Zoli C. (2000). Inverse sequential stochastic dominance: rank-dependent welfare, deprivation and poverty measurement. University of Nottingham, Discussion Papers No. 00/11

We provide characterisations of sequential stochastic dominance conditions which are dual to those introduced in Atkinson and Bourguignon (1987). Instead of evaluating social welfare according to the utilitarian approach, we apply the dual approach to the measurement of welfare and inequality suggested in Weimar (1981) and Yaari (1987,1988). Different interpretations of the results, in terms of either welfare comparisons of populations decomposed into needs-based subgroups, or inter temporal income comparisons are suggested.
The dual SWF is shown to be consistent with a class of satisfaction and deprivation indices. The sequential dominance criteria based on this class of indices is introduced, they require comparisons involving generalized satisfaction curves and deprivation curves of the reference groups in the population. The connections with dominance criteria associated to rank-dependent poverty indices and the sequential dominance results introduced is investigated.