Traditional ethical frameworks often struggle to model decision-making under uncertainty, treating it as a simple constraint on action. This paper introduces the Principle of Proportional Duty (PPD), a novel framework that models how ethical responsibility scales with an agent's epistemic state. The framework reveals that moral duty is not lost to uncertainty but transforms: as uncertainty increases, Action Duty (the duty to act decisively) is proportionally converted into Repair Duty (the active duty to verify, inquire, and resolve uncertainty). This dynamic is expressed by the equation D_total = K[(1-HI) + HI * g(C_signal)], where Total Duty is a function of Knowledge (K), Humility/Uncertainty (HI), and Contextual Signal Strength (C_signal). Monte Carlo simulations demonstrate that systems maintaining a baseline humility coefficient (lambda > 0) produce more stable duty allocations and reduce the risk of overconfident decision-making. By formalizing humility as a system parameter, the PPD offers a mathematically tractable approach to moral responsibility that could inform the development of auditable AI decision systems. This paper applies the framework across four domains, clinical ethics, recipient-rights law, economic governance, and artificial intelligence, to demonstrate its cross-disciplinary validity. The findings suggest that proportional duty serves as a stabilizing principle within complex systems, preventing both overreach and omission by dynamically balancing epistemic confidence against contextual risk.