New Tool Reveals How Easily Ranked-Choice Elections Can Flip

A single researcher, Edouard Heitzmann, presents "audit graphs" as a visual tool for measuring the stability of Single Transferable Vote elections, according to a paper posted to arXiv. STV is an algorithmic election rule: round by round, a profile of ranked-choice ballots is reinterpreted to determine which decision to make next, and candidates are seated or eliminated until a full winner set emerges. Because of this algorithmic nature, STV is theoretically more brittle than other election rules — uncertainty about an early round might percolate irreversibly into the rest — and for that reason a generalized non-trivial Risk-Limiting Audit framework has remained elusive for STV. Such a framework must concoct a set of null hypotheses, or assertions, whose rejection would bound the probability that the outcome of the election was incorrectly reported. The paper presents audit graphs as a solution to design the assertions needed for RLAs of arbitrary STV elections, as well as to quantitatively describe the uncertainty (or lack thereof) of their outcomes. These audit graphs explore election paths that are "close" to the recorded one by considering the alternative decisions the STV algorithm might have made if a small number of ballots were perturbed.