Giving Gini direction: An asymmetry metric for economic disadvantage

- Agendas for inequality are usually concerned with too many people on low incomes.
- A new metric, the entropic v, reflects distributional aspirations as seen by the subjects.
- The entropic v utilises the double smoothing property of left and right entropic shifts.
- The entropic v can be given a dollar redistribution dimension and is straightforward to compute.
- In conjunction with the Gini coefficient it can summarise both dispersion and skewness.

A high Gini coefficient could signal either dispersion or else skewness, often of more social concern. Supplementary metrics such as the Atkinson index diagnose the asymmetry with preassigned parameters that reflect user social values. An alternative is proposed that reflects redistribution aspirations as they might be seen by the subjects themselves. The resulting v-metric has a dollar redistribution dimension. The metric, essentially a form of double averaging, can be simplified in terms of means of the left and right entropic distribution shifts, with the partition entropy reflecting implied partition into incomes above or incomes below.