An axiomatization of the single-series Ginis

Abstract In this paper, characterizations of the single-series Gini social evaluation functions and their illfare-ranked counterparts, functions introduced and discussed by Donaldson and Weymark [10] and Weymark [19], are provided. It is shown that the single-series Ginis (resp. illfare-ranked single-series Ginis) are the only sequences of social evaluation functions allowing for the derivation of both relative and absolute ethical inequality measures which satisfy a high income (resp. low income) group aggregation property. In the case of the illfare-ranked single-series Ginis, the aggregation condition is important for the construction of ethical indices of poverty.

[1]  S. Kolm.  The Optimal Production of Social Justice , 1969 .

[2]  M. Rothschild,et al.  Some further results on the measurement of inequality , 1973 .

[3]  David Donaldson,et al.  Ethical Indices for the Measurement of Poverty , 1980 .

[4]  Serge-Christophe Kolm.  Unequal inequalities. I , 1976 .

[5]  H. Dalton.  The Measurement of the Inequality of Incomes , 1920 .

[6]  A. Sen,et al.  Notes on the measurement of inequality , 1973 .

[7]  Andreas Pfingsten,et al.  Progressive taxation and redistributive taxation: Different labels for the same product? , 1988 .

[8]  D. Primont,et al.  Duality, Separability, and Functional Structure: Theory and Economic Applications , 1978 .

[9]  M. Yaari,et al.  A controversial proposal concerning inequality measurement , 1988 .

[10]  A. Atkinson.  On the measurement of inequality , 1970 .

[11]  U. Ebert.  Measurement of Inequality: An Attempt at Unification and Generalization , 1988 .

[12]  John A. Weymark,et al.  GENERALIZED GIN 1 INEQUALITY INDICES , 2001 .

[13]  Charles Blackorby,et al.  Measures of relative equality and their meaning in terms of social welfare , 1978 .

[14]  Charles Blackorby,et al.  A Theoretical Treatment of Indices of Absolute Inequality , 1980 .

[15]  A. Sen.  On Economic Inequality , 1974 .

[16]  John A. Weymark,et al.  A single-parameter generalization of the Gini indices of inequality , 1980 .

[17]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .