We address the problem of decision making under “deep uncertainty,” introducing an approach we call Robust Portfolio Decision Analysis. We introduce the idea of Belief Dominance as a prescriptive operationalization of a concept that has appeared in the literature under a number of names. We use this concept to derive a set of non-dominated portfolios; and then identify robust individual alternatives from the non-dominated portfolios. The Belief Dominance concept allows us to synthesize multiple conflicting sources of information by uncovering the range of alternatives that are intelligent responses to the range of beliefs. This goes beyond solutions that are optimal for any specific set of beliefs to uncover defensible solutions that may not otherwise be revealed. We illustrate our approach using a problem in the climate change and energy policy context: choosing among clean energy technology R&D portfolios. We demonstrate how the Belief Dominance concept can uncover portfolios that would otherwise remain hidden and identify robust individual investments.