Assertion-Based Approaches to Auditing Complex Elections, with Application to Party-List Proportional Elections
This work addresses the problem of auditing complex elections for election officials and researchers, though it is incremental as it extends an existing framework to new election types.
The paper tackles the lack of a systematic method for building assertions in risk-limiting audits (RLAs) by showing that assertions with linear dependence on vote transformations can be transformed into canonical form for the SHANGRLA framework, enabling direct application to party-list proportional elections like Hamiltonian free list and D'Hondt methods.
Risk-limiting audits (RLAs), an ingredient in evidence-based elections, are increasingly common. They are a rigorous statistical means of ensuring that electoral results are correct, usually without having to perform an expensive full recount -- at the cost of some controlled probability of error. A recently developed approach for conducting RLAs, SHANGRLA, provides a flexible framework that can encompass a wide variety of social choice functions and audit strategies. Its flexibility comes from reducing sufficient conditions for outcomes to be correct to canonical `assertions' that have a simple mathematical form. Assertions have been developed for auditing various social choice functions including plurality, multi-winner plurality, super-majority, Hamiltonian methods, and instant runoff voting. However, there is no systematic approach to building assertions. Here, we show that assertions with linear dependence on transformations of the votes can easily be transformed to canonical form for SHANGRLA. We illustrate the approach by constructing assertions for party-list elections such as Hamiltonian free list elections and elections using the D'Hondt method, expanding the set of social choice functions to which SHANGRLA applies directly.