Risk-Limiting Bayesian Polling Audits for Two Candidate Elections

TL;DR

This paper introduces a unified framework for Risk-Limiting and Bayesian audits in two-candidate elections, providing a computationally efficient method that combines the strengths of both approaches.

Contribution

It derives a general Bayesian audit expression without prior restrictions and proposes a Bayesian Risk-Limiting Audit that enhances audit efficiency.

Findings

Derived a general Bayesian audit expression without prior restrictions.

Introduced a simple comparison test for Bayesian audits enabling pre-computation.

Proposed a Bayesian Risk-Limiting Audit combining Bayesian and risk-limiting principles.

Abstract

We propose a simple common framework for Risk-Limiting and Bayesian (polling) audits for two-candidate plurality elections. Using it, we derive an expression for the general Bayesian audit; in particular, we do not restrict the prior to a beta distribution. We observe that the decision rule for the Bayesian audit is a simple comparison test, which enables the use of pre-computation---without simulations---and greatly increases the computational efficiency of the audit. Our main contribution is a general form for an audit that is both Bayesian and risk-limiting: the {\em Bayesian Risk-Limiting Audit}, which enables the use of a Bayesian approach to explore more efficient Risk-Limiting Audits.