🚀 go-pugleaf

[From Dick Robertson,990507.0747CDT]

[From Fred Nickols (990505.1740 EDT)] --

Here's another snipped from the LO list.  I am particularly interested
in
how Bruce A and Bill P will comment on this posting.

>I would like to start off this contribution by introducing the work of
>Richard Herrnstein (who is now deceased), and his matching law for
>behavior.
>
>Herrnstein was able to show in numerous settings and contexts that the
>probability of a given behavioral response was directly related to the
>availability of reinforcement for the behavior (in relation to the
>availability of reinforcement available for competing behavioral
>responses).  This relationship that he articulated and demonstrated has
>been replicated by many other researchers as well, and forms the
>foundation of much of what I have written about over the past 6 months.

Is this true for each and every person, or do the results reflect the
averages of group of subjects?
If the latter, what was the range of individual actions that were pooled
in the so-called findings?
Third, is the point being made here substantially different from the
common-sense belief that "people are
more likely to do what they get rewarded for than what they don't get
rewarded for?  If so, how?
>
>Herrnstein's matching law, in its general form, can be expressed in the
>following equation:
>
>Pr(A) = k( Ra/Ra+Re ) Where
>
>Pr(A) = probability of behavioral response A
>k = highest # of possible behavioral responses available (total # of
responses)
>Ra = Reinforcement experienced for response A
>Re = Reinforcement experienced for extraneous behavior (behavior other
>than the response of interest)
>
>This relationship, has been reliably demonstrated to account for over 90%
>of the variance in responses. One point of interest, this relationship is
>not necessarily a reinforcement maximization rule, and, at times, will
>predict patterns of behavioral response that are counterintuitive.
>
>In order to further explain, allow me to illustrate the matching law first
>in the simplest of settings.  The simplest expression of the matching law,
>modeling a choice between 2 possible behavioral responses, is as follows:
>
>Proportion of responses on A = Responses on A/ (Responses on A + Responses
>on B) = Reinforcements on A/(Reinforcements on A + Reinforcements on B
>
>or
>
>Pr(A) = Ra/Ra+Rb = rA/rA+rB
>
>[Host's Note: Hmm... I think there should be (..) in the denominators here
>and in the similar fractions below? ...Rick]
>
>giving us the proportion of responses which will be accounted for by
>response A.
>
>To give an example, we can place two schedules of reinforcement against
>each other and see if the relationship expressed in the equation holds
>true (it does).  So if we had a constrained choice between two equivalent
>responses A and B, with choice A being reinforced on an VR3 schedule, and
>choice B on a VR6 schedule (see LO20774 for an explanation of schedules of
>reinforcement), we can plug these values in the equation and see what
>split of responding might be expected.
>
>Pr(A) = (1/3)/(1/3)+(1/6) = .667
>
>So we would predict that choice A would be preferred over choice B by a
>ratio of 2:1 (choice A would be chosen 66.7% percent of the time).  And,
>as it turns out, this is very consistent with what has been demonstrated
>empirically.  Notice that the prediction isn't in line with a maximization
>prediction which would predict that Choice A would receive all of the
>responses, resulting in the maximum possible reinforcement.

OK so it becomes clear that so far we aren't talking about people, but
about rats pushing feed levers, and the question is why don't they
always push the lever that gets a food pellet in half the time, right?
Again we
come to the question, do all the rats follow this 2/3 rule?

On the couple of occasions when I have allowed myself to go along to a
slot machine place, I have sometimes put my nickel in one or more
adjoining slots to the one I was feeding mostly, to  see whether the
payoff was
better there.  Is that similar to, or different from, what the rats
were  doing
when they diverged from the "maximiation prediction?"
>
>Another example:  Choice A on a VR4 schedule and Choice B on a VR11
>schedule
>
>Pr(A) = (1/4)/(1/4) + (1/11) = .25/(.25 + .09091) = .733331
>
>or, Choice A would be chosen 73.3% percent of the time and Choice B chosen
>the remaining 26.7% of the time.

How long did it take for a rat to figure out the different payoffs of
the different choices? And what were they doing on the way to that
knowledge?

>....
>
>So we have the following three dimensions:
>
>1) A measure of effort in the form of the frequency of reinforcement given
>a response (the probability/certainty of reinforcement.
>
>2) The delay of the occurrence of the reinforcement from the occurrence of
>the behavior
>
>3) The magnitude of the reinforcer (extent to which it is perceived as
>positive or negative).
>
>Giving us the following equation for the matching law given 2 competing
>responses, A and B:
>
>Pr(A)= Ra/(Ra+ Rb) =
>(rA*(1/Da)*Ma)/(rA*(1/Da)*Ma) + (rB*(1/Db)*Mb)
>
...
> And the application of the relationship has
>been explored in areas far outside the animal lab, including consumer
>choice behavior in internet shopping.

This might be interesting.  Could we see some details?

> The system becomes more and more
>complex as we extrapolate into "reality", but the relationship has
>continually demonstrated its utility (does this make me a pragmatist? ;-).
>Using the matching law, we can then begin to apply the lens to the world
>around us and seek to understand many behaviors that are seemingly
>"irrational" (which I would propose falls closely in line with a
>reinforcement maximization model, as opposed to a matching model).

This is not clear to me here; do you mean the maximization model would
seem to be the "rational" one and the matching model would seem to be
the "irrational" one?  Also, "seeking to understand many behaviors..."
is a
powerful stimulant to me, whether we are talking about rational or
irrational, but to say that many studies have confirmed that real
organisms follow
the matching law in many circumstances does not qualify as _explanation_
in
my vocabulary.  I would call it establishing (a) phenomena (-on), and
that
is well and good.  Science begins, I believe, with curiosity about the
underlying workings of interesting phenomena, but _explanation_ requires
the elucidation of how the phenomena  work, or in this case, WHY rats or
humans follow a matching rule rather than a maximization rule in the
cases in
question.
>
>Fred Nickols


Best, Dick R.