Multidimensional Inequality-Sensitive Development Ranking

This chapter starts by stating a number of properties that any multidimensional development indexDevelopment index may be intuitively expected to satisfy. It then investigates whether (or under what conditions) we can rank any pair of economies X and Y unambiguously in terms of their levels of development, i.e. whether we can check the veracity of the statement that X is at least as developed as Y as per all development indices having the desired properties. It turns out that, as in the unidimensional case, here too there would be some grey areas of non-comparability. However, the notion of fuzzy binary elations can again be used to formulate fuzzy versions of the proposed conditions on the development indexDevelopment index and to obtain fuzzy rankings of economies. These, in turn, can be utilised to obtain crisp (i.e. non-fuzzy) development ranking rules that would reduce these grey areas. An appendix shows that the development ranking method proposed in the chapter can be used to formulate a unifying approach to the problem of obtaining multidimensional versions of various specific unidimensional inequality indices. In the existing literature the multidimensional versions of different unidimensional indices have been characterised by different sets of conditions with no apparent linkage between them. This appendix uses a procedure for obtaining vector representations of distribution matricesDistribution matrix to suggest a simple procedure for the task under consideration.