Look at a map, and you will see that many post-communist states perform relatively well on the HDI, especially relative to what their income levels alone would predict. Caucasus states, much of Eastern Europe, Kazakhstan - all have “very high” HDI scores despite being classified as “upper-middle income” by the World Bank, or “emerging market” in other indices. There is a large and growing category of such nations that are becoming prosperous, yet do not quite reach the living standards we see in North America, Western Europe, Oceania, and some Gulf or East Asian countries. These tend to be concentrated amongst the former Eastern Bloc, with Russia being a particularly prominent example.
HDI comprises of proxies for human capital alongside income levels. Average years of schooling and life expectancy. There are three index scores, normalised:
Let Ih be the health index. Its minimum is 20 and maximum is 85. Hence Ih = (E[life]-20)/(85-20)
Let Ie be the education index. Mean and expected years of schooling enter as separate variables. Expected years of schooling is state policy. Mean measures the average of how many years people actually study for. However, the former is normalised and capped at 15 whilst the latter is capped at 18. So Ie = (mean/15 + expected/18). Note that university education is excluded!
Income is GNI per capita at current PPP. This is both logged yet capped at $75k with an $100 minimum. Iy = ln y - ln100. This normalisation leaves income differences between countries heavily compressed as a result. By design, the index places a relatively low weight on income.
From this, you obtain HDI = (ΠiIi)^(1/3) for i=(h,e,y)1. You get a geometric mean for your score. Whilst this plus the normalisation makes the calculation tractable, the vast differences in living standards across the world are understated by design. This is due to a revision change in 2010 from a simple arithmetic mean: designed to weight each index more equally, yet penalising rich outliers. The very exponential compounding we're adjusting for is what leads to long-run prosperity in the first place!
Moreover, each additional year of life increases your HDI by HDI/(3Ih). Hence this implies the gains to living standards from life expectancy increases are roughly proportional to income, yet income (given the capped logged form) yields diminishing returns. Income is quasiconcave yet the other indices are linear! I know of no QALYs nor other hedonic price adjustments that arise from this functional form. By design, HDI implicitly weights gains to health and education more heavily than gains to income, which biases towards countries adopting universal coverage and schooling in these areas, even at extortionate and distortionary taxes that harm growth.
Then expected years of schooling is an input that can be increased simply as a matter of policy. Indeed, communist states invested heavily in (years of) schooling, hence on this front they perform better on this index than their dysfunctional economies suggest. In this sense, HDI is biased towards left-leaning polities.
Putting aside the somewhat arbitrary selection of proxies for human capital or public goods provision (quantity is not quality after all!), with no reliance on market prices or values for such inputs whatsoever, this implies a major flaw in Sen's capabilities approach to me.
Despite this, I'm not a GDP maximalist either. Non-market income and leisure are excluded from measurement, which is often noisy and (especially in counties with dysfunctional institutions and poor state capacity) heavily politicised. “Running an economy hot” via printing money and injecting fiscal stimulus will (in the short-run) boost output. You could maximise the long-run growth rate (potential output), yet no one really knows what this figure is. Communist five-year plans are essentially textbook Solow (capital investment). We have reason to believe it could be negatively correlated with fertility too; throwing the welfare calculus into question.
GDP is a good proxy for living standards. Revealed preferences clearly show the overwhelming pattern of migration at every stage in history has been from poorer to richer nations. Many correctly argue that it's correlated 0.9 with most of what we care about. Yet with AIs, why not build a model of all the variables you care about when evaluating the standard of living of a location yourself, in a granular manner? You can use whichever functional form you wish: nonparametric even. Alternatively, revealed preference captures much of what enters as a residual in any measurement exercise.
When evaluating the living standards of a country, you must factor in Arrow, again. We lack any reliable means of aggregating social preferences in a coherent manner. This applies to how one weights material prosperity, GDP, non-market activity or leisure, and so on too. This is also an argument against institutions that promote the tyranny of the majority. In general, the lesson I draw is that governments should, as much as possible or feasible, leave individuals and organisations to decide for themselves what makes for a good life. The best metric for living standards, I think, is liberty. This is highly correlated with the other common proxies such as GDP anyhow. Non-market indicators such as social cohesion (how safe you are) or participation (philanthropy, perhaps faith, and our relationships) also matter.
You could prioritise Pareto efficiency, yet in cases such as public goods or enforcing property rights over pavements (for obvious reasons public ownership, so a second-best equilibrium at best), this framework is unfeasible, then second-best or VCG mechanisms are highly state-contingent and introduce ambiguity.
In general, any reliance on any single metric, whether HDI or GDP or so on, is highly likely to neglect some important dimensions that matter for our happiness, virtue, and prosperity. These value judgements are the exact reason we will never converge onto agreement on the best policies or institutions to adopt. Their subjective, nonparametric nature often leaves these normative assumptions implicit and hidden: no one knows their exact social welfare functions of course! Nonetheless, to find common ground in our polarised world, and agree to efficient or second-best compromises, we should place more effort into describing what we think makes for a good world.
Yes this ordering I've done on purpose!