This chapter discusses several applications of the REPOMP procedure (Randomized Expert Panel Opinion Marginalizing Procedure). It analyzes the subjective opinion of an expert panel in a multi-criteria decision making situation. It starts with an expert panel constructing a hierarchical structure of criteria to evaluate the alternatives. At a next stage, the same expert panel evaluates the relative weight of each criterion and the degree of compliance of each alternative with those criteria. Then a randomized procedure is applied to calculate the marginal indicator of each alternative and make the final ordering based on it. Additional simulation procedure is applied to analyze the distribution of that marginal indicator. The alternatives are also being allocated to indifference classes using hypothesis testing procedures. The analyzed examples refer to issues in environmental management, energy efficiency and spatial data infrastructures.