The scrutiny surrounding vote-by-mail (VBM) in the United States has increased in recent years, highlighting the need for a rigorous quantitative framework to evaluate the resilience of the absentee voting infrastructure. This paper addresses these issues by introducing a dynamic mathematical modeling framework for performing a risk assessment of VBM processes. We introduce a discrete-time Markov chain (DTMC) to model the VBM process and assess election performance and risk with a novel layered network approach that considers the interplay between VBM processes, malicious and non-malicious threats, and security mitigations. The time-inhomogeneous DTMC framework captures dynamic risks and evaluates performance over time. The DTMC model accounts for a spectrum of outcomes, from unintended voter errors to sophisticated, targeted attacks, representing a significant advancement in the risk assessment of VBM planning and protection. A case study based on real-world data from Milwaukee County, Wisconsin, is used to evaluate the DTMC model. The analysis includes hypothetical worst-case attack scenarios to stress-test VBM processes and to assess the efficacy of security measures and the impact of different attack timings. The analysis suggests that ballot drop boxes and automatic ballot notification systems are crucial for reducing the attack surface to ensure secure and reliable operations.

翻译：近年来，美国对邮寄投票（VBM）的审查日益严格，凸显出建立严谨定量框架以评估缺席投票基础设施韧性的必要性。本文通过引入动态数学建模框架来应对这些问题，该框架用于对VBM流程进行风险评估。我们引入离散时间马尔可夫链（DTMC）对VBM流程建模，并采用一种新颖的分层网络方法评估选举表现与风险，该方法考虑了VBM流程、恶意与非恶意威胁以及安全缓解措施之间的相互作用。时齐性DTMC框架可捕获动态风险并随时间评估表现。该DTMC模型涵盖从无意的选民错误到复杂定向攻击的一系列结果，代表了VBM规划与保护风险评估领域的重大进展。基于威斯康星州密尔沃基县真实数据的案例研究用于评估所提出的DTMC模型。分析包括假设的最坏情景攻击案例，以对VBM流程进行压力测试，并评估安全措施的有效性及不同攻击时机的影响。分析表明，选票投递箱和自动选票通知系统对于缩小攻击面、确保安全可靠运行至关重要。