This can also happen when the gain of one of the two opposing controllers is much lower than that of the other. I discovered this when I was doing some research on conflict. It turns out that when there is a large gain difference between two agents controlling the same variable in a conflict the agent with the higher gain controls better than he would have without the opposition.
This result was a huge surprise to me and I thought it was inconsistent with the PCT model of the agents, which would have required some revision of the model. But I ran simulations with two PCT agents of very unequal gain controlling the same variable and the results were the same as with a real person as the high gain controller; it works that way when there is a transport lag in the high gain agent is longer than that in the low gain agent.
This finding was dubbed (by Bill) the “Marken effect” and was discussed at some length in the earliest days of CSGNet. Here’s one discussion of it by Bill from 1994:
[From Bill Powers (940602.2040 MDT)]
RE: the Marken Effect.
Discovering that the model had to reproduce the real subject’s transport lag in order to get this effect did, as you suggest, reveal the conditions under which this effect is seen. But it also explained_ the effect.
The explanation is this. The auxiliary control system, with a modest loop gain, simply tried to keep the controlled variable constant, operating in mild conflict with the main control system, either Rick or the model of Rick. What made control a little better with the auxiliary system in operation was the fact that it did NOT have a transport lag in it. Thus, on the average, a disturbance that caused a change in the controlled variable was counteracted, to some extent, by the auxiliary control system during Rick’s transport lag. This reduced the effective disturbance that Rick or the model of Rick experienced, resulting in slightly but reliably better control. A test of the Marken Effect by simulation failed at first because the model used for Rick’s behavior did not include a transport lag. The model of Rick could therefore act just as fast as the auxiliary control system could, so there was a simple conflict and no improvement in control. When the model of Rick was changed to match Rick’s actual transport lag, the improvement reappeared. This explanation goes considerably beyond merely noting the conditions under which the Marken Effect appears.
It’s amazing what you can learn when you actually compare the behavior of the model to that of an actual person.
My book didn’t include this this “very important methodological point” because I never encountered the problem of having to “include appropriate connections to higher levels” in my models (such as the model of the “Marken effect” described above). Maybe you could give me an example of where you have encountered the problem in your own research and I’ll include a discussion of that “very important methodological point” in the second edition of the book.
Best, Rick