[From Chris Cherpas (951027.1626 PT)]
[re: > Bill Powers (951027.0830 MDT) re: >> Chris Cherpas (951026.1026 PT)]
cc:
Thanks for the PCT 101. I just wanted mention something about the
matching law...
bp:
When you try to get more out of a system of equations than there is in
it, you start committing mathematical blunders. Herrnstein's matching
law for two simple ratio schedules says
b1/(b1 + b2) = r1/(r1 + r2)
cc:
Matching is based on interval schedules. With concurrent ratios, you usually
just get exclusive responding on the smaller ratio, which, of course,
still yields the matching law, since it's based on obtained, not
programmed, rates of reinforcement. If b1/r1 is the smaller ratio, you
get: b1/(b1 + 0) = r1/(r1 + 0) ==> 1 = 1. Of course, the matching law
itself doesn't tell you if the exclusive preference would be for the
smaller or the larger ratio!
bp:
This informative-looking expression reduces to
b1/r1 = b2/r2
But b1/r1 is simply m1, the ratio set by the apparatus for schedule 1,
and b2/r2 = m2 for the other schedule. Thus we conclude,
m1 = m2.
Therefore Herrnstein's matching law for this case says that the two
ratios are identical.
cc:
Viewed this way, matching is impossible in concurrent ratios unless
the ratios programmed are identical. If one alternative is FR10
(10/1) and the other is FR20 (20/1), can 10/1 = 20/1?
bp:
That is all it means: a tautology. If there is
matching, there is matching, and the matching is strictly of one
schedule to another. The organism's behavior is irrelevant.
cc:
The matching law is a tautology (e.g., see Rachlin, 1971). What
matches is local reinforcement rates (at steady state); matching
theory requires "melioration" theory to explain why you get it. As
for matching, per se, Rachlin (1982) has said:
"...it is only a small step to argue that animals match when
asleep in the chamber, or, for that matter, when dead." (p551)
However, as Rachlin (1973) points out, if the first law of
thermodynamics were found to be violated, one would assume
something wrong with the procedure or measurement, not the
(tautological) law.
By the way, in my post of (951026.1026), I erroneously referenced
Commons, Herrnstein, and Rachlin (1987) when it should have been
(1982).
Regards,
cc