Modern game theory is, I think, the first necessary element to the development of any psychohistorical mathematics. Game theory reduces strategies in games, or in any situation at all, to mathematics and thus produces a mathematically "best" strategy, which any perfectly rational entity would follow. Applying this to psychohistory, the entire population can be considered to act in their own interest.

So if, say, gold is discovered somewhere and it seems to much of the population that they have a 1 in 100 shot of becoming billionaires if they ship out, whereas if they don't go they are doomed to their menial lives. Everyone hitches out, and this is called a gold rush. It seems to me this is a very psychohistorical prediction. Getting a little more involved, it can be assumed that populations in general move towards positive stimuli and away from negative ones. Oppressive governments, for example. When the weight of the government overbalances the potential strife from revolution, the population will revolt, and not before. If the fruits of technological research exceed their cost in time and resources, guess what the population is going to do? This line of thinking can be applied to any situation at all. Whichever has the most positive outcome in the eyes of the agent in question will be the path taken.

Now, to construct a more accurate picture of what exactly a "population" is, multiple agents are necessary, with more agents for those with greater populations (or just appropriately weighted) however, there is no reason why the number of agents needs to equal the number of people. Psychohistory has absolutely no way to predict how many people will exist in any given population precisely. And all that is relevant is the relative presence or influence of the groups in question. Each agent or agents makes their decisions and it has its effect upon the model being analyzed.

I agree that game theory is one of the big players in this development. The concept of game theory is, as said, to find "winning strategies." Using this idea, we could, in theory, as everything is at this point, work backwards. For example, say you want someone to lend you a sum of money. you develop a plan to get them to give it to you. You can start with your goal, and find a choice that will get you there. Then you find a choice that will lead you there, and so on.

Obviously, it will be vastly more complicated than this, but the idea should remain the same. We start with a goal, and find choices that would make that happen, and go from there. This is where the social sciences come into play. By studying human behavior, we will gain the deeper understanding of human rationality or irrationality we need to make this work. If we worked on the premise that, given the choice between life or death, they would choose death, we wouldn't get off the ground.