This paper introduces Admissibility Alignment: a reframing of AI alignment as a property of admissible action and decision selection over distributions of outcomes under uncertainty, evaluated through the behavior of candidate policies. We present MAP-AI (Monte Carlo Alignment for Policy) as a canonical system architecture for operationalizing admissibility alignment, formalizing alignment as a probabilistic, decision-theoretic property rather than a static or binary condition. MAP-AI, a new control-plane system architecture for aligned decision-making under uncertainty, enforces alignment through Monte Carlo estimation of outcome distributions and admissibility-controlled policy selection rather than static model-level constraints. The framework evaluates decision policies across ensembles of plausible futures, explicitly modeling uncertainty, intervention effects, value ambiguity, and governance constraints. Alignment is assessed through distributional properties including expected utility, variance, tail risk, and probability of misalignment rather than accuracy or ranking performance. This approach distinguishes probabilistic prediction from decision reasoning under uncertainty and provides an executable methodology for evaluating trust and alignment in enterprise and institutional AI systems. The result is a practical foundation for governing AI systems whose impact is determined not by individual forecasts, but by policy behavior across distributions and tail events. Finally, we show how distributional alignment evaluation can be integrated into decision-making itself, yielding an admissibility-controlled action selection mechanism that alters policy behavior under uncertainty without retraining or modifying underlying models.