New perspectives on the Gini and Bonferroni indices of inequality

This paper rigorously demonstrates that for any unequal income distribution, the well-known Gini index of inequality is bounded above by recently revived Bonferroni index. The bound exactly attained if and only out n incomes in society, − 1 poor are identical. boundedness theorem shown to possess a duality-type implication. These two metrics, popular members general class indices generated Aaberge’s (J Econ Inequal 5:305–322, 2007) ‘scaled conditional mean curve’, may lead different directional rankings alternative distributions because some important differences between them. We then explicitly examine their sensitivity Weymark’s (Math Soc Sci 1:409–430, 1981) ‘comonotonic additivity’ postulate.