Multidimensional Lorenz Dominance

In this chapter, we begin to take cognisance of the multidimensional nature of development. However, we approach the matter in steps. Since we desire an inequality-sensitive measureMeasures of development, we first consider the problem of how to measureMeasures multidimensional inequality. This is the subject matter of this chapter. As in the unidimensional case, here again, inequality can be measured in various ways. Again, however, there is no guarantee that if inequality as measured by a particular multidimensional inequality indexMultidimensional inequality index is seen to decrease, the same will be true of inequality measured by a different index. This suggests that a more appropriate procedure would be to look for a way to extend the concept of Lorenz dominance from the unidimensional context to the multidimensional one. The chapter starts by stating a number of conditions or properties that one would intuitively expect any notion of multidimensional Lorenz dominanceMultidimensional Lorenz dominance to satisfy and using these conditions to formulate a definition of a multidimensional Lorenz dominanceMultidimensional Lorenz dominance relation. It then examines a number of “candidate” relations that have been proposed in the literature and shows that all of these fail to satisfy the definition formulated here. The question, therefore, arises as to whether there exists a Lorenz dominance relation as defined here. The chapter gives an affirmative answer to the question.