Ratings without compensations and their application

Basing on the explicit formula for the enumerating preference function, representing the threshold rule (leximin) for the comparison of alternatives, the paper introduces two rating indices such that one of them takes into account weights and the other one does not. In situations when compensations are not involved (i.e., bad properties of alternatives cannot be compensated by their good properties) the indices express quantitative as well as qualitative exponents. The example of application of indices for rating scholars, whose progress in their studies is characterized by vector grades of high dimension with integer components in given.