Abstract
This paper examines the partial orderings of discrete distributions derived from various poverty indices and sets of welfare functions. The poverty ordering with respect to some indexP is the ordering obtained whenP ranks consistently over a range of admissible poverty lines. The poverty orderings derived from the headcount ratio, the per-capita income gap and another “distribution-sensitive” index are characterized in some detail when the poverty standard is allowed to take any positive value, and these orderings are shown to coincide with the natural interpretation of first, second and third degree “welfare dominance”, respectively. Additional results are then obtained for the situation in which the admissible poverty lines cannot exceed some finite upper bound.
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We are particularly indebted to Nick Kiefer for initial insights into the issues addressed in this paper. We have also had helpful comments from Amartya Sen, from an anomymous referee, and from many seminar audiences. Financial support from the Krannert Endowment Trust and the Leverhulme Trust is gratefully acknowledged.
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Foster, J.E., Shorrocks, A.F. Poverty orderings and welfare dominance. Soc Choice Welfare 5, 179–198 (1988). https://doi.org/10.1007/BF00735760
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DOI: https://doi.org/10.1007/BF00735760