Gini Index

In doing some tests on the Gini index, the results reveal some serious flaws in its ability to describe income inequality. Let's set up five income groups with incomes of 10, 25, 50, 100, 200. When equal portions are in each group, the Gini index for this population is .473. When the population is moved to intentionally produce greater inequality, say by taking everyone from the middle group (50) and distributing them equally to the extremes (10 and 200), the Gini index doesn't move much; it's now .488. And when the population is moved entirely to the 2 extremes: 50% each to both the 10 and 200 cohort, the index drops to .452. This is odd, given that this is the most extreme inequality possible with this cohort setup - half in the richest group, half in the poorest.

Moving people from the 200 cohort to the 10 cohort raises the Gini index, but doing the reverse actually lowers it. At 30% in the 10 and 70% in the 200, the Gini is .279. Vice versa, it's .596. But the total income difference is identical in both cases. The difference is the mean which is the denominator. And when the mean is highly unrepresentative of a large portion of the population, the index produces absurd results. This is likely a potential problem with any inequality measure which is normalized by a mean.