We consider a multicriteria decision analysis (MCDA) problem where importance of criteria, and evaluations of alternatives with respect to the criteria, are expressed on a qualitative ordinal scale. Using the extreme-point principle of Data Envelopment Analysis (DEA), we develop a two-parameter method for obtaining overall ratings of the alternatives when preferences and evaluations are made on an ordinal scale. We assume no parametric setup other than the two parameters that reflect minimum intensities of discriminating among rank positions: one parameter for the alternatives’ ranking and one for the criteria ranking. These parameters are bounded by the ordinal input data, and they imply a universal tie among the alternatives when both parameters are selected to be zero. We describe the model, discuss its theoretical underpinning, and demonstrate its application.