Poverty Orderings

This paper reviews the literature of partial poverty orderings. Partial poverty orderings require unanimous poverty rankings for a class of poverty measures or a set of poverty lines. The need to consider multiple poverty measures and multiple poverty lines arises inevitably from the arbitrariness inherent in poverty comparisons. In the paper, we first survey the ordering conditions of various individual poverty measures for a range of poverty lines; for some measures necessary and sufficient conditions are identified while for others only some easily verifiable sufficient conditions are established. These ordering conditions are shown to have a close link with the stochastic dominance relations which are based on the comparisons of cumulative distribution functions. We then survey the ordering conditions for various classes of poverty measures with a single or a set of poverty lines; in all cases necessary and sufficient conditions are established. These conditions again rely on the stochastic dominance relations or their transformations. We also extend the relationship between poverty orderings and stochastic dominance to higher orders and explore the possibility and the conditions of increasing the power of poverty orderings beyond the second degree dominance condition. It will be desirable, ..., not to rely upon the evidence of a single measure, but upon the corroboration of several. (Hugh Dalton, 1920)