In decision-making involving multiple criteria or attributes, a decision maker first identifies all relevant evaluative attributes in making decisions. Then, a dominance principle is often invoked whenever applicable: whenever an option x is better than an option y in terms of some attribute and no worse than y in terms of any other attributes, x is judged to be better than y. If, however, this dominance principle is not applicable, then the decision maker determines the relative importance between the identified evaluative attributes, consults with contextual features of the options under consideration, and makes a decision. It is shown that the combination of these principles runs into problems in the presence of rationality properties, such as transitivity, and a weak continuity requirement on decisions. The paper gives examples from welfare economics, and theories of individual and group decisions.