3+ Seat risk-limiting audits for single transferable vote elections

Constructing efficient risk-limiting audits (RLAs) for multi-winner single transferable vote (STV) elections is a challenging problem. An STV RLA is designed to statistically verify that the reported winners of an election did indeed win according to the voters’ expressed preferences and not due to mistabulation or interference, while limiting the risk of accepting an incorrect outcome to a desired threshold (the risk limit). Existing methods have shown that it is possible to form RLAs for two-seat STV elections in the context where the first seat has been awarded to a candidate in the first round of tabulation. This is called the first winner criterion. We present an assertion-based approach to conducting full or partial RLAs for STV elections with three or more seats, in which the first winner criterion is satisfied. Although the chance of forming a full audit that verifies all winners drops substantially as the number of seats increases, we show that we can quite often form partial audits that verify most, and sometimes all, of the reported winners. We evaluate our method on a dataset of over 500 three- and four-seat STV elections from the 2017 and 2022 local council elections in Scotland.