Gini Coefficient, explained.
The Gini coefficient measures relative inequality in a distribution using pairwise differences or the gap between its Lorenz curve and equal shares.
Why it happens
Scaling everyone’s holdings by the same positive factor leaves relative inequality unchanged. Moving a fixed total toward one holder increases pairwise differences, but does not by itself say whether anyone has enough.
The Gini coefficient summarizes relative inequality in a nonnegative distribution, rather than its total wealth or fairness.
Read the result
Shift the top holder’s share and inspect both Gini and the Lorenz curve. The total remains one hundred. For five holders, this uncorrected population calculation reaches 0.8 when one person owns everything.
A worked example
A fixed pool with unequal shares
With a top share of sixty, the other four each receive ten.
The Lorenz curve accumulates the lowest holdings first: forty tokens are held by the bottom 80% of people.
The population Gini is 0.4; doubling every holding would preserve it while changing average resources.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
The top holder receives the selected share; the other four split the remainder equally. Pairwise absolute differences produce the uncorrected population Gini. The maximum for five holders is 0.8.
Where this idea is useful
A practical use
Two communities can have the same inequality coefficient and very different average incomes.
A common misconception
“Gini is a complete measure of fairness or poverty.”
It describes relative distribution, not needs, living standards, opportunities or the justice of a particular allocation.
What this explanation leaves out
- Five invented holders are not a survey. Gini alone does not describe needs, poverty, justice or the full distribution.
Why does the maximum here stop below one?
In a finite five-person population, the uncorrected pairwise formula’s maximum is (5−1)/5. Other conventions can apply finite-sample adjustments.
Which facts about a distribution would you need in addition to its inequality index?
Further reading
Explore the original research or the teaching reference behind this experiment.