From Unidimensional to Multidimensional Inequality, Welfare and Poverty Measurement

In this handout we review results concerning representation of partial orders via stochastic orders and investigate their applications to some classes of stochastic dominance conditions applied in inequality, poverty and welfare measurement. The results obtained in an unidimensional framework are extended to multidimensional analysis. In particular we provide an overview of the main issues concerning aggregation of multidimensional distributions into synthetic indicators as the Human Development Index or Social Welfare Functions. Moreover we explore the potential for multidimensional evaluations based on the partial orders induced by different criteria of majorization. The lecture is divided into 4 parts: (i) an introduction to basic results concerning unidimensional evaluations of inequality, welfare and poverty (ii) an illustration of the problems of aggregation of evaluations when applied in the multidimensional context where individuals exhibit various attributes, (iii) the discussion of the potentials and limits of the application of generalizations of the majorization approach to comparisons of multidimensional distributions (iv) a brief overview of some results on multidimensional stochastic orders. ∗Claudio Zoli, Dipartimento di Scienze Economiche, Università di Verona, Viale dell’Università 4, 37129-Verona, Italy. E-MAIL: [email protected]