That principles of human nature may be as immutable and consistent as other aspects of nature is likely untrue (too many uncontrollable chaos-related variables), so Psychohistory will prolly remain (like caseless ammo, fusion reactors and robots with the strength and mobility of humans) fiction. 

One thing that seems to be almost 100% predictable about Humanity is that catastrophes caused by large numbers of human beings acting badly or failing to act when they should, are for all intents and purposes unavoidable - regardless of how obvious or inevitable they seem beforehand. 

It's almost as if the Human Race has a reflex like vomiting - once initiated the reflex cannot be reversed.