Size and distribution trade-offs for the leximin ordering

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.