Journal article: We propose and operationalize normative principles to guide social decisions when individuals potentially have imprecise and heterogeneous beliefs, in addition to conflicting tastes or interests. To do so we adapt the standard Pareto principle to those preference comparisons that are robust to belief imprecision and characterize social preferences that respect this robust principle. We also characterize a suitable restriction of this principle. The former principle provides stronger guidance when it can be satisfied; when it cannot, the latter always provides minimal guidance.