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We consider a setting in which a social planner has to make a sequence of decisions to allocate scarce resources in a high-stakes domain. Our goal is to understand stakeholders' dynamic moral preferences toward such allocational policies. In particular, we evaluate the sensitivity of moral preferences to the history of allocations and their perceived future impact on various socially salient groups. We propose a mathematical model to capture and infer such dynamic moral preferences. We illustrate our model through small-scale human-subject experiments focused on the allocation of scarce medical resource distributions during a hypothetical viral epidemic. We observe that participants' preferences are indeed history- and impact-dependent. Additionally, our preliminary experimental results reveal intriguing patterns specific to medical resources---a topic that is particularly salient against the backdrop of the global covid-19 pandemic.