Concurrent random-interval schedules and the matching law.
Random-interval schedules still produce under-matching, so plan for an exponent around 0.8, not 1.0.
01Research in Context
What this study did
Innis (1978) tested pigeons on two random-interval (RI) schedules running at the same time.
Birds could peck left or right keys. Each side paid off on its own clock.
The team asked: do the birds still follow the matching law when both clocks are random?
What they found
The birds did not match perfectly. The exponent a landed near 0.84, not 1.0.
Random timing alone did not push the exponent up or down in a clear way.
How this fits with other research
Davis et al. (1972) saw the same under-matching earlier with extra VI food. The new data say random clocks keep the same bend.
Vyse (1986) later showed wild wagtails do match in nature. Lab pigeons fall short, but real birds in a field obey the rule.
Rose et al. (2000) found the k value moves when sucrose strength changes. That clash warns us: fixed parameters in the law may be wishful thinking.
Why it matters
Expect less-than-perfect matching when you use RI schedules in a concurrent setup. Build the 0.8 exponent into your prediction, not 1.0. If you switch reinforcer size or type, recheck the curve—parameters can drift.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Plot your client’s response split across two RI options; fit the line with a 0.8 exponent, not 1.0.
02At a glance
03Original abstract
In Experiment I, a group of eight pigeons performed on concurrent random-interval schedules constructed by holding probability equal and varying cycle time to produce ratios of reinforcer densities of 1:1, 3:1, and 5:1 for key pecking. Schedules for a second group of seven were constructed with equal cycle times and unequal probabilities. Both groups deviated from simple matching, but the two forms of the schedules appeared to produce no consistent patterns of deviation. The data were found to be consistent with those obtained in concurrent variable-interval situations. The parameters of the matching equation in the form of Y=k X(a) were estimated; the value of k was unity and a was 0.84. In Experiment II, six pigeons were exposed to two conc RI RI schedules in which one component increasingly approximated an FI schedule. The value of k was not 1.0. Concurrent RI RI schedules were shown to represent a continuum from conc FI VI to conc VI VI schedules. The use of the exponential equation in testing "matching laws" suggests that a<1 will continue to be observed, and this will set limits on the form of new laws and the assumed or rational values of the component variables in these laws.
Journal of the experimental analysis of behavior, 1978 · doi:10.1901/jeab.1978.30-301