One number for how unequally a pie is shared. Sort a population poorest to richest, plot the cumulative share of income they hold against their cumulative share of the population — that sagging curve is the Lorenz curve. The gap between it and the line of perfect equality, doubled, is G: 0 when everyone is identical, approaching 1 when one person holds everything. Down the center, data flows: a distribution goes in, the engine builds the Lorenz curve, the index comes out. This is a descriptive statistic of a distribution — not financial or investment advice.
source · AMBER Gini, C. (1912) Variabilità e mutabilità, Bologna (Tipografia di Paolo Cuppini) — the Gini index. The 1912 Italian monograph has no stable open link; English extracts in Ceriani & Verme, J. Economic Inequality 10:421 (2012). Rendered, not quoted.
Line up everyone poorest-first. Walk along the population axis x from 0 to 1; at each point read off L(x), the fraction of all income held by the poorest x. That is the Lorenz curve — it starts at (0,0), ends at (1,1), and sags below the 45° equality line.
The index is the gap, doubled:
G = 2 × area(between equality line and Lorenz) = 1 − 2∫L(x)dx
Current distribution, cumulative shares (population % → income %):
| pop ≤ | income share |
|---|
Corrado Gini gave the gap a single number in 1912. It became the standard scalar behind every distributional debate: G = twice the Lorenz-curve area, 0 at equality, 1 at total concentration, and — by the Pigou–Dalton principle — rising whenever income moves from poorer to richer.
Next door in THE FOLD, the justice register (LILLITH · Lady Justice) argues over what a fair gap is; this sphere only measures it. Each sphere is the next one's premise: you cannot debate the gap until you can compute it.
The blue team's live check: recompute G on the known cases — equality → 0, the sample [1,2,3,4] → 0.25, one-has-all(1000) → 0.999 — and confirm the [0,1] range. If red tampers, this badge is where it shows.
The input is a list of incomes across a population — nothing more. The engine sorts it, forms the running total, and normalises so the poorest 0% hold 0% and the whole population holds 100%.
| n | min | mean | max |
|---|---|---|---|
| — | — | — | — |
Any non-negative list works: incomes, wealth, land, citations. G only asks how spread out it is — never how large.
Incomes are generated as xᵢ = iα. α=0 makes everyone identical (G=0); larger α steepens the curve. Move any control — G is recomputed from the Lorenz area on the spot, never looked up.
What the machine produces, proven for every distribution: G = 1 − 2∫L lies in [0,1]; perfect equality gives G = 0 (to 1e−9); one-has-all gives (n−1)/n → 1; the Lorenz curve is convex, below the diagonal, from (0,0) to (1,1); and a poor→rich transfer raises G (Pigou–Dalton). Cross-checked against the mean-absolute-difference form Σ|xᵢ−x⫺|/(2n²μ).
Inequality bands (low/moderate/high) are conventional reading aids AMBER — not thresholds of law, and not investment advice.
Assumptions AMBER: a well-defined population and a single income measure; a snapshot, not lifetime; income ≠ wealth (wealth Ginis run far higher); ceteris paribus. This is a descriptive statistic — "law"-like only as an identity about areas, not a claim about the world. Economics is not physics.
"A higher Gini means a poorer country." Cut. G measures dispersion, not level — scaling every income by 10 leaves G unchanged. Rich and poor countries can share a Gini.
"Gini fully describes inequality." Cut. It collapses a curve to a point; distributions with crossing Lorenz curves get equal G. Report the curve, not only the number.
"You can compare any two Ginis directly." Kept, corrected. Only within the same base — income vs consumption vs wealth Ginis are not interchangeable; state which you mean.
The red team's move: quietly drop the factor of 2 — compute G from the area above the whole Lorenz curve instead of twice the gap. Perfect equality would no longer read 0. The blue team's witness (window 7) is watching.
Drop the doubling and equality gives G=0.5, not 0 — the [0,1] anchor breaks. The witness recomputes, disagrees with the known values, and turns red. Nothing is faked; the attack is real and it is caught.