We introduce the concept of a representative set of parameters for multiple criteria outranking methods: ELECTREGKMS and PROMETHEEGKS which apply the principle of robust ordinal regression. We exploit the necessary and the possible results provided by these methods to choose a single instance of the preference model, which would represent all other compatible instances. The representative set of parameters is selected within an interactive preference-driven procedure which allows combining some pre-defined targets into different scenarios. Each target concerns enhancement of the results of robust ordinal regression. Precisely, the DM may emphasize either the advantage of some alternatives over the others, acknowledged by all compatible outranking models, or ambiguity in the comparison for some other pairs of alternatives. Selecting the representative set of parameters, we satisfy the desire of some DMs of assigning precise values to variables of the model. We also enable exploitation of the outranking relation for these parameters in order to arrive at a representative recommendation in a traditional way.