The Matching Law And Amount-dependent Exponential Discounting As Accounts Of Self-control Choice.
Reward size does not make clients more patient; timing drives choice.
01Research in Context
What this study did
Parmenter (1999) let pigeons choose between two keys. One key gave a small food reward right away. The other key gave a bigger food reward after a delay.
The team kept the delay times the same but changed the size of the food portions. They wanted to see if the birds cared more about delay when the food amount was large.
What they found
The birds picked the keys the same way no matter how big the food pile was. Large rewards did not make the pigeons more willing to wait.
The results matched the simple matching law: birds chose in proportion to how soon each reward arrived. Bigger food did not change that rule.
How this fits with other research
Green et al. (2014) later saw the same null effect in humans. People discounted $20 and $500k losses the same way, showing the pigeon finding holds across species and reward types.
Horner-Johnson et al. (2002) also support the story. They showed that hyperbolic curves fit human data better than straight exponential ones, echoing the matching-law math Parmenter (1999) used.
Gentry et al. (1980) looked at only delay, not amount, and still saw choice shift when absolute wait times grew long. Their early work set the stage for asking whether amount would matter; Parmenter (1999) answers with a clear “no.”
Why it matters
If reward size does not bend delay curves, you can ignore magnitude when planning schedules. Focus on immediacy instead of trying to “sweeten” the deal with bigger tokens or treats. When shaping patience, stretch delay in small steps and keep the payoff quick; saving the “big” reinforcer for later will not help the learner wait.
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02At a glance
03Original abstract
Studies with humans have found evidence for amount‐dependent temporal discounting, that is, that the sensitivity of choice to reinforcer delay varies inversely with reinforcer magnitude. To test whether similar results could be obtained with nonhumans, pigeons were trained on a two‐component concurrent‐chains procedure in which the durations of food reinforcement in the terminal links were equal within components but unequal between components. Terminal‐link schedules were varied over four conditions to allow separate estimates of sensitivity to delay to be obtained for the large and small reinforcer‐magnitude components. Although sensitivity to delay was greater in the small‐magnitude component for all subjects, the effect was quite small. The difference in sensitivity was generally less than one standard error, and t tests on parameter differences failed to reach significance. Several models for temporal discounting, including an amount‐dependent exponential function, were fitted to the data from the first four conditions. The resulting parameter estimates were used to make predictions for a self‐control condition in which one terminal link arranged a smaller, less delayed reinforcer and the other arranged a larger, more delayed reinforcer. For all models, predictions were considerably more accurate when sensitivity to delay was the same regardless of reinforcer magnitude. The results support the independence of delay and magnitude as required by a version of the matching law, and provide strong evidence against amount‐dependent exponential discounting as an account of self‐control choice. A new two‐parameter discounting function, consistent with the matching law, is proposed that has wide empirical generality for both human and nonhuman data.
Journal of the experimental analysis of behavior, 1999 · doi:10.1901/jeab.1999.71-27