A probabilistic dominance measure for binary choices: Analytic aspects of a multi-attribute random weights model (Q1114632)

The following quotations from the authors' abstract give a good notion of the article: This paper examines a probabilistic dominance measure to assess the extent to which a given multi-attribute alternative might be preferred over another. It determines analytically the probability of choosing the first alternative (of a given pair) when using an additive utility function with uniformly random weights. Two uniform random weight models are examined. In one, the weights (i.e. scalar coefficients) of the additive utility function are each uniformly distributed on [0,1] prior to being rescaled to sum up to one. In the other, the weight vector \(\tilde w=(\tilde w_ 1,...,\tilde w_ n)\) is presumed to be uniformly distributed on the simplex defined by \(\sum w_ i=1\) and \(w_ i\geq 0\) for all i.... The analytic results are demonstrated numerically with four dimensions, using data from a college admission's experiment. Various applications of this particular measure for probabilistic dominance are examined. The concluding sections assess to what extent our measure satisfies weak stochastic transitivity and other important characteristics.