Stochastic dominance relations for integer variables (Q435897)

Stochastic dominance analysis is frequently employed for ranking alternative social states. In many applications the sum of the scores need not be constant. The objective of this paper is to extend the integer-majorization analysis to the case of variable-sum vectors.NEWLINENEWLINEThe most innovative feature of this article is the demonstration that if one profile of functioning scores integer-generalized Lorenz dominates another, then the former can be obtained from the latter by a sequence of transformations satisfying monotonicity and non-increasingness of marginal social evaluations, where monotonicity demands that if the functioning score of a person increases by one, then the resulting profile of scores cannot have a lower social evaluation than the original one.NEWLINENEWLINEAnother innovative aspect is the determination of the minimal number of transformations that are necessary to move from one distribution to another, where the latter integer-generalized Lorenz dominates the former.NEWLINENEWLINEThe authors use an axiomatic framework to establish equivalence between several intuitively reasonable conditions.