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

TL;DR

This paper extends the SHANGRLA framework for risk-limiting audits by developing systematic methods to create assertions for complex social choice functions like party-list elections, enhancing election verification techniques.

Contribution

It introduces a systematic approach to constructing assertions with linear dependence for complex elections, broadening SHANGRLA's applicability to party-list and D'Hondt methods.

Findings

Successfully constructed assertions for Hamiltonian free list elections

Extended SHANGRLA to include D'Hondt method

Demonstrated the flexibility of assertions in complex social choice functions

Abstract

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.