This study investigates an axiomatic approach to in-kind assignment problems with a single-unit demand such as triage. We consider multiple ethical criteria regarding which agents should be assigned that conflict with one another. To make compromises between criteria, we introduce two methods for configuring social choice rules that map from various problems to agents who are assigned slots: the method of procedure and the method of aggregation. From inter-problem regularities, we demonstrate characterization results, implying that the method of procedure emphasizes consistent respect for individual criteria across problems, whereas the method of aggregation emphasizes consistent respect for individual agents across problems. These methods are incompatible because only ethical dictatorships are induced by both methods. We show that the method of aggregation is superior when we can utilize detailed information about ethical concerns such as cardinality and comparability, while the method of procedure is superior when there are severe informational limitations.