How Do You Put Inequality in One Number? Compare Everybody With Everybody
By the BrainSnail editorial team. How these articles are written and checked, and how to tell us when one is wrong.
A single figure between zero and one summarises how unequally something is distributed, and it is quoted constantly. What it cannot tell you is at least as important as what it can.
What the number means
The figure runs from zero, where everybody has exactly the same, to one, where a single person has everything and everybody else has nothing. It is calculated from the difference between how income or wealth is actually distributed and how it would be distributed if everybody had an equal share, expressed as a proportion of the maximum possible difference. An equivalent definition is the average difference between every possible pair of people, divided by twice the average, which is why the measure is described as comparing everybody with everybody rather than looking at the top or the bottom alone.
How it is drawn
The graphical construction explains the number directly:
- •Rank everybody from poorest to richest along the horizontal axis
- •Plot the cumulative share of total income up the vertical axis
- •Perfect equality gives a straight diagonal line
- •Real data gives a curve sagging below that diagonal
- •The figure is the area between the two, as a share of the triangle
- •A deeper sag means a larger figure and more inequality
What it cannot distinguish
The central limitation is that quite different distributions can produce the same figure, which is unavoidable when compressing a whole distribution into one number. A society where the very top holds an enormous share and everybody else is similar can score the same as one where the difference is spread evenly across the range, and those are different societies with different problems. The measure is also more sensitive to changes around the middle than at either extreme, so a large gain at the very top moves it less than intuition suggests. Reporting it alongside the shares held by the top and bottom tenths addresses both problems and is standard practice among people who use it carefully.
What the numbers look like
A sense of the range makes published figures readable. Measured on income after taxes and transfers, the most equal wealthy countries sit in the middle of the range between zero and one but well towards the low end, clustering around a quarter to three tenths, and the most unequal large economies reach four to five tenths. Wealth is far more unequally distributed than income everywhere, with wealth figures typically running well above seven tenths even in countries whose income figures are low. Global inequality between all individuals is higher than within any single country, which is a point frequently lost when national figures are compared.
Why comparisons are harder than they look
Figures quoted for different countries or different years are frequently not comparable, and the reasons are technical rather than political. The measure can be calculated on income before tax, on income after tax and transfers, or on consumption, and those give markedly different results for the same population, with redistribution showing up as a substantial gap between the first two. It can be calculated per individual or per household, with or without adjusting for household size. Coverage of the very top is poor in survey data, since the wealthiest are under-sampled and under-report, so most published figures understate the top end. Any comparison therefore requires checking that the same thing is being measured.
The takeaway
The figure compares the actual distribution against perfect equality, running from zero to one, and equals the area between a cumulative share curve and the diagonal. Quite different distributions can share a figure, and it responds more to changes near the middle than at the extremes. Numbers calculated before and after tax, or on income against consumption, are not comparable.