Concurrent performances: reinforcement interaction and response independence.
Two choices, two pay rates: relative behavior equals relative payoff, as long as you count both earning and collecting time.
01Research in Context
What this study did
CATANIA (1963) ran pigeons on two levers at once. Each lever paid off on its own variable-interval clock.
The birds could switch any time. The team wrote a simple equation that linked peck rates to grain rates.
What they found
The equation fit the data. Relative pecks matched relative pay-offs. This became the first clean test of the matching law.
No extra rules were needed. Two levers, two clocks, one straight line.
How this fits with other research
Macdonald et al. (1973) kept the same two-lever set-up and still saw matching. They showed the rule works inside each schedule and across schedules, giving the law more reach.
Frederiksen et al. (1978) added change-over data. They kept the 1963 baseline but added new math for switch timing. The old fit stayed; the new math just explained extra detail.
Hall (2005) looked like a clash at first. When the two levers also differed in how long birds had to wait to collect food, the simple ratio failed. The author added an 'earning vs. obtaining' term and the line fit again. The 1963 form still works once you include both parts of the deal.
Why it matters
When you set up concurrent reinforcement for a client—two tasks, two reward rates—start with the 1963 ratio. If behavior drifts, check whether one reward is slower to collect or harder to cash in. Add that second term and the matching line returns. You get a quick visual test for fair reinforcement in classrooms, clinics, or homes.
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Join Free →Plot the client’s response split against the reinforcer split; if points fall off the diagonal, time how long each reward takes to collect and add that to your ratio.
02At a glance
03Original abstract
When a pigeon's pecks on two keys were reinforced concurrently by two independent variable-interval (VI) schedules, one for each key, the response rate on either key was given by the equation: R(1)=Kr(1)/(r(1)+r(2))(5/6), where R is response rate, r is reinforcement rate, and the subscripts 1 and 2 indicate keys 1 and 2. When the constant, K, was determined for a given pigeon in one schedule sequence, the equation predicted that pigeon's response rates in a second schedule sequence. The equation derived from two characteristics of the performance: the total response rate on the two keys was proportional to the one-sixth power of the total reinforcement rate provided by the two VI schedules; and, the pigeon matched the relative response rate on a key to the relative reinforcement rate for that key. The equation states that response rate on one key depends in part on reinforcement rate for the other key, but implies that it does not depend on response rate on the other key. This independence of response rates on the two keys was demonstrated by presenting a stimulus to the pigeon whenever one key's schedule programmed reinforcement. This maintained the reinforcement rate for that key, but reduced the response rate almost to zero. The response rate on the other key, nevertheless, continued to vary with reinforcement rates according to the equation.
Journal of the experimental analysis of behavior, 1963 · doi:10.1901/jeab.1963.6-253