Transitional and steady-state choice behavior under an adjusting-delay schedule.
Adjusting-delay sessions give a fast numeric snapshot of how any learner trades time for value and show that early choice swings fade with steady practice.
01Research in Context
What this study did
Valencia and colleagues put rats in a two-key box.
One key always gave two food pellets right away.
The other key gave four pellets after a delay that changed every session.
The computer lengthened or shortened the delay until the rat picked each side about half the time.
They tracked how long it took to reach that steady point and what the final delay was.
They also watched for tiny up-and-down swings in choices after the delay locked.
What they found
Rats needed more sessions to settle when the delay started long.
Their final indifference delay matched the curve predicted by hyperbolic discounting.
Bigger reinforcers needed longer delays to feel equal to small immediate ones.
Early in each condition the rats flipped back and forth in a wave-like pattern.
Those swings got smaller the longer the rats stayed in the condition.
How this fits with other research
Gaily et al. (1998) ran the same adjusting-delay game with pigeons and found the same hyperbolic fit.
The animal species changed but the math stayed, so the rule looks universal.
Cullinan et al. (2001) turned the rat rule into a kid lesson.
They slowly stretched the wait time for children with ADHD until the kids took a big reward after 24 hours.
The lab model predicted the clinic fix.
Lane et al. (1984) warned that birds sometimes peck the wrong key during long waits.
Valencia saw the same wavering in rats, but the adjusting-delay method let them watch the waver shrink as training continued.
The two papers together say: early swings are normal; keep training and they fade.
Why it matters
You now have a clear, numbers-first way to measure how much delay erodes value for any client.
Run brief adjusting-delay trials in your clinic to find the exact wait time that balances a small now versus big later reward.
Use that number to set the first delay in a self-control program, then lengthen it just like Valencia lengthened rat delays.
Watch for early flip-flopping; it is data, not failure.
Stay consistent and the swings will quiet down as the learner locks in the better choice.
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02At a glance
03Original abstract
Twelve rats made repeated choices on an adjusting-delay schedule between a smaller reinforcer (A) that was delivered immediately after a response and a larger reinforcer (B) that was delivered after a delay which increased or decreased by 20% depending on the subject's choices in successive blocks of trials. In two phases of the experiment (100 sessions and 40 sessions), reinforcer sizes were selected which enabled theoretical parameters expressing the rate of delay discounting and sensitivity to reinforcer size to be estimated from the ratio of the indifference delays obtained in the two phases. Indifference delays, calculated from adjusting delays in the last 10 sessions of each phase, were shorter when the sizes of A and B were 14 and 25 µl of a 0.6 M sucrose solution than when they were 25 and 100 µl of the same solution. The ratio of the indifference delays was significantly smaller than that predicted on the basis of an assumed linear relation between reinforcer size and instantaneous reinforcer value, consistent with a previous proposal that this relation may be hyperbolic in form. Estimates of the rate of delay discounting based on the ratio of the two indifference delays (mean, 0.08 s(-1)) were similar to values obtained previously using different intertemporal choice protocols. Estimates of the size-sensitivity parameter (mean 113 µl) were similar to estimates recently derived from performance on progressive-ratio schedules. In both phases of the experiment, adjusting delays in successive blocks of trials were analyzed using the Fourier transform. The power spectrum obtained from individual rats had a dominant frequency that corresponded to a period of oscillation of the adjusting delay between 30 and 100 trial blocks (mean, 78). Power in the dominant frequency band was highest in the early sessions of the first phase and declined with extended training. It is suggested that this experimental protocol may have utility in neurobehavioral studies of intertemporal choice.
Journal of the experimental analysis of behavior, 2011 · doi:10.1901/jeab.2011.95-57