🚀 go-pugleaf

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

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

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. 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. 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.

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

Best,

Bill P.