Instant-runoff voting (IRV) is used in several countries around the world. It requires voters to rank candidates in order of preference, and uses a counting algorithm that is more complex than systems such as first-past-the-post or scoring rules. An even more complex system, the single transferable vote (STV), is used when multiple candidates need to be elected. The complexity of these systems has made it difficult to audit the election outcomes. There is currently no known risk-limiting audit (RLA) method for STV, other than a full manual count of the ballots. A new approach to auditing these systems was recently proposed, based on a Dirichlet-tree model. We present a detailed analysis of this approach for ballot-polling Bayesian audits of IRV elections. We compared several choices for the prior distribution, including some approaches using a Bayesian bootstrap (equivalent to an improper prior). Our findings include that the bootstrap-based approaches can be adapted to perform similarly to a full Bayesian model in practice, and that an overly informative prior can give counter-intuitive results. Via carefully chosen examples, we show why creating an RLA with this model is challenging, but we also suggest ways to overcome this. As well as providing a practical and computationally feasible implementation of a Bayesian IRV audit, our work is important in laying the foundation for an RLA for STV elections.

翻译：即时决选投票（IRV）在全球多个国家被采用。它要求选民按偏好顺序对候选人排序，并使用比简单多数制或计分规则等系统更复杂的计票算法。当需要选出多名候选人时，还会采用更复杂的单一可转移投票（STV）系统。这些系统的复杂性使得选举结果的审计变得困难。目前除了对选票进行完整人工清点外，尚无已知的STV风险限制审计（RLA）方法。近期有学者提出了一种基于狄利克雷树模型的新型审计方法。我们针对IRV选举的选票抽检贝叶斯审计，对该方法进行了详细分析。我们比较了多种先验分布的选择，包括使用贝叶斯自助法（等价于不当先验）的若干方法。研究发现：基于自助法的方法在实践中可调整至与完整贝叶斯模型性能相当，而过度信息化的先验分布会产生反直觉的结果。通过精心设计的案例，我们揭示了为何使用该模型构建RLA颇具挑战性，同时也提出了克服这些困难的方法。本研究不仅提供了实用且计算可行的贝叶斯IRV审计实现方案，更对奠定STV选举RLA基础具有重要价值。