[From Bill Powers (2009.10.14.0838 MDT)]
Richard Kennaway (2009.10.13.1315 BST) --
My point though is that there's already a huge context for this sort of thing, but one that I don't think is as strongly wedded as psychology is to theoretical models positively antithetical to the idea of control systems. The broader theoretical idea is only that agents work by simple rules (and what could be simpler than o = k(r-p)!) from which complex social phenomena emerge.
The reference you cite does look promising. There's one principle of modeling as I see it that isn't clear in what I read. Some models seem aimed at directly representing the phenomena, or the behaviors, that are observed. I'm reminded of Kelso's approach to how organisms walk: he sees it as a "pendular" movement of the legs, which of course is the appearance we would want a model to generate, but the image of a pendulum is misplaced since the location of the foot during a step is fixed, the foot swinging only when not bearing weight. And you don't model a pendulum by starting with a component that already swings like a pendulum.
As I have always understood modeling and simulation, we begin by looking at the components of the system and how they each, in isolation, convert causes into effects, inputs into outputs. Once the components have been characterized, they are connected together, the outputs of some components being inputs to others, with the exception of those that receive inputs from outside the system, or send their outputs to places outside the system. We don't try to put the behavior we expect into the system at the start; in fact, we pretend we don't know what this assemblage of components will do when connected together, and set up the simulation to show us what will happen. As you say above, the whole point is for the behavior to EMERGE honestly from the organization of the system, rather than being programmed into it.
If you program the behavior into the model, I call the result an animation, not a simulation. You can make animations do anything you like just by drawing successive frames, which is why most animations of organisms don't behave very naturally. It doesn't take much of a deviation from the real physics of movements to make animated movements look unnatural. But models which produce movement by simulation look much more realistic; ironically, simulated systems show behavior that the creator of the simulation might view with surprise, or dismay. That's why they're more convincing than animations when you get them right.
The idea of working by rules is, I think, closer to animation than simulation. Of course in playing games and in other circumstances we do work by rules, so a model based on rules would be appropriate. But in most cases the apparent rules are artifacts. My example of the rules built into Pribram's TOTE unit shows what I mean. The behavior of a raindrop can be modeled as
Test: if raindrop has not hit ground yet,
Operate: keep falling, Test again
otherwise ...
Exit: splash!
So: Test, Operate, Test, Operate, Test, ... Splash! TOTOTE.
This rule, a program, describes what happens, but not the reason why it happens. I see similar things in linguistics: rules that appear to capture how people talk, but no simulation from which talking emerges. The rules can actually get much more complicated than the actual "how" of the behavior. Describing in words how a hierarchy of control systems works is a very lengthy process -- it once took me a whole book to do it. But a simulation of a working control system can be done in a few lines of Pascal code.
You ask "what could be simpler than o = k(r-p)!". The answer is o = k*e, because e is the input to the output function and o is the output, or e = r - p, because the comparator converts the two inputs, r and p, into the output e. The system equations for a control system represent one component each; solving them simultaneously establishes the connections between components and shows you the result of those connections.
This is what I'm trying to get at with my simple economic models. I don't put any economic behavior into the model: I just try to set up a collection of components, each component being a simple input-output relationship such as the fact that if I buy goods from you at a given price a certain amount of money leaves my bank account and moves into yours, and a certain quantity of goods leaves your inventory and moves into mine. I say that a manager tries to control inventory by adjusting the price, while a consumer tries to control the bank account by adjusting how many goods are bought and how many hours are worked. What will happen when you connect these simple relationships together? What should happen is that the model will behave in a way that's like the way real people behave. Actually, my model doesn't behave quite right, so it needs modification. But the modification won't consist of making the model produce the right behavior. It will consist of changing the assumptions about how some component of the system works, and seeing how that changes the behavior of the whole system when the simulation is set in motion.
What's you assessment of how Epstein and Axell do their modeling?
Best,
Bill P.