There is, in truth, no reason why psychohistory, as depicted by Isaac Asimov in his Foundation novels, can’t work in real life. Unquestionably there are observable patterns in human behavior that are within the ken of statistical prediction, and outside of the individual control commonly associated with historical processes.
The difficulty in the social sciences lies in that there is no such thing as a simple test. In sciences like physics, it is possible to simply toss one ball vertically into the air. There are two factors, gravity and air resistance. The mass of the earth and the mass of the ball. Results can be measured with precision, and data collected from repeatable experiments. Such an experiment is impossible when dealing with people. Even one person is far too complex a system to be analyzed with a single formula like the ball experiment. But it gets worse. The social sciences are not given one person and told to make sense of how they work, oh no. Social scientists are presented with entire countries based on as little as a few centuries of yellow-in-multiple-senses history. The type of rigor associated with the material sciences is not only impractical, it is utterly impossible unless that scientist happens to have a computer powerful enough to simulate every interaction taking place in the country, as well as every interaction that has taken place in all history relevant to that country. Which, essentially, means all history period. The patterns are not merely unintuitive, they are straight-up buried in a sea of unreliable muck, and even the sea is much too small to be useful.
That being said, the basic principles still hold. Though the system is, by definition, more complicated than the sum of all human experience combined, its behavior can still be predicted axiomatically. And, through abstraction, we can reduce the complexity of a practical representation of that system to the point where it becomes useful. Let’s consider a very simple person. Let’s call him Bob. Bob has a problem. He is obsessive about food. It’s all he can think about; the consumption of vast quantities of food, the tastier the better. But Bob isn’t stupid, he knows enough that he can actively move towards the acquisition of food. Bob’s simplicity lends itself to the easy selection of strategies for him. Using that as a basis, we can predict his behavior with formidable accuracy. For example, Bob’s complete obsession with food means that he is prepared to pay any price he can actually afford for it. And although Bob is prepared to pay exorbitant prices for food, he knows that if it’s cheaper then he can buy more of it. But he knows full well that if the person selling him food knew of his obsession, the vendor’s price would skyrocket. So Bob realizes he needs to keep his obsession secret. Also, Bob’s need for consuming food entails the acquisition and storage of food, probably in huge and ever-increasing quantities. Because Bob knows that money translates directly into food without the issue of spoilage, he begins to obsessively obtain and hoard money, siphoning it off to eat as much as he physically is able to. He could turn to a life of crime, either stealing money or just ripping off food from grocery stores and suchlike. This becomes a viable strategy if and only if Bob’s gains exceed his potential penalties. (If you doubt this statement, would you take $1 million if you had a 5% chance of spending 2 weeks in jail?)
However, psychohistory would be much more rigorous, and far larger in scale than the caricature I have outlined. But we know enough of human behavior now to begin on turning the social sciences into a formal discipline instead of a sort of wishy-washy all-answers-are-correct morass of opinion and artistic misconception. The goal of social sciences is to understand human behavior, society, government, etc. etc. and the logical consequence of that is to eventually describe human behavior rigorously. However, there is a problem. If knowledge of psychohistory becomes too common, then it becomes useless because the fact that everyone knows they are being sociologically guided changes their behavior. More interestingly, any rigorous analysis would have to take into account the possible effects of other rigorous analyses. If half the population has heard your prediction and believes it to be true, the conditions you made that prediction under are now completely different, rendering the prediction more or less void. This is somewhat akin to the problem of observing a quantum particle. You cannot know both its position and its velocity because the act of measuring its position changes its velocity, and the act of measuring its velocity changes its position, operating at the time scale of a single planck time so you can’t exactly just take both at the same time.
Psychohistory is, to all available evidence, feasible. It has its flaws; it appears impossible simply as a knee-jerk reaction, it will be difficult to make it usable, and will probably have little application until it nears maturity. Worst of all, predictions would be limited in strength by the possibility that input information was incorrect, or that variables exist that are unaccounted for, or the impact of future events that cannot be predicted. As a sidenote, I currently speak of natural effects such as a hurricane or whatnot. But in a similar fashion, those too should be predictable despite the insane complexity of the Earth’s environmental system. However, in the face of all of that, the possibilities of being able to predict the human future are enormous. More to the point, it becomes possible to push the compass towards a better future by subtle action in the present.