Abstract
This paper reviews and extends the theory of ethical inequality indices. It presents a novel axiom (strict separability of social welfare orderings in rank-ordered subspaces). This axiom allows to provide joint characterizations of the most important inequality measures (Atkinson family, Kolm-Pollak family and Generalized Ginis) and of some new more general classes of indices. The whole derivation is based on weak assumptions. In an ordinal framework only continuity of the underlying ordering is required and no cardinal properties are employed.
Similar content being viewed by others
References
Aczel J (1966) Lectures on functional equations and their applications. Academic Press, New York London
Atkinson AB (1970) On the measurement of inequality. J Econ Theory 2:244–263
Atkinson AB (1983) Social justice and public policy. MIT Press, Cambridge
Berrebi ZM, Silber J (1981) Weighting income ranks and levels. Econ Lett 7:391–397
Blackorby C, Donaldson D (1980) A theoretical treatment of indices of absolute inequality. Int Econ Rev 21:107–136
Blackorby C, Donaldson D (1982) Ratio-scale and translation-scale full interpersonal comparability without domain restrictions: admissible social-evaluation functions. Int Econ Rev 23:249–268
Blackorby C, Donaldson D (1984a) Social criteria for evaluating population change. J Publ Econ 25:13–33
Blackorby C, Donaldson D (1984b) Ethically significant ordinal indexes of relative inequality. In: Rhodes G, Basmann R (eds) Advances in econometrics. Vol. III, JAI Press, Greenwich, pp 131–147
Blackorby C, Donaldson D, Auersperg M (1981) Inequality within and among population subgroups: ethically consistent subindices. Can J Econ 14:665–685
Bourguignon F (1979) Decomposable income inequality measures. Econometrica 47:901–920
Cowell FA (1980) On the structure of additive inequality measures. Rev Econ Stud 47:521–531
Cowell FA, Kuga K (1981a) Inequality measurement. An axiomatic approach. E Econ Rev 15:287–305
Cowell FA, Kuga K (1981b) Additivity and the entropy concept: An axiomatic approach to inequality measurement. J Econ Theory 25:131–143
Dasgupta P, Sen S, Starrett D (1973) Notes on the measurement of inequality. J Econ Theory 6: 180–187
Donaldson D, Weymark JA (1980) A single-parameter generalization of the Gini indices of inequality. J Econ Theory 22:67–86
Ebert U (1984) Measures of distance between income distributions. J Econ Theory 32:266–274
Ebert U (1987) Size and distribution of incomes as determinants of social welfare. J Econ Theory 41:23–33
Ebert U (1988a) On the decomposition of inequality: partitions into nonoverlapping subgroups. In: Eichhorn W (ed) Measurement in economics. Physica, Heidelberg, pp 399–412
Ebert U (1988b) A family of aggregative compromise inequality measures. Int Econ Rev (forthcoming)
Eichhorn W (1978) Functional equations in economics. Addision-Wesley, Reading
Fishburn PC (1970) Utility theory for decision making. John Wiley, New York
Foster JE (1983) An axiomatic characterization of the Theil measure of income inequality. J Econ Theory 31:105–121
Gehrig W (1983) Two characterizations of Theil's concentration measure. Paper presented at ESEM 83, Pisa
Kolm SC (1969) The optimal production of social justice. In: Margolis J, Guitton H (eds) Public economics. Macmillan, London, pp 145–200
Kolm SC (1976a) Unequal inequalities I. J Econ Theory 12:416–442
Kolm SC (1976b) Unequal inequalities II. J Econ Theory 13:82–111
Marshall AW, Olkin I (1979) Inequalities: Theory of majorization and its applications. Academic Press, New York
Mehran F (1976) Linear measures of income inequality. Econometrica 44:805–809
Roberts KWS (1980) Interpersonal comparability and social choice theory. Rev Econ Studies 47: 421–439
Russell RR (1985) A note on decomposable inequality measures. Rev Econ Stud 52:347–352
Sen A (1973) On economic inequality. Clarendon Press, Oxford
Sen A (1974) Informational bases of alternative welfare approaches. J Publ Econ 3:387–403
Shorrocks AF (1980) The class of additively decomposable inequality measures. Econometrica 48: 613–625
Shorrocks AF (1984) Inequality decomposition by population subgroups. Econometrica 52:1369–1385
Thon D (1982) An axiomatization of the Gini coefficient. Math Soc Sci 2:131–143
Weymark JA (1981) Generalized Gini inequality indices. Math Soc Sci 1:409–430
Yaari M (1986) A controversial proposal concerning inequality measurement. Research Memorandum No. 73, Hebrew University, Jerusalem
Yitzhaki S (1983) On an extension of the Gini inequality index. Int Econ Rev 24:615–628
Author information
Authors and Affiliations
Additional information
I thank two anonymous referees for helpful comments and suggestions.
Rights and permissions
About this article
Cite this article
Ebert, U. Measurement of inequality: An attempt at unification and generalization. Soc Choice Welfare 5, 147–169 (1988). https://doi.org/10.1007/BF00735758
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00735758