  Classical measures of inequality use the mean as the benchmark of economic
dispersion. They are not sensitive to inequality at the left tail of the
distribution, where it would matter most. This paper presents a new inequality
measurement tool that gives more weight to inequality at the lower end of the
distribution, it is based on the comparison of all value pairs and synthesizes
the dispersion of the whole distribution. The differences that sum to the Gini
coefficient are scaled by angular differences between observations. The
resulting index possesses a set of desirable properties, including
normalization, scale invariance, population invariance, transfer sensitivity,
and weak decomposability.
