Abstract
A relative invariant and an absolute invariant inequality ordering satisfying extreme bottom-sensitivity, are proposed. It is shown that the leximin social welfare ordering can be expressed in terms of a ranking of distributions on the sole basis of their size, measured by the mean, and the degree of inequality, measured according to these inequality concepts. Leximin thus exhibits extreme bottom-sensitivity. This property does not withstand that leximin prefers a larger size of the cake at the cost of higher inequality in a number of cases. These trade-offs between size and equality are characterised in terms of degrees of dominance of the lower parts of the ordinary and absolute Lorenz curves that are accepted by leximin for a given increase in the mean.
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Capéau, B. Size and distribution trade-offs for the leximin ordering. J Econ Inequal 11, 237–248 (2013). https://doi.org/10.1007/s10888-012-9219-2
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DOI: https://doi.org/10.1007/s10888-012-9219-2