🚀 go-pugleaf

[From Bruce Abbott (990507.0955 EST)]

>Bill Powers (990506.2-004 MDT) --

>>Bruce Abbott (990506.1715 EST)

>>Sorry, Bill, but I must remind you once again that the matching law does not
>>and was never meant to describe the relationship between relative rate of
>>responding and relative rate of reinforcement on concurrent ratio schedules.

>But in the post to which I replied that is how it was described.

Please cite the relevant description.  I don't see it.  Where does it say
that the matching law was developed to describe performance on concurrent
ratio schedules?

>That's
>what the equations say, when you reduce them to simplest form. I don't care
>what they were "meant" to describe.

_What_ is what the equations say?  You're being vague.  The equations say
that the ratio of response to reinforcement will be the same across
schedules.  _YOU_ (not the equations) state that this cannot happen if the
_schedules_ are different.  This is correct only if you assume ratio
schedules, but the matching law does not apply to performance on concurrent
ratio schedules.  When applied to, say, concurrent VI VI, what the equations
say not only _can_ happen when the schedules differ, it _does_ happen.

>Many a person has foundered because of
>not realizing what his own mathematical manipulations imply. Perhaps in
>reality there is some other relationship involved, but my transformations
>of the cited equations are exactly correct, and the original set of
>equations says the same thing -- identically the same thing -- that my
>final version does: Ra/rA = Rb/rB. Unless you can repeal mathematics, no
>other conclusion is possible.

Yeah, and my transformations of Boyle's law are exactly correct, too, but
that doesn't make the law apply to liquids.  The problem isn't with your
math, it's with your assumption that the equations are supposed to say
something about responding on concurrent ratio schedules.  They aren't, and
they don't. I don't know how to state that any more clearly.  So long as you
persist in assuming that the matching law was designed to account for
responding on concurrent ratio schedules, you are going to draw conclusions
which, though accurate given that assumption, do not hold for those cases to
which the matching law actually applies.

>The best I can say is that whatever Herrnstein was trying to express, his
>equations don't say it.

The fault isn't with Herrnstein or his equations.  The problem is
exclusively with your attempt to apply the matching law where it does not apply.

>I think I know what Herrnstein was trying to say. He wanted to say that
>given a choice of keys with different schedules, the animal will devote the
>most time to the schedules that yield the greatest average ratio of
>reinforcement to behavior.

No.  What Herrnstein's equations state is that the relative rate of pecking
at a key will match the relative rate of reinforcement delivered on the VI
schedule associated with that key.

>He may have thought that his equations were
>saying this, but they were not. Instead, his equations say that the yield
>of reinforcements per unit behavior is the same on all keys.

That's just another way of saying the same thing.

>He simply
>didn't know how to write out, mathematically, the idea he was trying to
>express. What he did write down says something very different from what he
>wanted to say. And evidently he wasn't enough of an algebraist to realize
>that his complex-looking forms can actually be reduced to a much simpler
>form that make his mistake easy to see.

The only one doing any blundering here is William T. Powers.

>I suspect that the mistake goes deeper than this, but the proof or disproof
>would take more thought than I have given it.

It doesn't take much thought -- I've already explained what you're doing
wrong (for the second time now in two posts).  Are you going to persist in
ignoring that problem?  For what purpose?

Regards,

Bruce