Ratio models and reinforcement theory

[From Samuel Saunders (950702:0105 EDT)]

A number of recent posts on the list have suggested that there is some mystery
in the perceived reluctance of EAB to address the "unpredicted" relation between
rate of reinforcement and rate of response in ratio schedules. While I don't
want to compete with Bruce Abbot for the job of defender of the straw man, I
think a review of the history of this topic on this list may be in order to
provide some perspective.

Last fall, there was a discussion of the "matching law". Some modeling was
attempted, but the results generally appeared ad hoc, and were very brittle to
minor changes in condition. Some effort was expended in simplifying the problem
by considering single variable interval schedules, rather than the pairs on VI
schedules used in the attempts at "matching law" models. It became clear that
modeling VI schedules was a problem for PCT, due to a lack of essential data. A
switch to ratio schedules was suggested, and Bruce Abbott volunteered to collect
some data from rats, since even for ratio schedules the available data were not
complete from a PCT perspective. This discussion then remained quiescent for
several months, while Bruce was unable to find the time to proceed with the
experiments. Recently, with the possibility of proceeding to data collection,
Bruce again began posting about models for ratio schedules, and presenting data
which might provide some hints about what could be expected. That is the
context in which the present consideration of ratio schedules arose.

The discussion has been about ratio schedules because this is a PCT group, and
ratio schedules appear to provide a relatively simple situation for PCT. For
EAB, however, this is not the case. From the EAB point of view, VI schedules
should provide the clearest view of the relationship between reinforcement
frequency and response frequency. This follows from the lack of constraints on
responding in VI. The animal's response rate can vary substantially without
having a significant effect on reinforcement rate, so response rate is "free to
vary with response strength" , where response strength is a function of rate of
reinforcement. Ratio schedules are constrained, since there is a direct
relationship between response rate and reinforcement rate, and thus response
rate would not be expected to be "free to vary" with "response strength". Given
this analysis, finding the recently considered effects in ratio schedules would
hardly be a large red flag for EAB theorists, particularly when the expected
relationship continued to be supported with VI schedules, the "appropriate"
experimental context in which to examine such effects from the EAB view.

It may turn out that a reinforcement treatment _cannot_ be developed to account
for performance on ratio schedules, or requires many ad hoc adjustments. It may
turn out that a PCT treatment can account for performance on both ratio and
interval schedules. At that point a clear choice would be indicated between the
two approaches, and there would be reason to rail against the intransigence of
EAB zealots who refuse to see the light. That time has not yet come.

//Samuel Spence Saunders,Ph.D.