We examine some ordinal measures of inequality that are familiar from the literature. These measures have a quite simple structure in that their values are determined by combinations of specific summary statistics such as the extreme values and the arithmetic mean of a distribution. In spite of their common appearance, there seem to be no axiomatizations available so far, and this paper is intended to fill that gap. In particular, we consider the absolute and relative variants of the range, the max-mean and the mean-min orderings, and quantile-based measures. In addition, we provide some empirical observations that are intended to illustrate that, although these orderings are straightforward to define, some of them display a surprisingly high correlation with alternative (more complex) measures.

中文翻译：

---

极值、均值和不等式测量

我们研究了文献中熟悉的一些不平等的有序度量。这些度量具有非常简单的结构，因为它们的值由特定汇总统计量的组合确定，例如分布的极值和算术平均值。尽管它们看起来很常见，但到目前为止似乎没有可用的公理化，本文旨在填补这一空白。特别是，我们考虑了范围的绝对和相对变体、最大均值和均值最小排序以及基于分位数的度量。此外，我们提供了一些经验观察，旨在说明，尽管这些排序很容易定义，但其中一些显示出与替代（更复杂）度量的惊人高相关性。