We propose a model of "frugal aggregation" in which the evaluation of social welfare must be based on information about agents' top choices plus general qualitative background conditions on preferences. The former is elicited individually, while the latter is not. We apply this model to problems of public budget allocation, relying on the specific assumption of separable and convex preferences. We propose and analyze a particularly aggregation rule called "Frugal Majority Rule". It is defined in terms of a suitably localized net majority relation. This relation is shown to be consistent, i.e. acyclic and decisive; its maxima minimize the sum of the natural resource distances to the individual tops. As a consequence of this result, we argue that the Condorcet and Borda perspectives - which conflict in the standard, ordinal setting - converge here. The second main result provides a crisp algorithmic characterization that renders the Frugal Majority Rule analytically tractable and efficiently computable.