论文标题

通过Dirichlet-Tree模型对即时投票选举进行投票审核

Ballot-Polling Audits of Instant-Runoff Voting Elections with a Dirichlet-Tree Model

论文作者

Everest, Floyd, Blom, Michelle, Stark, Philip B., Stuckey, Peter J., Teague, Vanessa, Vukcevic, Damjan

论文摘要

Instant-Runoff投票(IRV)用于世界上几个国家。它要求选民按偏好顺序对候选人进行排名,并使用计数算法,该算法比诸如第一任务或评分规则之类的系统更为复杂。当需要选举多个候选人时,使用一个更复杂的系统,即单一可转让投票(STV)。这些系统的复杂性使得很难审核选举结果。目前,除了选票的全部手动计数外,目前尚无针对STV的限制风险审核(RLA)方法。 最近,根据Dirichlet-Tree模型提出了一种新的审核这些系统的方法。我们对这种方法进行了对IRV选举的贝叶斯审核的详细分析。我们比较了先前分布的几种选择,包括使用贝叶斯引导程序(相当于先验不当的方法)的一些方法。我们的发现包括,基于自举的方法可以适应与实践中的完整贝叶斯模型相似的性能,并且过于有用的先验可以给出违反直觉的结果。通过精心选择的示例,我们展示了为什么使用此模型创建RLA是具有挑战性的,但我们也建议方法来克服这一点。 除了提供贝叶斯IRV审核的实用和计算可行的实施外,我们的工作对于为STV选举的RLA奠定基础很重要。

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.

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