This paper discusses inequality orderings based explicitly on closing up of income gaps, demonstrating the links between these and other orderings, the classes of functions preserving the orderings and applications showing their usefulness in comparison of economic policies.
Preston, I. (2007), "Inequality and Income Gaps", Lambert, P.J. (Ed.) Equity (Research on Economic Inequality, Vol. 15), Emerald Group Publishing Limited, Bingley, pp. 33-56. https://doi.org/10.1016/S1049-2585(07)15003-1
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