We're sorting of hitting the 'arguing about two seperate issues' point.

What I am saying is that the HDI is a fairly legit way to measure a country, but not to contrast to others as a means of fine comparison. In many ways it's basically worthless, because it's pretty obvious and unnecessary to compare dirt hovel places with western countries, and the western countries are simply too close to measure policy off of. You don't need the HDI, nor does it serve any useful purpose, if you're trying to show Country X has a superior literacy program to Country Y. The specific program itself can be used and really is the only useful standard. The thing is not accurate in that way, not to say 'Ah look, X had .01 higher on the HDI, let's assume that is a sign of superior policy' because it just isn't accurate enough.

I want to emphasize, yes, 1/3 can carry on beyond 1 digit, but only if it's been treated as a clean derivative. There has to be a justificaiton for that. 1/2mv^2 can easily be shown to be the integral of mv, the 1/2 comes from that, it is the clean byproduct of a mathematical equation, not a empirical result. It is not a coefficient that has simply been taken from the data, it is very specifically 1/2. Saying 1/3 for weighting is simply an unjustified assumption, unproven, therefore no more or less accurate than saying 1/3.0002 or 1/3.4. Does it make sense to equally weight them when no legitimate justification exists for more accurate weighting and they all seem very important? Yes, sure. But that doesn't mean it becomes highly accurate as a measure of anything but itself. And the more one tries to yank specific comparisons of policy out, the more one is subject to biased interpretations and corrections as well as giving people a big reason to try it. There are simply too many variables in it that have distortion or are distortable to compare, not only do you have the 'no more accurate than least accurate' problem but also that innaccuracies stack.

If I measure the momentum of object by it's mass and velocity, and each is only measurable to within 1%, the momentum isn't accurate to 1%, it's accurate to the range of the of their combined inaccuracy.

This isn't something subject to debate, the variables involved, while allowing for a decent measure of accuracy for HDI, do not allow the HDI to be used as a useful tool for comparison of policy. You are, I believe, trying to argue the accuracy of the HDI itself, I am arguing is accuracy as a useful index for comparison. There's no polite way to put this, but in this regard, I am right. There can be no argument without empirical proof that 1/3 is a more accurate value than 1/4 or .356, and no such empirical proof exists. As such a change in waiting would noticeably alter the rankings, the HDI can not possibly be considered anything but a loose benchmark, and therefore the ranking order as it is can not be used as a legitimate measure of policy between parallel entities.