[From Bill Powers (951214.0640 MST)]
Samuel Saunders (951214:1:13:21 ) --
In all formulations that I know of for application of
'reinforcement theory' to real organisms, it is necessary to
consider both cost and benefit.
Suppose there is a cost attached to each behavioral act. In a ratio
schedule, the assumed benefit per act is proportional to 1/m where m is
the schedule ratio. If a fixed cost c is assumed, attached to each act,
the net value to the organism per act is 1/m - c (omitting various
constants that make the units consistent). This would change the
reinforcement equation to
dB/dt = k1*C*(1/m - c) - k2*B.
The result is that the effect of the cost is equivalent to a change to a
higher ratio. This does not alter the form of the differential equation,
nor does it prevent runaway. All that is changed is the coefficient in
the exponent, which changes the _rate_ of runaway. The basic problem is
not the size of the coefficient, but the fact that the exponent is
positive rather than negative.
When you say it is "necessary" to consider cost, I think what you mean
is that if cost is not considered, the basic equations predict the wrong
form of behavior. Considering cost is done not because there is any
independent way to measure cost, but because if cost is not postulated,
reinforcement theory appears to be wrong.
However, your two mentioned sources of cost do not take care of the
problem. In order to convert the positive exponential runaway predicted
by the basic definition of a reinforcement effect into a negatively-
accelerated curve, you must not only propose a source of cost, but you
must propose that it increases nonlinearly, and at some behavior rate
becomes large enough to halt the runaway effect. What you need is for
the slope of the cost function to be low for low values of behavior
rate, so that behavior will tend to rise in a positive-feedback way, and
then to increase so that above the desired (observed) level of behavior,
the cost is increasing faster than the benefit. For example, in the
expression 1/m - c above, the parameter c must start at a small value so
there is a net benefit, and then rise with behavior rate so it equals
the incremental benefit at the rate of behavior where the curve is
supposed to level out. This can always be accomplished by adjusting the
parameters in the assumed equation for c. You might say, for example,
that c = a*B^2 or c = a* B^3, so cost rises as the square or cube of
behavior rate. By adjusting the parameter _a_, you can cause the rising
exponential to level off at whatever value will fit the observations.
The reinforcement runaway is a straw man (or the vision of a
sophomore student who didn't bother to take the advanced course).
Which advanced course, systems analysis or ad-hoc rhetoric? Your
proposed sources of cost are described qualitatively, without any
mathematical analysis to show that they actually take care of the
problem. In fact they don't, not unless you make your ad-hoc proposal
much more detailed by introducing a specific nonlinear cost function.
And when you do that, all you end up with is a fudge factor that can be
adjusted to make any wrong prediction appear to be right.
Empirical support- in paired baseline sessions, you see very little
bar pressing and a lot of eating.
Excuse me, but with my meager sophomore education, I fail to see how
that proves your point. Perhaps you could write out the mathematical
relationships and show me what you mean.
You don't have to convince me that the actual behavior you observe
doesn't look like an exponential runaway. All that proves is that you
can't use the basic definition of reinforcers to explain it. If you want
to explain the actual observations, you have to find a fudge factor that
will bend the runaway curve over so it decelerates instead of
accelerating, to conform with the data.
I should also point out that even if you introduce just the right cost
function, you would still have to predict that a continuing arbitrary
addition of reinforcer to that provided by behavior would cause an
increase in behavior. The PCT model predicts that the result will be a
decrease in behavior. Which prediction is right?
It's all very much easier if you start with a model that produces the
decelerating rise in the first place, as the PCT model does.
···
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(The question asked "how could you demonstrate empirically..."
when, for the experimenter, it is not a matter of demonstrating
empirically but of definition (he built it that way), unless you
meant to question his assertion that the devise actually did what
he claimed it did.)
Yes, that is what I meant. Don't you always check to see that the
apparatus is actually behaving the way it is supposed to behave? I was
trying to bring out the fact that you can verify empirically that the
pattern of reinforcements is totally dependent on the pattern of
behavior, and that if you observe a pattern of behavior you can
precisely predict the pattern of reinforcements (give or take any random
effects you have deliberately introduced).
To account for the pattern of behavior, on the other hand, you have to
_propose_ an effect of reinforcement on behavior. You state an equation,
combine that equation with the apparatus equation to deduce the net
pattern of behavior and reinforcement predicted by the combined
equations, and see if the result is like the actual pattern of behavior
and reinforcement. I think you will have to admit that this procedure,
which is at the foundation of real system analysis, is unfamiliar to
EABers.
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Best,
Bill P.