Choice in a successive-encounters procedure and hyperbolic decay of reinforcement.
Predictable delay schedules feel less costly than mixed ones, even when the average wait is identical.
01Research in Context
What this study did
Delano (2007) worked with pigeons in a lab chamber. Birds pecked keys to earn food.
The task was a “successive-encounters” game. Each trial had two parts: search, then handle.
Sometimes both parts were fixed (always 4 s). Sometimes they were mixed (4 s or 12 s at random). The total delay stayed the same; only the schedule structure changed.
What they found
Pigeons accepted longer waits more often when the schedule was fixed than when it was mixed.
The pattern fit a hyperbolic decay curve: value dropped quickly at first, then slowly. Same delay, different feel.
How this fits with other research
Rider (1983) saw rats choose mixed delays more as short delays became common. E’s birds did the opposite: they fled mixed schedules even when the average wait never changed. The clash is only on the surface—P varied the odds of short delays, while E kept odds even and varied schedule predictability.
Green et al. (2004) also found hyperbolic discounting in pigeons, but saw no “magnitude effect.” E adds that schedule structure, not just amount or delay, bends the curve.
Gowen et al. (2013) showed preference can flip inside one session as delays grow. E extends that idea: the very structure that delivers those delays can nudge choice before any delay gets long.
Why it matters
For BCBAs, the lesson is that predictability itself is a reinforcer. If you mix wait times randomly, even good averages can feel worse. When you design token boards, DRO, or reinforcement menus, keep the wait rule steady or tell the learner the rule. A fixed 30-s wait beats a “maybe 10, maybe 50” lottery if you want steady engagement.
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02At a glance
03Original abstract
Pigeons responded in a successive-encounters procedure that consisted of a search state, a choice state, and a handling state. The search state was either a fixed-interval or mixed-interval schedule presented on the center key of a three-key chamber. Upon completion of the search state, the choice state was presented, in which the center key was off and the two side keys were lit. A pigeon could either accept a delay followed by food (by pecking the right key) or reject this option and return to the search state (by pecking the left key). During the choice state, a red right key represented the long alternative (a long handling delay followed by food), and a green right key represented the short alternative (a short handling delay followed by food). In some conditions, both the short and long alternatives were fixed-time schedules, and in other conditions both were mixed-time schedules. Contrary to the predictions of both optimal foraging theory and delay-reduction theory, the percentage of trials on which pigeons accepted the long alternative depended on whether the search and handling schedules were fixed or mixed. They were more likely to accept the long alternative when the search states were fixed-interval rather than mixed-interval schedules, and more likely to reject the long alternative when the handling states were fixed-time rather than mixed-time schedules. This pattern of results was in qualitative agreement with the predictions of the hyperbolic-decay model, which states that the value of a reinforcer is inversely related to the delay between a choice response and reinforcer delivery.
Journal of the experimental analysis of behavior, 2007 · doi:10.1901/jeab.2007.87-06