Assertion-Based Approaches to Auditing Complex Elections, with Application to Party-List Proportional Elections

Risk-limiting audits (RLAs), an ingredient in evidence-based elections, are increasingly common. They a rigorous statistical means of ensuring that electoral results correct, usually without having to perform expensive full recount -- at the cost some controlled probability error. A recently developed approach for conducting RLAs, SHANGRLA, provides flexible framework can encompass wide variety social choice functions and audit strategies. Its flexibility comes from reducing sufficient conditions outcomes be correct canonical `assertions' have simple mathematical form. Assertions been auditing various including plurality, multi-winner super-majority, Hamiltonian methods, instant runoff voting. However, there is no systematic building assertions. Here, we show assertions with linear dependence on transformations votes easily transformed form SHANGRLA. We illustrate by constructing party-list elections such as free list using D'Hondt method, expanding set which SHANGRLA applies directly.