SanchezPerez, Joss and PlataPerez, Leobardo and SanchezSanchez, Francisco (2012): An elementary characterization of the Gini index.

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Abstract
The Gini coefficient or index is perhaps one of the most used indicators of social and economic conditions. In this paper we characterize the Gini index as the unique function that satisfies the properties of scale invariance, symmetry, proportionality and convexity in similar rankings. Furthermore, we discuss a simpler way to compute it.
Item Type:  MPRA Paper 

Original Title:  An elementary characterization of the Gini index 
Language:  English 
Keywords:  Gini index, income inequality, axiomatization 
Subjects:  D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement D  Microeconomics > D3  Distribution > D31  Personal Income, Wealth, and Their Distributions I  Health, Education, and Welfare > I3  Welfare and Poverty > I31  General Welfare 
Item ID:  36328 
Depositing User:  Joss Erick SanchezPerez 
Date Deposited:  09. Feb 2012 09:34 
Last Modified:  13. Feb 2013 11:14 
References:  [1] Aaberge, R. (2001) “Axiomatization Characterization of the Gini Coefficient and Lorenz Curve Orderings”, Journal of Economic Theory, Vol. 101, pp. 115132. [2] Atkinson, A.B. (1970) “On Mesurement of Inequality”, Journal of Economic Theory, Vol. 2, pp. 244263. [3] Blackorby, Ch. and D. Donaldson (1978) “Measures of relative equality and their meaning in terms of social welfare”, Journal of Economic Theory, Vol. 18, pp. 5980. [4] Blackorby, Ch. and D. Donaldson (1980) “A theoretical treatment of índices of absolute inequality”, International Economic Review, Vol. 21, pp. 107136. [5] Blackorby, Ch. and Donaldson (1984) “Ethical significant ordinal indexes of relative inequality”, in R. Basmann and G. Rhodes, eds. Advances in Econimetrics, Vol. 3 (JAI Press Greenwich), pp. 131147. [6] Bossert (1990) “An axiomatization of the singleseries Ginis”, Journal of Economic Theory, Vol. 50, pp. 8292. [7] Dalton,H. (1920) “The Mesurement of the Inequality of Income”, Economic Journal, Vol. 30, pp. 348361. [8] Donaldson, D. and J.A. Weymark (1980) “A singleparameter generalization of the Gini indices of inequality” Journal of Economic Theory, Vol. 22, pp. 6786. [9] Dutta, B. (2002) “Inequality, Poverty andWelfare” in Arrow K., A Sen and K. Suzumura (editors), Handbook of Social Choice and Welfare Vol. 1, pp. 597633. [10] Dutta, B. and J. Esteban (1992) “Social welfare and equality”, Social Choice and Welfare, Vol. 9, pp. 267276. [11] Ebert, U. (1987) “Size and distribution of incomes as determinants of social welfare”, Journal of Economic Theory, Vol. 41, pp. 2333. [12] Foster, J., Greer J. and Thorbecke E. (1984) “A class of decomposable poverty measures”. Econometrica, Vol 52 (3), pp. 761—766. [13] Foster, J. and Sen A. (1997) “On economic inequality”, Oxford University Press. [14] Gini, C. (1912) Italian: “Variabilità e mutabilità” (Variability and Mutability), C. Cuppini, Bologna, 156 pages. [15] Kakwani N.C. (1980) “Income Inequality and Poverty”, Oxford University Press, New York. [16] Mehran F. (1976) “Linear measures of income inequality”, Econometrica, Vol. 44, pp. 805809. [17] Pyatt G. (1976) “On the interpretation of disaggregation of Gini coefficients”, Economic Journal, Vol. 86, pp. 243255. [18] Sen, Amartya (1973) “On Economic Inequality”, Clarendon Press, Oxford. First Edition. [19] Thon, Dominique (1982) “An axiomatization of the Gini Coefficcient”, Mathematical Social Sciences, Vol. 2, pp. 131143. [20] Weymark, J.A. (1981) “Generalized Gini Inequality Indices”, Mathemathical Social Sciences, Vol 1, pp. 409430. [21] Yitzhaki, S. (1983) “On the extension of the Gini inequality index”, International Economic Review, Vol. 24, pp. 617628. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/36328 