🚀 go-pugleaf

[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.  (By the way, it's
from a fellow who wanted to know more about my point of view and to whom I
recommended joining the CSG list and "lurking" for a while -- so don't get
out the meat axes -- the scalpels of gentle critique will do.)

As a not so aside aside, this thinking, or something like it, is what PCT
must deal with and eventually reconcile with, integrate, subsume, destroy
or whatever...

Those who don't want to bother with this are free to hit the delete key or
press page down...  :-)

>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.  Richard Herrnstein was a behaviorist (in the Skinnerian
>tradition) who many (in the world of behavior analysis) consider to have
>made nearly as large a contribution to behavior analysis as Skinner
>himself did.
>
>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.
>
>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.
>
>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.
>
>This first example allows us to see that the relative frequency of
>reinforcement given a response is an important dimension in understanding,
>and even predicting, behavior.  This is the source for my assertion that
>the first dimension which effects a consequences ability to act as a
>reinforcer for behavior is the probability (or certainty) of the outcome
>to result given the behavior.
>
>One way that this variable can be "controlled" is to change the schedule
>of reinforcement, given equivalent responses (for example, in many lab
>experiments of the matching law, this has taken the form of bar pressing
>behavior for rats and key pecking for pigeons, with each of two different
>bars or keys with differing schedules of reinforcement available for
>pressing or pecking).  However, this variable also gives us a means for
>capturing the effect of the relative effort required to perform the two
>competing responses.  A response requiring greater expenditure of effort
>than a competing response, when placed on an identical schedule of
>reinforcement, will respond similarly to an identical response placed on a
>"thinner" schedule of reinforcement.  This line of thinking moves us in
>the direction of the flow of units of behavioral energy required to attain
>the reinforcer.
>
>But this isn't the whole picture.  Another characteristic that impacts the
>ability of an outcome to reinforce is the delay of the reinforcement from
>the time of responding (we can't forget the decay of delay).  In my
>previous discussion of the impact of delay, I mentioned that the decay is
>not a linear one.  Research using the matching law suggests that relative
>frequency of responding matches the reciprocals of the delays (given that
>the delays are expressed in the same units of time).
>
>Pr(A) = Ra/Ra+Rb = (1/Da)/(1/Da)+(1/Db)
>
>To illustrate, lets consider an example where 2 equivalent responses, A
>and B, are both on an equivalent schedule of reinforcement, but, with
>Choice A, the delivery of reinforcement (occurrence of the outcome) is
>delayed by 2 seconds, and, with Choice B, the delivery of reinforcement is
>delayed by 4 seconds.  In this situation, we have the following:
>
>Pr(A) = Ra/Ra+Rb = (1/2)/(1/2)+(1/4) = .5/(.5+.25) = .667
>
>Again, according to the matching law, we see that Choice A is preferred
>over Choice B 2/3 of the time.  And, again, if we were to test this out,
>this is essentially what we would find.
>
>The third dimension which effects the ability of a consequence to
>reinforce behavior is the magnitude of the reinforcer.  In my discussions
>of behavior to this point, I have brought up this dimension only in the
>form of discussing whether the outcome is perceived to be positive or
>negative by the performer.  Actually, to be accurate, we would have to
>consider to what extent the outcome is perceived to be positive or
>negative, relative to the outcomes for other, competing behaviors.  The
>more positive the outcome, the greater its ability to attract the
>behavioral response, and the more negative the outcome, the greater its
>ability to repel the behavioral response.  This dimension we could call
>the magnitude of the available reinforcement (m), giving us:
>
>Pr(A) = Ra/Ra+Rb = Ma/Ma+Mb
>
>controlling for our other dimensions (holding them constant).
>
>In order to illustrate this, we need to have some unit of reinforcement.
>This is possible in a lab setting, but it becomes more difficult outside
>of that environment (perhaps we might use some form of currency, but even
>this relationship is not perfectly linear (perhaps it is on some kind of
>logarithmic scale).  For our example here, we can again contrast two
>equivalent responses, A and B, on identical schedules (cancelling out),
>with identical delays (again cancelling out), but with different
>magnitudes of reinforcement.  Choice A gets reinforced with 2 units of
>reinforcement (for example, 2 food pellets, or 4 seconds of pleasureable
>electrical stimulation), while choice B gets 1 unit of reinforcement (for
>example, 1 food pellets, or 2 seconds of pleasu reable electrical
>stimulation).
>
>We would then have the following:
>
>Pr(A) = Ra/Ra+Rb = 2/2+1 = .667
>
>Again, Choice A is preferred 2/3 of the time over Choice B.  And we have
>the source of the third dimension of a consequence that effects its
>ability to reinforce/attract a behavior that I have articulated in
>previous posts, the extent to which the consequence is seen as positive
>(or, in the case of punishing/repelling, negative).  This constitutes the
>magnitude of the consequence.
>
>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)
>
>The matching law was originally articulated in sometime in the 50's or
>early 60's, and has been the focal point of an enormous amount of
>research.  I have tried to illustrate the relationship by providing
>examples of its application to 2 competing responses.  However, the
>research that has been done regarding the matching law has not been
>limited to 2 choices, but has extended the relationship to many competing
>choices with similar success.  And the application of the relationship has
>been explored in areas far outside the animal lab, including consumer
>choice behavior in internet shopping.  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).
>
>I hope that I have been able to demonstrate that the ideas conveyed in my
>posts over the past 6 months have not been made up by me (I am not nearly
>this imaginative), or pulled out of a hat, but rather are based on 50+
>years of research conducted by many different researchers in many
>different contexts.  Most of the information that I have shared regarding
>behavior analysis can be read for oneself in any graduate level text on
>learning and behavior (should you be curious).  If anyone has spotted any
>problems with my articulation of these ideas and concepts, please let me
>know.
>
>This brings us back to the general form of the matching law that I
>originally stated:
>
>Pr(A) = k( Ra/Ra+Re )
>
>and the Digestor model that At articulated in LO21272 in the form of free
>energy:
>
>/_\F(un) = -/_\n*mSU*[E(mSY, Msy) - E(mSU, Msu)]
>
>where
>F = free energy
>n = basic building blocks of system (ion pairs)
>m = size of the crystal - quantitative summary in units of lowest orders
>of the surroundings (e.g., the number of ion pairs - the basic building
>blocks - that have been digested by the crystal, making up its size).  The
>variable m is expressed in n units.
>
>M = qualitative assessment of the perfection of the lattice structure/the
>regular pattern of arrangement of ions in the crystal.
>
>E = energy
>
>I would propose that the matching law is the equivalent of the Digestor
>model as it would apply to behavior with the following "translation":
>
>The variable n, in the translation, is the variable k in the general
>matching law equation converted into units of behavioral energy (the basic
>building blocks of the system of behavioral energy).
>
>The variable m is the proportion of behavioral energy allocated to the
>various potential responses (attracted by the competing "crystal seeds" -
>mSY and mSU), or the measure of the size of the "behavioral crystal".
>
>The M variable for behavior is a perfection measure of the "bond" between
>the behavioral response and its consequences, consisting of the three
>dimensions that I have articulated above - ratio of reinforcement to
>response, delay of reinforcement, and magnitude of reinforcement.
>
>The combination the m variable and the M variable for behavior form the
>Madelung forces which attract behavioral energy towards a potential
>response (yes, this explanation is a bit teleological).  On an individual
>level, the consequences/reinforcement for a given behavioral response form
>the "sy" portion of the equation, and the consequences for all other
>potential responses (the extraneous reinforcement in the matching
>relationship) form the "su" portion of the equation.
>
>Or maybe the Digestor model is the matching law for behavior extrapolated
>to the world of crystallography.  Is this obfuscation?  IMHO, I don't
>think so. In both cases, the relationships were uncovered independently.
>Which relationship was "discovered" first?  What should we do with this?
>
>IMHO, the efforts that At has made to show the difference between
>spontaneous changes and nonspontaneous changes and empowered systems, the
>attempt that Leo Minnigh made to illustrate how the digestor model might
>be applied in an organizational setting (LO21360), and the wrestlings of
>Winfried Dressler to reconcile the model with his own thinking are, at the
>very least, excellent examples of the learning process that we have been
>able to witness, and, at most, important forays into a world that may have
>enormous impact on our understanding of organizations, learning, and their
>interaction.
>
>With the Digestor model/Matching law, we have a lens through which we may
>understand evolutionary change that results from low entropy production in
>systems close to equilibrium.  We have a lens for understanding CONTINUOUS
>changes and improvements.  With the Brusselator model, and the parallels
>that I have attempted to convey in the relationship between behavior and
>its consequences, we have a lens for understanding DISCONTINUOUS,
>revolutionary changes and improvements that result from high rates of
>entropy production in systems far from equilibrium.  To bring this home to
>roost with a thread from months ago, these models together give us a means
>for understanding the process of CONTINUAL improvement (advocated by
>Deming).  We really haven't gone that far off the course set for us by
>Senge, Forrester, Deming and others.  But we are extending the line beyond
>what has been drawn before.
>
>Which begs another question:  At what point does
>generalization/extrapolation of any theory become obfuscation?  I'm not
>sure that the conclusion can be drawn with foresight.  As far as I can
>tell, the difference lies in the utility of the model.  Maybe after the
>fact this differentiation can be made, but if we are indeed after the fact
>in this case, and these ideas have been conclusively disproven, please
>show me where the evidence is so that I can quit wasting my time.
>
>Hypotheses generated by the theory/model must be articulated in a way that
>they can be tested and disproven.  From what I have read on both sides,
>these ideas have withstood much rigorous examination and been shown to be
>robust.  I am not an expert in the physical sciences.  The Ph.D. that I
>hold is not in physics, or chemistry, or biology.  But I have read
>numerous texts on chaos theory, relativity, quantum physics, and 3 books
>by Ilya Prigogine on thermodynamics, entropy and entropy production.  The
>accounts that At has given of these ideas are representative of what I
>have read in these other sources.  I have read numerous works by Skinner
>and Herrnstein and numerous other behavioral theorists.  I have read
>Senge, and Forrester and other systems thinkers.  I believe that if anyone
>else has studied in these areas, they would vouch that my portrayals of
>these areas are representative as well.
>
>I, for one, find these parallels to be compelling, and I have invested a
>considerable amount of time articulating the connections that I have made
>for others to examine.  To me, the obvious next step is to see how much
>further the model can be extended.  Is this really a step into oblivion?

Regards,

Fred Nickols
Distance Consulting "Assistance at A Distance"
http://home.att.net/~nickols/distance.htm
nickols@worldnet.att.net
(609) 490-0095