of large elections. While they provide rigorous guarantees of correctness, widespread adoption has been impeded by both efficiency concerns and the fact they offer statistical, rather than absolute, conclusions. We attend to both of these difficulties, defining new families of audits that improve efficiency and offer qualitative advances in statistical power. Our new audits are enabled by revisiting the standard notion of a cast-vote record so that it can declare multiple possible mark interpretations rather than a single decision; this can reflect the presence of marginal marks, which appear regularly on hand-marked ballots. We show that this simple expedient can offer significant efficiency improvements with only minor changes to existing auditing infrastructure. We consider two ways of representing these marks, both yield risk-limiting comparison audits in the formal sense of Fuller, Harrison, and Russell (IEEE Security & Privacy 2023). We then define a new type of post-election audit we call a contested audit. These permit each candidate to provide a cast-vote record table advancing their own claim to victory. We prove that these audits offer remarkable sample efficiency, yielding control of risk with a constant number of samples (that is independent of margin). This is a first for an audit with provable soundness. These results are formulated in a game-based security model that specify quantitative soundness and completeness guarantees. These audits provide a means to handle contestation of election results affirmed by conventional RLAs.

Figures (6)

• Figure 1: Generalization of conventional CVRs to the conservative setting, where multiple interpretations are declared, and the Bayesian setting, where one associates probabilities with each interpretation. Blanks cells in the Bayesian indicate probability $0$; for brevity, the "No Vote" columns reflect both the no-mark case and the overvote case (with marks for both candidates).
• Figure 2: The $\mathsf{RLA}_{\mathtt{MAudit},\mathtt{Env}}(E, \mathsf{cvr})$ auditing game for comparison audits with multiple interpretations.
• Figure 3: The auditor $\mathtt{MAudit}[(\mathsf{Stop}, \mathsf{R})]$.
• Figure 4: The $\mathsf{RLA}_{\mathtt{MAudit},\mathtt{Env}}(E, \mathsf{cvr})$ auditing game for comparison audits with multiple interpretations.
• Figure 5: The competitive auditing game $\mathsf{CompeteA}$ with auditor $\mathtt{Judge}$, environment $\mathtt{Env}$, election $E$, and advocate CVRs $\{ \mathsf{cvr}_\mathsf{A}^{+} \mid \mathsf{A} \in \mathcal{C}\}$.

Theorems & Definitions (39)

• Definition 1: Interpretations, ballots, and ballot families
• Definition 2
• Definition 3: Election winners, losers, and margin
• Definition 4: Bayesian Cast-Vote Record Table
• Definition 5: Bayesian declared margin
• Definition 6: Bayesian validity
• Definition 7: Bayesian discrepancy
• Lemma 1
• proof : Proof of Lemma \ref{['lem:disc works']}
• Definition 8