Let us not make the mistake of attempting to prove that individuals have negligible overall effect on the system. In Asimov's novels there was one Mule, but in real life, there are many of them.
This does not mean, however, that any attempt at developing a working Psychohistory is automatically rendered invalid. I will attempt to show this below.
There is in fact a class of "celebrities", for lack of a better word, made up of great scientists, philosophers, political leaders, infamous criminals, cultural icons, et cetera. This class is relatively small, and can be defined as including any individual who may have the potential to influence events to an extent that is not mathematically negligible. This is basically a class of "Mules".
However, this class is, as I have said before, relatively small, and thus can be dealt with separately. An overwhelming majority of the population, maybe on the order of 99.5%, can be accounted for with "traditional" Psychohistory, as developed by Hari Seldon. So there need to be two parts to Psychohistory, two sets of equations. One for those masses of people whose net contribution to the outcome of events is negligible -- it will resemble thermodynamics. And another set of equations, much more complex, for individuals who act like individuals and have a non-negligible impact on the outcome of events.
How would this second set of equations work? I myself couldn't think of anything for a long time, until I came across <a href=http://www.4degreez.com/misc/rec.mv?stat=2>this website</a>. It is a poll, which gives participants a fairly long list of the names of various celebrities, and asks if they have ever heard of them.
The idea that follows from this is simple enough -- you would need a set of equations estimating how quickly different people and different kinds of "Mules" (scientists, rock stars, politicians, etc.) fade from the public consciousness, how much impact they have on the outcomes of events before they do, and what historical conditions make them famous in the first place.
Under idealized conditions, the speed with which a celebrity falls into obscurity would follow the same equation as radioactive decay. Unfortunately, conditions are not ideal (due to inter-person interaction) and this will be a bit more difficult.
It is logical that the amount of impact a person will have upon the outcome of events can be expressed as a function of how well-known they are; if you radically oversimplify everything, it could be expressed as the integral of the function outlined in the paragraph above, determining how quickly one falls from fame into obscurity.
The third factor, what historical conditions give rise to a certain kind of celebrity, could probably be determined through rigorous historical analysis and cross-comparison.
As the "fame factor" of a person becomes lower, the amount of impact they will have on the outcomes of events presumably also becomes lower. Eventually, it becomes negligible, as it is for the vast majority of the population.
Thus, the new psychohistorical equations describing any one person would be the combination of a "thermodynamics factor", which would apply to everyone, and an "individual factor", which would quickly become negligible as you move from celebrities to more and more obscure, everyday folks, and could easily be dropped for simplicity's sake for about 99.9% of the population.
