Project Cybersyn and the origins of the Big Data nation
newyorker.com
newyorker.com
It alternates between novel and essay about Khrushchev-era USSR, when people on both sides of the curtain thought there was a pretty good chance that the Soviets would succeed, if not as a Socialist Utopia at least in economically overtaking the west in output and quality of life.
Also, this excellent essay about the computational aspects of Gosplan, the USSR's mostly human-powered predecessor to Cybersyn: http://crookedtimber.org/2012/05/30/in-soviet-union-optimiza... (which is where I learned about Red Plenty)
http://crookedtimber.org/2012/05/30/in-soviet-union-optimiza...
You can, if you are interested in the topic, find the book at http://ricardo.ecn.wfu.edu/~cottrell/socialism_book/
Although not dealing so much with big data, it was still a "socialist" attempt at mathematical optimization being applied in society.
And within a chaotic system there are several types of stability that can be readily predicted over a long period of time such as Lyapunov stability and asymptotic stability.
Why do you think this system would be chaotic in the first place?
And while, yes, there is definitely good work being done in studying dynamic systems, applying those things to human beings is very difficult and dangerous. We already often face situations where humans are expected to conform to a limited set of predicted responses rather than the system being seen as flawed for failing to predict all possible responses. And human beings react very, very poorly to being restricted in these ways.
Chaos isn't an intrinsic behaviour of humans, it's a property arising from specific conditions in a dynamical system. I do think there's been interesting results in trying to model human behaviour (http://www.wilmott.com/pdfs/090610_mandelbrot.pdf), but like you I'm hesitant to apply these mathematical models to us irrational humans. Anyway, I'm just being a pedantic math nerd.
P.S. Sensitivity to initial conditions alone does not imply a dynamical system is chaotic.