As artificial intelligence (AI) systems are increasingly used in ethically sensitive domains such as education, healthcare, and transportation, balancing accuracy and interpretability has become a central concern. Coarse ethics (CE) motivates coarse-grained evaluations under cognitive, institutional, and contextual constraints, but it still lacks a simple mathematical formalization of admissible coarse-graining and its informational consequences. This paper introduces coarse-grained partitions (CGPs) as a discrete framework for modeling coarse evaluation on a finite totally ordered score scale. A CGP represents coarse evaluation as a partition into grains with an index assignment, and induces a coarse-grained distribution by pushforward. To compare admissible coarse-grainings, we introduce categorical unification (CU), which constructs a canonical fine-scale reconstruction from the coarse representation under minimal assumptions. On this basis, we define a KL-based measure of information loss, $D_{\mathrm{KL\text{-}CU}}$, as the divergence between the original fine-grained distribution and its CU-based reconstruction. We prove that $D_{\mathrm{KL\text{-}CU}}=0$ if and only if the original distribution is already uniform within each grain. This shows that zero loss, in the sense of the proposed measure, is a highly exceptional limiting case rather than a realistic benchmark for ordinary evaluative practice. We also show that the framework leads naturally to an optimization problem for comparing alternative admissible CGPs. Applications to educational grading and explainable AI (XAI) illustrate how the framework clarifies trade-offs among informational fidelity, interpretability, and coarsening cost.

翻译：随着人工智能系统日益广泛应用于教育、医疗和交通等伦理敏感领域，平衡准确性与可解释性已成为核心关切。粗粒度伦理在认知、制度和情境约束下提倡粗粒度评估，但仍缺乏关于可容许粗粒度及其信息影响的简明数学形式化。本文引入粗粒度划分作为在有限全序评分尺度上建模粗粒度评估的离散框架。CGP将粗粒度评估表示为带索引分配的粒度划分，并通过前推导出粗粒度分布。为比较可容许粗粒度，我们提出分类统一化方法，该方法在最小假设下从粗粒度表示构建规范细尺度重构。在此基础上，我们定义基于KL散度的信息损失度量$D_{\mathrm{KL\text{-}CU}}$，作为原始细粒度分布与其CU重构之间的散度。我们证明当且仅当原始分布在每个粒度内已均匀时，$D_{\mathrm{KL\text{-}CU}}=0$成立。这表明在建议度量意义下的零损失是高度特殊的极限情况，而非普通评估实践的实用基准。我们还证明该框架自然引出了用于比较替代可容许CGP的优化问题。在教育评分和可解释AI中的应用例证了该框架如何阐明信息保真度、可解释性与粗粒度化代价之间的权衡关系。