Multidimensional Lorenz dominance: A definition and an example

This paper seeks to extend the unidimensional notion of Lorenz dominance to the multidimensional context. It formulates a definition of a multidimensional Lorenz dominance relation (MLDR) on the set of alternative distributions of well-being in an economy by incorporating generalizations of the well-known Pigou-Dalton condition of unidimensional theory. Besides the definitional requirements, an MLDR is also desired to satisfy two other conditions which seem to be intuitively reasonable. The paper notes that the existing literature does not seem to contain an example of an MLDR with these characteristics and seeks to close this gap.