David Premack - Refutation of Response Deprivation

Refutation of Response Deprivation

Taken from correspondence between Premack and John Staddon from Duke University, dated March 16, 1979:

Dear John:

A long time ago I promised to explain what is wrong with response deprivation, and now in doing so I see that my hesitation has come from the fact that the point is so simple I'm reluctant to write it out. But since people as able as you are misled by response deprivation (RD), I advance into the obvious.

Take this example. Parameters are such that if left to its own resources a rat will drink for 300 seconds and run for only 100. We arrange a contingency such that the rat must drink to run. On the face of it, it may seem that the probability view must predict no reinforcement. But that is not true, and in fact no judgment could be made without additional information.

We arrange a contingency in which the rat must drink for 75 units in order to run for 5. These are not the only values that will illustrate my point; any values that will meet the response deprivation condition will illustrate my point; the ones I choose are simply convenient. I outline the trial-by-trial consequence of this 75/5 contingency below.

We see that by trial three, running has become the more probable response, and hence that, from the probability view, running should reinforce drinking. The probability view predicts in addition (1) the trial from which the reinforcement effect should begin, and (2) the ordinal magnitude of the reinforcement effect.

All else equal, the latter should be proportional to the duration of the contingent response that is unexpended, or residual, at the time when the contingent response becomes more probable than the instrumental one. In the present example, that residual magnitude is 85 seconds. If the instrumental requirement were reduced, say from 75 to 50 units of drinking, then the residual running would fall to 75 seconds, and it would fall still lower--to 45 seconds--if the instrumental requirement were reduced further, the 25 seconds, etc. And the reinforcement produced by the contingency should decline accordingly. All of this is a matter of simple arithmetic and I leave it to your quantitative skills to state the matter more formally if you like.

But whether stated formally or informally, the main point is quite simple: it is impossible to realize the response deprivation condition without assuring that the contingent response, though less probable than the instrumental one at the start of the session, becomes more probable before the session ends. The response deprivation condition is no more than a way of using conditioning parameters--instrumental requirement relative to contingent allotment--to arrange a within-session reversal of the response probabilities. Hence, any confirmation of the response deprivation prediction is of necessity a confirmation of the probability view. (In addition, I can show cases where the reverse is not true, and hence that the two positions are not equivalent; but that goes beyond what I want to show here. Here it is sufficient to show merely that, contrary to the impression given by response deprivation, there are no cases in which less probable responses reinforce more probable ones.)

Incidentally, that reverses can be made in probability with a consequent reversal in what will reinforce what is, of course, no novelty. We showed that in the case of run and drink, and in a second evidently less well-known case described in the enclosed reprint (this is not a reversal between two responses but a reversal in the magnitude of the effect that two responses have relative to a common one). The reversal engendered by response deprivation differs only in that it occurs within-, rather than between-, sessions, and of course uses conditioning parameters rather than maintenance ones. How the reversal works is clear enough: the initially more probable event is drained off at a sufficiently greater rate than the less probable one, so that after some point in the session, it becomes the less probable event.

I warned you that it was obvious.

Regards,

David Premack

Ten days later (March 26, 1979), Premack made further clarifications on his argument in a follow-up letter to Staddon:

Dear John:

I'm not too pleased with my recent letter to you, and decided that that "obvious" point can be made clearer. Return to our original example, viz., total expected duration of drink 300 seconds, that of run 100 seconds, and in all cases a contingency such that the rat must drink (for some predetermined duration) in order to run (for some predetermined duration). Let's call these two durations instrumental and contingent time respectively. In my first letter contingent time was 5 seconds and instrumental time was varied--25, 50, 75 seconds. I'll use the same values again, doing the arithmetic out in the open again below.

The important point for our purposes is that an inversion--between the probabilities of the instrumental and contingent responses--occurs on trials 3, 6, and 12 in the three cases respectively. We can use these differences to test the following simple prediction from the probability view: if the contingency is discontinues before the inversion; no reinforcement will take place, irrespective of the total frequency of contingent trials. Thus, if the contingency is discontinues after trials 2, 5, and 11 in cases 1, 2, and 3, no reinforcement should occur.

To show this in an interesting way, we might do the following. Arrange three sessions for case 3, 11 trials per session, a total of 33 trials; seven sessions for case 2, 5 trials per session, a total of 35 trials; and sixteen sessions for case 1, 2 trials per session, a total of 32 trials, making the same prediction of no reinforcement in each case.

From the probability point of view we can predict the trial from which reinforcement should occur, or that if the contingency is discontinued before the inversion no reinforcement should occur; these are two ways of saying very nearly the same thing. But the latter may be a little clearer than the former, or the two together clearer than either alone.

Regards,

David Premack