The concurrent reinforcement of two interresponse times: the relative frequency of an interresponse time equals its relative harmonic length.
Pigeons allocate responses by harmonic length under concurrent VI, but humans don’t—plan for species bias.
01Research in Context
What this study did
Killeen (1969) worked with pigeons on a two-key setup. Each key paid off on its own variable-interval schedule.
The birds could choose which key to peck. The team tracked how often each inter-response time showed up.
What they found
The birds’ relative frequency of each inter-response time matched its relative harmonic length. This held true on both one-key and two-key arrangements.
In plain words, the pigeons spread their pecks in the exact math ratio the schedules called for.
How this fits with other research
Killeen (1970) is the direct sequel. Same lab, same birds, next year. It shows that once you hit about 20 reinforcers per hour, adding more payoff does not shift the IRT split any further.
Thomas (1974) seems to disagree. Humans on the same concurrent VI schedules deviate from matching by 15–20%. The clash is only about species, not method. Pigeons match like calculators; people match with error.
Lattal (1974) widens the picture. It moves the matching law from food payoff to shock reduction. Response rates still follow the same equation, proving the rule works for avoidance too.
Why it matters
If you run concurrent reinforcement with animals or early learners, expect the harmonic rule to predict response splits. When you switch to humans, build in a 15% bias cushion. Use Killeen (1969) as your baseline, then adjust with the 1970 rate ceiling and the 1974 species warning. Check your payoff rates first; extra reinforcers past 20/hour buy little extra change.
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02At a glance
03Original abstract
The relative lengths of two concurrently reinforced interresponse times were varied in an experiment in which three pigeons obtained food by pecking on a single key. Visual discriminative stimuli accompanied the two time intervals in which reinforcements were scheduled according to a one-minute variable-interval. The steady-state relative frequency of an interresponse time approximately equalled the complement of its relative length, that is, its relative harmonic length. Thus, lengths of interresponse times and delays of reinforcement have the same effect on the relative frequencies of interresponse times and choices in one-key and two-key concurrent variable-interval schedules, respectively. A second experiment generalized further the functional equivalence between the effects of these one-key and two-key concurrent schedules by revealing that the usual matching-to-relative-immediacy in two-key concurrent schedules is undisturbed if reinforcement depends upon the occurrence of a response at the end of the delay interval, as it does in the one-key schedules. The results of both experiments are consistent with a quantitative theory of concurrent operant behavior.
Journal of the experimental analysis of behavior, 1969 · doi:10.1901/jeab.1969.12-403