This paper defines and characterizes the concept of an increase in inverse downside inequality and show that, when the Lorenz curves of two income distributions intersect, how the change from one distribution to the other is judged by an inequality index exhibiting inverse downside inequality aversion often depends on the relative strengths of its aversion to inverse downside inequality and inequality aversion. For the class of linear inequality indices, of which the Gini coefficient is a member, a measure characterizing the strength of an index’s aversion to inverse downside inequality against its own inequality aversion is shown to determine the ranking by the index of two distributions whose Lorenz curves cross once. The precise condition under which the same result generalizes to the case of multiple-crossing Lorenz curves is also identified.

本文定义并刻画了反向逆向不平等性增加的概念，并表明，当两个收入分配的劳伦兹曲线相交时，如何通过显示反向逆向不平等性厌恶的不平等指数来判断从一种分配向另一种分配的变化通常取决于它对逆向下行不平等和不平等厌恶的厌恶的相对优势。对于基尼系数为成员的一类线性不平等指数，显示了一种指标，该指标表征了指标相对于自身不平等厌恶的反向下反向不等式的强度，从而确定了两个分布的指数（其洛伦兹曲线），从而确定了排名交叉一次。还确定了将相同结果推广到多次交叉洛伦兹曲线的情况的精确条件。