I’ll just say that that’s one way of approaching the general question of “we need to know what large numbers of will respond to some circumstance” and is the “scientific” approach of understanding things. This does potentially run up against the issue that theres too many different factors for complicated human beings. An alternative would be to focus on the question of what engineering and science is needed to be able to reliably infer the behaviour of very large scale populations of people from practically doable experiments "

Just a question- (I know the original question stated no constraints etc), but to what degree does the above get us into dangerous territory? If such a scientific theory/tool/methodology existed/does exist, what would you rate as the probability of its use vs the probability of its misuse?
If creating such a tool would have a high probability of leading to the wielder having vast power (vast GENERAL power, not merely for the sake of protecting an biosphere) is this problematic, or necessary?

Also... "Needed: scientific sociology." ... seems to imply that there does no exist any science of sociology... which I'm sure people will debate over (Is economics really a "scientific" subject? What about anthropology?)
But... doing so seems dangerous to me. In the end its just a subjective debate of the meaning of the word "subjective"
There is the term "physics envy", where other subjects attempt to find statements as precise as the laws of thermodynamics or gravity. But be honest- do you EXPECT to see such laws when exploring an ecology? Or the workings of a cell?
Or a civilisation?
So... so perhaps there IS a large amount of scientific sociology. Its just less elegant than what mathematicians and social scientists are used to...

*shrug* I dunno, probably useless comment- a response to something old, and I'm sure you knew what you meant at the time... you even said "if such materials exist"...
Hmmm.. I feel that this may be other peoples conversation, but such like this interests me, so oh well.

... I wonder what Google are up to...

Oh, and while I'm here, perhaps I should answer original question
"However, what if we push the limits? If all the barriers were removed, then what would you do?"
Space program, colonise Mars. - yes the biosphere is problem, but the question stated to assume no constraints... so that's what I'd do.
Assuming ecological constraints...

Strongly encourage "buy once" style products. Make manufactures responsible for both their product and its packaging indefinitly (to encourage reusable or biodegradable products).
Investigate the academic publishing system and its alternatives- which systems actually HELP people.
Investigate all current governmental systems, and rate them on their performance- in particular investigate which ones lead to smoothest transitions after revolutions (EG, so the newly elected _____ does not then become a military dictator, nor face massive resistance).
Investigate closed system biology- are we yet at the stage where we could build a dome and have it sustain itself indefinitely? If not why not? If so, how can we scale up these technologies?
Investigate the Patenting and Trademarking system- how do these systems encourage/discourage innovation? How do they effect the USE of such innovations? To what extent do these systems help/hinder medical/agricultural/sociological change? What are possible/probably effects of changing these systems?
Invest heavily in antibiotics research.
Enforce a rule that requires all economics papers with at least one equation are reviewed by at least one mathematician (I currently have a 70% hit rate for ones that actually make sense mathematically)

Investigate the manufacture of sturdy, environmentally friendly, solar powered E-readers. Install as much agricultural/scientific/ cultural knowledge on them as possible, and make them freely available- perhaps starting off with one or two per village.
Scratch that- reading is a problem. Damn.... hmmm... okay, I'll have to think about that one more carefully.

Start an "international cooperation" political party in as many countries as possible. I wouldn't expect them to get a majority of votes anywhere, but I think there may be several countries where they could gain a useful minority. Even having them as a recognized political force could be of use. (NOTE: I do not consider each of these units to be part of a collective, merely a number of parties in different countries with a similar mandate). I know that many political parties already act in a cooperative manner, but I think placing it as the mandate for one of them could be worth while.

Okay... that's all I've got for now.....

This is a fun question.