Abstract. The paper focuses on the problem of parametric description of a decision-making situation of nonparametric type, i.e., where it is impossible to reveal the objective parameter determining the consequences of decisions. For the case of strict uncertainty, the classes of matrix schemes containing those and only those schemes that can be used to model certain nonparametric situation are described and the formula for class cardinality is proved. The cases are established where there are grounds to choose the matrix scheme with the smallest, in its class, cardinality of values of the set of the parameter.

Keywords: strict uncertainty, decision making, lottery scheme, matrix scheme, parameterization.