Ranking distributions of monotone attributes

Abstract

This paper refers to the ranking of densities that describe the distribution of an attribute in a given set of populations. The key elements of the problem are: (i) The distributions refer to ordered categorical data (e.g. health statuses, educational achievements, prestige positions, satisfaction levels); (ii) The evaluation of each distribution is relative to the others with which it is compared. We propose an evaluation method that is cardinal, complete and transitive, which based on the consistent application of the "willingness to pay" principle and the likelihood of getting better results when making a random extraction. A characterization of this method, in terms of simple properties, is provided.