In high-stakes ML applications such as fraud detection, medical diagnostics, and content moderation, practitioners rely on consensus-based approaches to control prediction quality. A particularly valuable technique -- δδδ-margin majority voting -- collects votes sequentially until one label exceeds alternatives by a threshold δδδ, offering stronger confidence than simple majority voting. Despite widespread adoption, this approach has lacked rigorous theoretical foundations, leaving practitioners reliant on heuristics for key metrics like expected accuracy and cost. This paper establishes a comprehensive theoretical framework for δδδ-margin majority voting by formulating it as an absorbing Markov chain and leveraging Gambler's Ruin theory. Our contributions form a practical \emph{design calculus} for δδδ-margin voting: (1)~Closed-form expressions for consensus accuracy, expected voting duration, variance, and the stopping-time PMF, enabling model-based design rather than trial-and-error. (2)~A Bayesian extension handling uncertainty in worker accuracy, supporting real-time monitoring of expected quality and cost as votes arrive, with single-Beta and mixture-of-Betas priors. (3)~Cost-calibration methods for achieving equivalent quality across worker pools with different accuracies and for setting payment rates accordingly. We validate our predictions on two real-world datasets, demonstrating close agreement between theory and observed outcomes. The framework gives practitioners a rigorous toolkit for designing δδδ-margin voting processes, replacing ad-hoc experimentation with model-based design where quality control and cost transparency are essential.

翻译：在高风险机器学习应用中，如欺诈检测、医疗诊断和内容审核，从业者依赖基于共识的方法来控制预测质量。一种特别有价值的技术——δ-边际多数投票——通过顺序收集投票，直到某一标签的票数超过其他标签一个阈值δ，从而提供比简单多数投票更强的置信度。尽管被广泛采用，该方法一直缺乏严格的理论基础，导致从业者在关键指标如期望准确率和成本方面依赖启发式方法。本文通过将δ-边际多数投票建模为吸收马尔可夫链并利用赌徒破产理论，建立了其全面的理论框架。我们的贡献形成了一套实用的δ-边际投票设计演算体系：（1）共识准确率、期望投票时长、方差以及停时概率质量函数的闭式表达式，支持基于模型的设计而非试错法。（2）一种贝叶斯扩展，处理工人准确率的不确定性，支持在投票到达时实时监控期望质量和成本，采用单Beta和混合Beta先验。（3）成本校准方法，用于在不同准确率的工人池中实现等效质量，并据此设定支付费率。我们在两个真实世界数据集上验证了预测，展示了理论与观察结果之间的紧密一致性。该框架为从业者提供了设计δ-边际投票过程的严格工具包，用基于模型的设计取代临时实验，适用于质量控制和成本透明度至关重要的场景。