Artificial intelligence is increasingly embedded in human decision making. In some cases, it enhances human reasoning. In others, it fosters excessive cognitive dependence. This paper introduces a conceptual and mathematical framework to distinguish cognitive amplification, where AI improves hybrid human AI performance while preserving human expertise, from cognitive delegation, where reasoning is progressively outsourced to the AI system, risking long term atrophy of human capabilities. We define four operational metrics: the Cognitive Amplification Index, or CAI star, which measures collaborative gain beyond the best standalone agent; the Dependency Ratio, or D, and Human Reliance Index, or HRI, which quantify the structural dominance of the AI within the hybrid output; and the Human Cognitive Drift Rate, or HCDR, which captures the temporal erosion or maintenance of autonomous human performance. Together, these quantities characterize human AI systems in terms of both immediate hybrid performance and long term cognitive sustainability. We validate the framework through an agent based simulation in NetLogo across three reliance regimes and multiple dependency and atrophy configurations. The results distinguish degenerate AI dominated delegation, human preserving but weakly competitive interaction, and intermediate boundary regimes that approach the AI baseline while remaining structurally dependent. Across all tested configurations, no regime achieves genuine amplification. A constrained optimization over the atrophy parameter shows that reducing atrophy improves retained human capability, collaborative gain, and dependency structure, but even zero atrophy does not yield positive collaborative gain. The framework therefore provides a practical tool for evaluating whether human AI systems perform well in a way that also preserves human capability over time.

翻译：人工智能正日益嵌入人类决策过程。在某些情况下，它增强了人类推理能力；在另一些情况下，则导致了过度的认知依赖。本文提出一个概念性和数学性框架，用于区分认知增强（即人工智能在保持人类专业知识的同时提升混合人机系统性能）与认知委托（即推理过程逐步外包给人工智能系统，可能导致人类能力长期退化）。我们定义了四个操作性度量指标：认知增强指数（Cognitive Amplification Index, CAI*），用于衡量超越最优独立主体的协同增益；依赖比（Dependency Ratio, D）和人类依赖指数（Human Reliance Index, HRI），用于量化混合输出中人工智能的结构性主导地位；以及人类认知漂移率（Human Cognitive Drift Rate, HCDR），用于捕捉自主人类能力随时间侵蚀或保持的情况。这些量共同从即时混合性能与长期认知可持续性两个维度刻画人机系统。我们通过NetLogo中的基于主体仿真，在三种依赖模式及多种依赖与退化配置下验证了该框架。结果区分了退化的AI主导委托、保持人类能力但性能较弱的竞争性交互，以及接近AI基线但结构上仍存在依赖的中间边界模式。在所有测试配置中，没有一种模式实现了真正的增强。针对退化参数的约束优化表明，减少退化能改善保留的人类能力、协同增益和依赖结构，但即使将退化降至零，也无法产生正的协同增益。因此，该框架为评估人机系统是否在保持人类能力的同时实现了良好性能提供了一种实用工具。