[From Bill Powers (960403.1330 MST)]
Chris Cherpas (960403.0911 PT) --
A procedure is then described which, as Bill P. points out, can be
read as containing a crucial contradiction. However, I read this
as just loosely describing an "adjusting" schedule, in which a
single response _is_ immediately followed by food delivery (i.e.,
there is no time delay between a response and a food delivery), but
that responses also incremented a counter which would subsequently
have to time out for the next response to be (immediately) followed
by a food delivery. The ambiguity could be resolved.
...
I didn't think Bruce was doing this experiment, but since he _does_
run "cleverly designed" experiments, I began to be fooled again --
this time _hoping_ it was true, since this is a general area in
which I did my dissertation.
...
After all, this sounded like a "Melioration versus Maximization" (a
favorite) type of experiment.
Oh-oh. To me, this suggests that
(1) You have done a considerable amount of work with "adjusting"
schedules of this kind and have spent a lot of effort looking for
regularities in the behavior of animals under such schedules. You have
become an expert on behavior under "adjusting" schedules.
(2) You are not actively looking for an explanation of the observed
behavior that will call any of the conclusions of your dissertation into
doubt.
(3) You have an investment in the categories "melioration" and
"maximization" which will not easily be written off.
If I am right about (1), (2), and (3), or any two of them, then it will
be difficult for us to come to any kind of agreement about a PCT
explanation of this behavior, because the PCT explanation is quite
likely to be simpler than the one you have found, the regularities you
observed are likely to prove to be forced interpretations of a much
simpler situation, and the terms melioration and maximization will not
be used (control systems do not maximize, nor, probably, do they
meliorate. They control). If you realize that this is a quite possible
outcome, and still want to see what PCT might have to say about this
behavior, we can go ahead. But if my apprehension about getting into
this is justified, we would be better off leaving the subject alone.
I will assume the best.
···
----------------------------
In trying to imagine the actual arrangement of the adjusting schedule
from your description (if I misinterpret, please correct me), I have
been able to construct a rough picture of the feedback function.
Let c be the current counter value, b be the current behavior rate, and
k be the amount by which c is decremented per second. C is incremented
by m*b counts per second.
I assume that a behavioral event will produce a reinforcer only if the
timer has counted down to zero.
If k is less than m*b, that is, if the amount by which the counter is
decremented per second is less than the amount by which it is
incremented per second, the count will never reach zero and the
reinforcement rate will be zero.
If k is equal to m*b, the counter will be incremented and decremented
equally per unit time, and the outcome is ambiguous. If the timer is not
counting down to zero, it will never get to zero and there will be no
reinforcements.
If k is greater than m*b, the counter will count down faster than it is
incremented by the behavior, and will eventually reach zero. Once it
reaches zero, the next behavior will produce a reinforcement and the
counter will be incremented by m counts. The counter will then begin
counting down by k counts per second. Because the behavior rate is low
enough that k is greater than m*b, the counter will time out after each
behavior and there will be one reinforcement per behavior.
So if the behavior rate is less than or equal to k/m, there will be one
reinforcement per behavior; otherwise there will be zero reinforcements
per behavior.
The transfer function of the schedule can thus be plotted this way:
>
>
>
Reinf>
Rate | | B = k/m
> >
> v
><------------->*
> R = B *
> *
> *
> *
> *
> * <--- R = 0 --------------------->
> *
----------------* * * * * * * * * * * * * * * * * *>>
Behavior rate
Does this agree with your analysis, or are there some details I don't
know about? (Assuming you want to proceed).
-----------------------------------------------------------------------
Best,
Bill P.