Concurrent variable-interval schedule performance: Fixed versus mixed reinforcer durations.
Mixed reinforcer durations break the matching law, so watch time as closely as rate.
01Research in Context
What this study did
The team used pigeons on two side-by-side keys. Each key paid off on its own variable-interval timer.
Sometimes both keys gave the same food time. Sometimes the times mixed within the session. The birds chose freely.
What they found
When food times stayed the same, choice followed the matching law. When times mixed, the law fell apart.
Birds still shifted with the average duration, but the tidy math no longer fit. Duration noise breaks the equation.
How this fits with other research
Macdonald et al. (1973) and Frederiksen et al. (1978) showed clean matching on the same VI setup. Davison et al. (1984) adds the boundary: mix the durations and matching collapses.
Hinson (1988) later kept the mixed durations and also changed overall rate. Choice moved even farther from prediction, proving the problem is bigger than duration alone.
Hall (2005) stepped back and split ‘earning’ from ‘getting’. That paper gives you a new equation that covers both older clean data and the messy 1984 data.
Why it matters
If you run concurrent reinforcement in the classroom, keep reinforcer length steady within each alternative. When you must vary it, expect choice to drift off the textbook curve. Track time, not just count, and be ready to adjust your ratios.
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02At a glance
03Original abstract
Six pigeons were trained on concurrent variable-interval schedules. Two different reinforcer durations were arranged on the left key, and which of these was delivered was determined probabilistically. A single reinforcer duration was arranged on the right key. In Parts 1 and 3 of the experiment, the probability of the left-key reinforcer durations (1 and 7 seconds in Part 1; 3 and 10 seconds in Part 3) was varied from 0 to 1, keeping the schedules constant and the right-key reinforcer at 3 seconds. Response allocation to the left key fell as the probability of the shorter left-key reinforcer duration was increased. In Part 2, one left-key reinforcer duration was 3 seconds and the other was varied from 0 to 10 seconds, while again the schedules and right-key reinforcer duration (3 seconds) were kept constant. Left-key response allocation increased as the varied reinforcer duration on the left key increased. An extension of the generalized matching law failed to provide a good description of response allocation in these procedures. In Part 4, the left- and right-key reinforcer durations were 3 seconds and the variable-interval schedules were varied. Response allocation was well described by the generalized matching law. Part 5 arranged equal variable-interval schedules on the left and right keys, 3-second reinforcers on the right key, and the left-key reinforcer durations were varied from 1 to 10 seconds. The relationship between the log response and reinforcer-duration ratios was nonlinear. The effects of varying reinforcer durations in concurrent schedules cannot be described using the generalized matching law with constant parameters. It is suggested more generally that this quantitative relation may not describe performance either when reinforcing situations differ in duration (e.g., with delayed reinforcers) or when response requirements differ in duration.
Journal of the experimental analysis of behavior, 1984 · doi:10.1901/jeab.1984.41-169