Social Welfare, Inequality and Deprivation *

We provide a characterization of the generalised satisfaction -- in our terminology non-deprivation -- quasi-ordering introduced by S.R. Chakravarty (Keio Economic Studies 34 (1997), 17--32) for making welfare comparisons based on the absence of deprivation. We show that the non-deprivation quasi-ordering obeys a weaker version of the principle of transfers: welfare improves only for specific combinations of progressive transfers which require that the same amount be taken from richer individuals and allocated to one arbitrary poorer individual. We identify the subclass of extended Gini social welfare functions that are consistent with this principle and we show that the unanimity of value judgements among this class is identical to the ranking of distributions implied by the non-deprivation quasi-ordering. We extend the approach to the measurement of inequality by considering the corresponding relative and absolute ethical inequality indices.

[1]  C. Beach,et al.  Statistical inference for decile means , 1994 .

[2]  H. Ury,et al.  Tables of the Studentized Maximum Modulus Distribution and an Application to Multiple Comparisons Among Means , 1979 .

[3]  Walter Bossert,et al.  Income Inequality Measurement: The Normative Approach , 1999 .

[4]  John A. Bishop,et al.  Tests of Significance for Lorenz Partial Orders , 1999 .

[5]  Calyampudi R. Rao,et al.  Linear statistical inference and its applications , 1965 .

[6]  Shlomo Yitzhaki,et al.  Relative Deprivation and the Gini Coefficient , 1979 .

[7]  J. Malfait,et al.  Séquestration des flux de carbone forestier : Mise en place d'un projet d'additionnalité des usages du bois dans la construction , 2007 .

[8]  P. Moyes.  A new concept of Lorenz domination , 1987 .

[9]  J. Saracco,et al.  Conditional Spatial Quantile: Characterization and Nonparametric Estimation , 2008 .

[10]  Javier Ruiz-Castillo Ucelay,et al.  Searching by questionnaire for the meaning of income inequality , 1993 .

[11]  Claudio Zoli.  Inverse stochastic dominance, inequality measurement and Gini indices , 2002 .

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

[13]  Matthieu Clément,et al.  Economic Growth, inequality and environment quality: An empirical analysis applied to developing and transition countries , 2008 .

[14]  J. Quiggin.  Generalized expected utility theory : the rank-dependent model , 1994 .

[15]  Jacques Silber,et al.  Income Inequality Indices and Deprivation: A Generalization , 1985 .

[16]  Joseph L. Gastwirth,et al.  A General Definition of the Lorenz Curve , 1971 .

[17]  C. Fershtman,et al.  Social Status and Economic Performance: A Survey , 1998 .

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

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

[20]  Testing for second order stochastic dominance , 1985 .

[21]  Frank A. Cowell,et al.  Thinking about Inequality , 1999 .

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

[23]  S. Chakravarty,et al.  INCOME INEQUALITY AND RELATIVE DEPRIVATION , 1995 .

[24]  Eric Rougier,et al.  Recent exports matter: export discoveries, FDI and Growth, an empirical assessment for MENA countries , 2008 .

[25]  Serge-Christophe Kolm,et al.  Unequal inequalities. I , 1976 .

[26]  P. Moyes.  Stochastic Dominance and the Lorenz Curve , 1999 .

[27]  W. Runciman.  Relative Deprivation and Social Justice , 1966 .

[28]  F. Cowell,et al.  Inequality: Measurement , 2006 .

[29]  Frank A. Cowell,et al.  Measurement of income inequality: Experimental test by questionnaire , 1992 .

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

[31]  D. Champernowne,et al.  On Economic Inequality. , 1974 .

[32]  N. Kakwani.  On a Class of Poverty Measures , 1980 .

[33]  M. Yaari.  The Dual Theory of Choice under Risk , 1987 .

[34]  S. Chakravarty.  RELATIVE DEPRIVATION AND SATISFACTION ORDERINGS , 1997 .

[35]  James E. Foster,et al.  Poverty orderings and welfare dominance , 1988 .

[36]  Udo Edbert,et al.  Social Welfare when Needs Differ: An Axiomatic Approach , 1997 .

[37]  The Relative Deprivation Curve and Its Applications , 1984 .

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

[39]  U. Ebert,et al.  An axiomatic characterization of Yitzhaki’s index of individual deprivation , 2000 .

[40]  J. Malfait,et al.  Séquestration des flux de carbone forestier: Rotations des peuplements, prise en compte des produits bois et optimisation des stocks de carbone , 2007 .

[41]  A. Shorrocks.  Ranking Income Distributions , 1983 .

[42]  P. Thistle,et al.  Rank dominance and international comparisons of income distributions , 1991 .

[43]  Alain Chateauneuf,et al.  Measuring inequality without the Pigou-Dalton condition , 2005 .

[44]  C. Seidl,et al.  Perceptional inequality and preferential judgements: An empirical examination of distributional axioms , 1994 .

[45]  J. Quiggin.  Generalized expected utility theory , 1992 .

[46]  John D. Hey,et al.  Relative Deprivation and the Gini Coefficient: Comment , 1980 .

[47]  S. Chakravarty,et al.  Measures of Deprivation and their Meaning in Terms of Social Satisfaction , 1999 .

[48]  Wulf Gaertner,et al.  Income inequality, risk, and the transfer principle: A questionnaire-experimental investigation , 2003, Math. Soc. Sci..