We introduce a novel framework for deepening our understanding of bounded rationality in the presence of heterogeneity. Our analysis centers on a fundamental question: when, and under what conditions, can individual behavior be reliably inferred from aggregate data, especially when individuals may make mistakes? Answering this question requires bridging the gap between unobserved deterministic boundedly rational choices at the individual level and observed aggregate outcomes. To address this challenge, we first introduce the ``bounds'' framework that systematically restricts permissible deviations from rational choice. Each bound, or collection of bounds, characterizes a class of admissible individual choice behaviors and induces a corresponding probabilistic choice model. We show that these bound-induced models have empirical content and are fundamentally distinct from existing models. To identify their full behavioral implications, we introduce decomposability: a key property ensuring that aggregate choice behavior faithfully reflects the underlying structure of individual decision-making within a population.

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