The biggest change in method was that the new HDI is a geometric average rather than a normal (additive) average. Geometric average means you multiply the separate indices (each ranging between 0 and 1) for income, life expectancy, and education together and then take the cube root (I know your pulse starts to race here…)
Now, students, please notice the following: if one of these indices is zero, then the new HDI will be zero, regardless of how great the other indices are. The same mostly applies if one of the indices is close to zero. The new HDI has a “you’re only as strong as your weakest link” property, and in practice the weakest link turns out to be very low income (and guess which region has very low income).
You can see why the geometric average might have been attractive: by multiplying and then taking a root, it avoids the Bill-Gates-Walks-Into-A-Bar problem that besets arithmetic averages. But instead it makes errors in scaling or in linearity much worse. You gains on the swings, but you loses on the roundabouts.
And ultimately it’s always going to be about the scaling. $2 may make you twice as happy as $1, but $2 million is unlikely to make you twice as happy as $1 million, much less a million times as happy as $2.
It’s much, much easier, both mathematically and politically (because you get to avoid claims of subjectivity) to measure utility or development in linear terms of clear quantities like dollars or years of life or bushels of food. Too bad all you learn is ever more precisely where the house keys aren’t.