Events and Meetings of Italian Statistical Society, Statistics and Demography: the Legacy of Corrado Gini

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Another look on the generalized Gini social welfare functions
Brice Magdalou

Last modified: 2015-09-05


We propose in the paper an alternative approach to inequality and welfare measurement which exploits the flexibility of the dual model of choice under risk of M. Yaari (Econometrica 55 (1987), 99–115), also known in normative economics as the generalized Gini social welfare function. Typical welfare and inequality measurement is required to be Lorenz consistent which guarantees that inequality decreases and welfare increases as a result of a progressive transfer. We challenge this conventional practice by substituting the weaker differentials, deprivation and contentment (absolute) quasi-orderings for the Lorenz criterion. For each of these alternative criteria, we identify the elementary transformations – analogous to progressive transfers in the traditional approach – that allow one to derive in a finite number of steps the dominating distribution from the dominated one. Restricting attention to distributions of equal means we identify the restrictions to be placed, within the Yaari model, on the weighting function which guarantee that the corresponding welfare orderings are consistent with these quasi-orderings. We then drop the equal mean condition and indicate the implications of our approach for the ethical inequality indices. Finally, a comparaison of real income distributions at an international level, with statistical inference, is provided in order to illustrate our criteria. 

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