Concurrent choice: Effects of overall reinforcer rate and the temporal distribution of reinforcers.
Exponential VI schedules make choice follow reinforcer ratios more closely than arithmetic ones, but only up to a point.
01Research in Context
What this study did
The team set up two VI schedules side by side.
They compared exponential spacing of reinforcers with plain arithmetic spacing.
Pigeons pecked for grain while overall reinforcer rate was changed across sessions.
Each bird served as its own control in a single-case design.
What they found
Birds showed undermatching: response ratios were flatter than reinforcer ratios.
Exponential VI schedules produced steeper matching slopes than arithmetic ones.
When total reinforcers per hour rose, sensitivity did not climb in a straight line.
Instead, it first rose, then fell, showing a humped curve.
How this fits with other research
Williams (1971) saw a power-function slope of 0.5 under FI-VI schedules. Rapport et al. (1996) now show the slope itself can be stretched by how the VI is built.
Leslie (1981) found local response rate tracks local reinforcement probability. The new data say the global shape of the schedule also tunes choice.
Wallander et al. (1983) showed deprivation bends matching. Here, overall reinforcer rate bends it too, linking two levers you can pull in one equation.
Why it matters
When you run concurrent schedules, the math inside each VI line matters. Exponential spacing gives you sharper discrimination between alternatives. Arithmetic spacing flattens choice, even when reinforcer ratios stay the same. If you need a client to notice small differences in reinforcement, build the schedule with exponential steps. Watch for odd drops in preference when you raise overall reinforcer density; the curve can dip even when you think you are helping.
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02At a glance
03Original abstract
Six pigeons responded on a series of concurrent exponential variable-interval schedules, offering a within-subject comparison with previously published data from concurrent arithmetic variable-interval schedules. Both relative and overall reinforcer rates were varied between conditions. The generalized matching law described the data well, with undermatching much more frequent than strict matching. Time-allocation sensitivity consistently exceeded response-allocation sensitivity for both schedule types, and exponential-schedule sensitivity exceeded arithmetic-schedule sensitivity for both measures of choice. A further set of conditions using variable-interval schedules whose shortest interval was correlated with the mean interval, like arithmetic schedules, but that provided a constant conditional probability of reinforcement, like exponential schedules, produced sensitivities between those produced by conventional arithmetic and exponential schedules. Unlike previous arithmetic-schedule results, exponential sensitivity changed nonmonotonically with changes in overall reinforcer rate. The results clarify our knowledge of the effects of arithmetic and exponential schedules but confuse our understanding of the effects of overall reinforcer rate on concurrent choice.
Journal of the experimental analysis of behavior, 1996 · doi:10.1901/jeab.1996.65-445