  The pairwise winning indices, computed in the Stochastic Multicriteria
Acceptability Analysis, give the probability with which an alternative is
preferred to another taking into account all the instances of the assumed
preference model compatible with the information provided by the Decision Maker
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
assigning a score to each alternative on the basis of the pairwise winning
indices have been provided in literature. However, while all of them compute
this score just to rank the alternatives under consideration, our method,
expressing the score in terms of an additive value function, permits to
disaggregate the overall evaluation of each alternative in the sum of
contributions of considered criteria. This will permit 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. 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, show the goodness 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.
