Pareto's "80/20" is one point on a curve, not a constant of nature. Pin any top fraction to its share and the whole shape of inequality falls out: the Pareto exponentA Pareto power law: the survival function decays as a power of x, S(x) = (x_min / x)^α. The smaller α, the heavier the tail and the more concentrated the top. α, the GiniThe Gini coefficient: 0 is perfect equality (everyone has the same), 1 is total concentration (one person has it all). Under Pareto it's just 1/(2α−1)., how much the top 1% really keep, and how flat the bottom looks.
Solving for α from 20% holding 80%: α = log T ⁄ (log T − log S). The smaller α, the heavier the tail.
The straight line is perfect equality — the poorest 50% would hold 50%. The bow shows how much the curve sags under your inputs: the marker sits at 80% of the population holding 20% of the total. The area between curve and diagonal, normalised, is the Gini.
| Top slice | Share they hold |
|---|---|
| top 1% | 53% |
| top 5% | 66% |
| top 10% | 73% |
| top 20% | 80% |
| top 50% | 91% |
The top 1% holds about 53% of the total at α = 1.16. The same maths is behind the friendship paradox and the inspection paradox — a heavy-tailed population, sampled the wrong way, hides the middle and amplifies the top.