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Synapsia

The Matching Law

11/27/2024

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Rodin's The Thinking with a though bubble that states the matching law equation
From Wikipedia: If R1 and R2 are the rate of responses on two schedules that yield obtained (as distinct from programmed) rates of reinforcement Rf1 and Rf2, the strict matching law holds that the relative response rate R1 / (R1 + R2) matches, that is, equals, the relative reinforcement rate Rf1 / (Rf1 + Rf2).
The Matching Law states, in essence, that an organism will do what has been most reinforcing to them in the past.  That is, generally either what feels good when they do it - either because they have received something from the world (cake, kisses, money), - or because they have removed some discomfort (cold air, delaying a task, uncomfortable social setting).
 
The matching law is at once an incredibly powerful insight into human behavior and a deceptively simple notion.  Because while choosing to eat cake over a rotten fish is easy to understand, much of our reinforcement in life is far more complex and nuanced.  Take for instance, a person who commits suicide.  The matching law states that their history indicates that in the behavior of jumping off a cliff they anticipated more reinforcement than in doing anything else.
This would be a case of negative reinforcement, in which an attempt was made to feel better by relieving or removing some discomfort.   But what was so discomforting about being alive?  If there was no physical discomfort being endured, the pain was psychic, some kind of emotional torment.  And when we try to look at their life and biology, we might find a genetic mechanism by which the chemicals needed for joy, optimism, etc. were not being sufficiently processed.  But we might also find a history of trauma, of anti-social relationships, etc.  All of these become so numerous and tangled that the matching law almost seems irrelevant.
 
But it isn’t!  Our behavior must follow its declaration: we move towards comfort and away from discomfort.  An analysis of behavior attempts to identify the cycles of reinforcement (punishment too, but we’ll keep things simple here), as they play out across 4 parameters: one’s present motivational state (how much they want or do not want something, in this case relief from psychic pain) + the environmental stimuli (the world, the cliff, thoughts), + the behavior (jumping off a cliff) + the consequence (relief of suffering).  Our analysis takes what is sometimes called a “molar” view of behavior.  That is, an organism’s every behavior never exists in isolation, but is a dynamic, ongoing interaction between our physical body & mind, our environment, and what happened after all prior behaviors.
 
Some behaviors have died out (gone extinct), or have been replaced by other behaviors.  E.g. I used to try and feel good by getting negative attention from peers by acting goofy, but I grew older and found that I felt better when I learned to behave in ways that were more honest, thoughtful and productive when in social settings.  When I did that, I discovered new avenues of joy and comfort – new “reinforcers”.  (I think girls started to take me seriously – and sex is just about as reinforcing as anything, aside from maybe heroin).
 
Three classic critiques of behaviorism are as follows: 1. it is mechanistic and dehumanizing, 2. it is reductionist, and 3. it is inadequate for explaining complex human behavior.
 
All 3 are quite true in a way; behaviorism looks at the behavior, not the “whole human”, it looks for dependent variables in a systematic way that requires empirical humility, and it does not seek to explain what it cannot measure.
 
However, this is also its great strength.  Because for millennia humans have relied on myth, superstition, and intuition to determine why people do what they do.  Or, in more modern times, to develop elaborate (however often untested) theories about it.  To this day it is popular to talk about “free will”, “personal responsibility”, “common sense”, or “the problem of consciousness”.  Yet these are each mostly incoherent terms. 
 
“Free will” would seem to require acting without influence of neither one’s phenotypic makeup or one’s past learning history of the world.  This is a notion as mystical and fanciful as a unicorn, in that according to the laws of nature and determinism, no such thing is possible (I’ll avoid the notions of quantum indeterminacy here, but suffice it to say that the answer is in the name: appealing to indeterminacy to explain why someone does something is a contradiction in terms; one might as well wear a banana on their head as a hat because the position of the electrons in their brain’s sodium can’t be measured by speed and position simultaneously).
 
Personal responsibility can either refer to social rules or one’s determination of their own actions.  Since the latter is an incoherent notion (see paragraph above), the former is entirely compatible with a behavioral, determinist account: rules are essentially a learning history of relations between stimuli that don’t require direct experience.  That is, I avoid a rock flying towards me because I have experienced being hit in the head by objects and thus have been reinforced by (learned to) avoid them when they come at me.  But if I work in a rock crushing yard, I follow the rule of wearing a hard hat because even though I have not had one drop on me yet, I have learned (the rule) that it is possible and that my hat will protect me from discomfort (planning for negative reinforcement).  Our lives are filled by rules that are continually providing reinforcement as they guide us towards comfort and away from discomfort.
 
Common sense is simply my repertoire with certain stimuli.  I have experienced a set of events in the world, learned rules about them, and follow them according to how strongly I have thus far been reinforced.  A man who doesn’t wear a jacket in the snow lacks common sense” simply because – as the matching law states – he has not developed strong enough relations between the contingent event of being cold outside or the non-contingent event of putting on a jacket before leaving.  There can be all manner of reasons for this – often simply due to chemical mechanisms such as those that result in ADHD, in which attention to irrelevant stimuli were more reinforcing; think of the absent-minded professor who is daydreaming equations and forgets to put on his pants.  A lack of “common sense”, or “sense that has been directed elsewhere?
 
The problem of consciousness, it seems we often forget, first requires a definition.  What do we mean by “consciousness”?  Is it simply being alive and experiencing the world?  Bacteria do that.  Is it thinking about and planning for events?  Many animals do that, and many animals “reason” or learn from their local species’ culture – this is simply a learning history of stimuli relations; If I lick this stick and put it in this big hole and pull it out it will be lined with delicious (reinforcing) ants.  Is consciousness communication?  Skinner provided a very sophisticated taxonomy of verbal behaviors that a community develops by reinforcing vocal and gestural responses to stimuli, such as requesting, labeling, receptive identification and imitation.  While we can in no way claim to understand or be capable of explaining every magnificent manifestation of what we commonly call “consciousness”, much less the particular cellular mechanisms or networks of synapses in the brain that conspire to produce them, our understanding of the principles of behavior and learning – not in the least the matching law – has far more explanatory power than that with which we derive without it.
 
The simple idea that what any of us do, at any time of day, can be largely explained by this simple law: that we do what has brought us most comfort or relived most discomfort in the past, has a profound possibility of opening us up to treating each other with the kind of recognition, honor, sympathy, and respect that only the most holy and sainted among us might be imagined to display.  Your mean boss.  The bad driver on the road.  Your annoying stepmother, the playground bully, the thief, the murderer, the rapist, the pedophile – the very worst people in the world all have learning histories that tell a story of the interaction between their genes and their environment.
 
But so too the successful entrepreneur, or Nobel prize winner, or star athlete, or president, wise man, genius or anyone else who seems to display great aptitudes or attributes.  Man is a messy mixture of hormones, brain cells and various organs, sloshing around from meal to meal, relation to relation.  His world is a mess of privileges and disadvantages, social structures and lucky breaks. 
 
Yet the one thing he is not is an actor outside of these things.  And that one simple truth, born out in countless scientific studies – if not simple observation – reminds us that we are all only human (homo sapiens), nothing more.  We are no different than all the kingdoms of life from which we share a common ancestor.  We evolved on the same planet, from the same molecules, atoms, amino acids and fundamental forces of the universe.  Subject to electromagnetic radiation, the strong and weak forces, gravity and the laws that they each must obey.  So, to must we obey them. 
 
So, do we have choice?  What is our purpose if we are nothing but highly advanced automatons, trapped in an endless war with entropy?  To the former the answer is yes, and no.  We make choices, but the matching law determines what they will be.  We feel as though we are making them because society has always described our lives as such, and our intuition that we are acting without any cause outside our own “will” arises from our severely limited cognitive and observational capacity.  We can only ever hope to process a handful of the almost limitless physical processes and environmental interactions that have made us who we are and are presently operating on us.
 
As for our purpose, this is not for us to decide alone.  For as products of our environment, we cannot but act in ways in which we have learned.  As a species, we have applied our evolved physical and cognitive capabilities to develop incredible things: families, social structures, beliefs, religions, reasons, science, governments, countries, AI algorithms that we are at the cusp of being unable to comprehend.  The vast majority of what we do is obscure to us – we just do it.  We find enjoyment, make friends, find lovers, raise children, go to work – all of this not only creates meaning but is meaning.  That is, it brings us comfort and avoids discomfort, even if we often don’t really understand why.
 
Society has great power to make us act and think in ways in which its complex systems have designed.  Many rules we follow lead us to truth, while others towards falsity.  But the matching law is there to remind us that while we may not know why specifically, we know why generally. And while it is only a starting point to understand and analysis ourselves and those around us, it is a point at which we fail to recognize at our peril.
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