I did not state that very well, the surface layer is the aggregate result of all the behaviors/rules. I am guessing that your power function is extracting some attribute(s) of the surface layer.

I guess this depends on your view of the world. I would say that if you simply write a power function then that would indicate an arbitrary assumption to begin with, that has had to simplify a number of significant factors. Writing a power function might be simple, but I am not sure that it would be significant.

For example one view of the world would be at the surface layer, where you see the end result of a combination of small events. This is what I think you are doing with your power function, although I may be misunderstanding. Another view says that you will not worry about the surface layer, and will instead come up with a number of simple rules (some based on probabilities) for the various actions & interactions that can take place. The execution of the rules by the Agents over multiple turns gives the emergent behavior, or what I called the surface layer. If the surface layer emerges that you would expect (guns are better than knives in a war for example), then this indicates the model is hopefully not grossly off. So instead of getting one big function right, you instead have a number of small rules that determine actions and probable outcomes.

You could even play some games with determining probable power functions after running a number of these, by representing them as genetic strings and then doing standard genetic algorithms to see what gives the closest match over all the outcomes for the different scenarios/times. I think this is more powerful than starting with the power function because your assumptions are at a lower level that is easier to get right, not to mention simpler. This is also why I mentioned Epsteins book, its a great example of using simple rules to get emergent behavior.

If you are using an Agent based system, then determining power could be computed after outcomes based on the modeling attributes you have determined are important.

I would recommend 'Growing Artificial Societies: Social Science from the Bottom Up (Complex Adaptive Systems) ' by Epstein

I am quite impressed with the positive response & helpful comments that have come about from your post. I wanted to throw in my own two cents worth for an activity that is possible while having ALS that has potential in the trans-humanist arena.

For the past year I have been a member of the OpenSource EEG group, and educating myself on Neurofeedback. I have also been blogging on my educational experiences, mostly just for myself. Some of the experiences I have had doing Neurofeedback have been very striking. These experiences typically occur during high alpha wave production and brain synchronicity which just means multiple parts of the brain are producing the same waves at the same time.

Originally I started training mostly out of curiosity to see if I could increase creative problem solving abilities. I think it is also very useful for maintaining a positive outlook, and a state of mind that has more potential for choosing how attention is given/selected.

So, if I were to recommend one book, it would be Les Fehmi, PhD 'The Open Focus Brain'. This book reminds me of one of my favorite programming books 'The Little Lisper' because it has one of the most effective training methods on a CD for brain synchronicity. (Little Lisper was good because you quickly got the experience, and could go for the theory later)

For the EEG, I would recommend Neurosky mindset which is only a single channel (not ideal) and is only two hundred dollars including a pretty nice brain visualization tool. The OpenSource EEG is good as well, but takes awhile to get all the parts for & assemble/test. You might find the EEG is unnecessary, but if you do not get the state change from the CD, then some basic feedback could help.

Best of luck, hope this helps