Scoring from pairwise winning indices

The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another. They are computed taking into account all the instances of the assumed preference model compatible with the preference information provided by the Decision Maker mainly, but not exclusively, in terms of pairwise preference comparisons of reference alternatives. In this paper we present a new scoring method assigning a value to each alternative summarizing the results of the pairwise winning indices. Several procedures of this type have been provided in literature. However, our method, expressing the score in terms of a representative additive value function, permits to disaggregate the overall evaluation of each alternative in the sum of contributions of considered criteria. This permits not only to rank the alternatives but also to explain the reasons for which an alternative obtains its evaluation and, consequently, fills a certain ranking position. We also present a probabilistic model underlying our methodology. This probabilistic model is based on a simple piecewise linear approximation of the cumulative normal distribution, which allows the use of linear programming. To prove the efficiency of the method in representing the preferences of the Decision Maker, we performed an extensive set of simulations varying the number of alternatives and criteria. The results of the simulations, analyzed from a statistical point of view, prove the reliability of our procedure. The applicability of the method to decision making problems is explained by means of a case study related to the evaluation of financial funds.