Human Development Index

Before 2010 the HDI averaged its three dimension indices arithmetically, which made the dimensions perfectly substitutable — a deficit in health could be fully compensated by extra income. Since 2010 the index uses the geometric mean (the cube root of the product of the three indices), which is imperfectly substitutable: a low value in any dimension pulls the overall index down and cannot be fully offset by high values elsewhere. This better reflects the idea that the three dimensions are intrinsically important and that balanced achievement matters.

Goalposts are the fixed minimum and maximum values used to normalize each indicator onto the 0-to-1 scale — for example, life expectancy between 20 and 85 years, or GNI per capita between 100 and 75,000 PPP dollars. They convert raw indicators into comparable indices and anchor the index over time. Because they are fixed by the Human Development Report Office, the choice of goalposts is a normative decision that affects the level and, at the margins, the ranking, so comparisons should use a consistent set of goalposts.

The HDI reports the average achievement of a country in health, education, and income and is silent about how those achievements are distributed across people. The Inequality-adjusted HDI (IHDI) discounts each dimension by the amount of inequality observed in it, so it equals the HDI only under perfect equality and falls below it as inequality rises. The gap between the two — the 'loss' due to inequality — is itself an informative measure of how unequally human development is shared.