Real-life decision situations almost invariably involve large uncertainties. In particular, there are several difficulties connected with the elicitation of probabilities, utilities, and criteria weights. In this article, we explore and test a robust multi-criteria weight generating method covering a broad set of decision situations, but which still is reasonably simple to use. We cover an important class of methods for criteria weight elicitation and propose the use of a reinterpretation of an efficient family (rank exponent) of methods for modeling and evaluating multi-criteria decision problems under uncertainty. We find that the rank exponent (RX) family generates the most efficient and robust weighs and works very well under different assumptions. Furthermore, It is stable under varying assumptions regarding the decision-makers' mindset and internal modeling. We also provide an example to show how the algorithm can be used in a decision-making context. It is exemplified with a problem of selecting strategies for combatting COVID-19.