  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.
