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.

翻译：风险限制审计(RLAs)是循证选举的一个要素,越来越常见。它们是一种严格的统计手段,可以确保选举结果正确无误,通常不必进行昂贵的全额计票 -- -- 以某些受控制的误差概率为代价。最近制定的进行RLAs的方法(SHANGRLA)提供了一个灵活的框架,可以包括各种各样的社会选择功能和审计战略。其灵活性来自减少足够条件,使结果能够正确成为具有简单数学形式的卡通性`保证'。它们是一种严格的统计手段,用于审计各种社会选择功能,包括多元性、多赢家多元性、超级多数性、汉密尔顿式方法、以及即时决胜选。然而,没有系统的方法来建立说法。在这里,我们表明,对选票转换的线性依赖可以很容易地转变为SHANGRA的卡式形式。我们用汉密尔顿自由名单选举和使用D'Hont方法为政党名单选举和选举作出主张,扩大社会选择功能的范围。