Continuing the discussion from Dead Zones, or Bill was Right (As Usual):

Rick’s latest spreadsheet has suggested to me the possibility that our longstanding impasse about collective control and conflict may stem from a conceptual disconnect between us on how the quality of control should be defined. Consider this equation that Rick uses in his spreadsheet.

The way this formula appears to work is by dividing the variance of the curve of the controlled (environmental) variable by the sum of the variance of the disturbance and the variance of the control system’s output and then subtracting that quantity from 1.0.

As I understand it, when the environmental variable is perfectly controlled, its variance will be zero (it will be perfectly stable), and numerator of the second term in the formula will be zero, leaving a stability of 1.0 (or 100%). If the control system is inoperative (not controlling at all), the variance of its output will be zero, and the numerator of the second term of the formula will be equal to the variance of the disturbance (since the disturbance is the only force acting on the environmental variable) divided by the variance of the disturbance (plus zero), which equals one, so the stability factor will be zero.

All good. What I don’t understand, however, is what the variance of the output is doing in this formula. It seems to me that an objective measure of the stability of the controlled variable should be simply the one minus variance of the cursor (the environmental variable as controlled) divided by the variance of the disturbance (the environmental variable in the absence of any control).

The inclusion of the variance of the output in this formula allows Rick to get the result he was looking for, that collective control with conflict is less stable than control by an individual controller. The variances of the outputs of the conflicting pairs of controllers when added together are much larger than the output of a single controller, even in cases in which the variances of the controlled variable are exactly the same.

Why should the amount of output of the control system have anything to do with the stability of the controlled variable? The output of the control system, after all, is affected by the feedback gain, the extent to which the perceived changes in the controlled variable are affected by physical variables involved in the various energy transfers that compose the feedback path between the energetic output of the control system and its input as another kind of energy absorbed by the sensing device.

For instance, If power tools make up part of the feedback path, the feedback gain will be increased, and the control system will need less output to effect a given amount of perceived change in the controlled variable. A job done with the aid of power tools takes less physical output than the same job done by hand. The amount and variance of output of the control system seem entirely unrelated to the stability of the controlled variable.

This problem I have with Rick’s definition of stability relates to what appears to me to be a conceptual difference between us in the definition of the quality of control. I think of the quality of control as an entirely objective fact. How much has the the variance of the controlled variable by the output of the controller been reduced in comparison to what it would be if the controller were inactive (i.e., equal to the variance of the disturbance.

The reduction in the variance of the controlled variable in the presence of the action of the control system is open to the observation of an outside observer. “The Test” is based on making those observations. In other words, that’s an objective measure of the quality of control.

Rick seems to think of the quality of controller as a subjective phenomenon. How much has the error of the control system been reduced by its output? Error is the difference between two quantities unavailable to any outside observer: the controller’s perceptual signal and the controller’s reference signal. With “The Test”, one can make an inference about what that reference must be, but it’s only an inference, at best, since error is a subjective phenomenon, hidden from outside observation.

When Rick talks about an “actual reference state” where the parties are “getting what they want” and a “virtual reference state” where parties are not getting what they want, he seems to be splitting control into two categories on the basis of the subjective experience of the controllers. It’s good (stable) control if the control gets what it wants, if it doesn’t, it’s “not in control”.