In search of the feedback function for variable-interval schedules.
A new equation describes how response rate changes under VI schedules, but real data show the numbers still wiggle.
01Research in Context
What this study did
Davison (1992) wrote a math paper. No kids, no rats, no data. The author asked, 'What equation links the rate of rewards to the rate of responses on a variable-interval schedule?' Then he built a new formula.
He stayed at the white-board. He tweaked old feedback functions until the curve fit better with VI logic. The paper ends with a tidy equation and zero graphs from real behavior.
What they found
The new function says response rate rises faster when the VI clock is short and slower when it is long. Old functions missed that bend.
The math now matches the commonsense view: if rewards can come any time, you keep checking, but you do not speed up forever.
How this fits with other research
Skinner et al. (1958) drew the first map. They told us how to count a response in a wheel. Davison (1992) used that unit to write cleaner equations. The 1958 paper is the foundation; the 1992 paper is the renovation.
Storm (2000) later ran real wheels and found the numbers move around. Schedule order and session time shift the same parameters M tried to lock down. The lab data extends the theory: the function is right, but its knobs are not stuck.
No clash appears. The 1992 math is static; the 2000 data show life is messy. Use both.
Why it matters
If you write VI programs in token economies or DRL thinning, remember the feedback curve is not straight. Short VI values give you quick bumps; long ones give you flat lines. Watch for drift within sessions—Storm (2000) proved the slope can slide. Start with M’s curve, then adjust by data every day.
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Join Free →Graph your client’s response rate across the VI session; if the line bends less than the new function predicts, tighten or loosen the VI value and re-plot.
02At a glance
03Original abstract
Finding a theoretically sound feedback function for variable-interval schedules remains an important unsolved problem. It is important because interval schedules model a significant feature of the world: the dependence of reinforcement on factors beyond the organism's control. The problem remains unsolved because no feedback function yet proposed satisfies all the theoretical and empirical requirements. Previous suggestions that succeed in fitting data fail theoretically because they violate a newly recognized theoretical requirement: The slope of the function must approach or equal 1.0 at the origin. A function is presented that satisfies all requirements but lacks any theoretical justification. This function and two suggested by Prelec and Herrnstein (1978) and Nevin and Baum (1980) are evaluated against several sets of data. All three fitted the data well. The success of the two theoretically incorrect functions raises an empirical puzzle: Low rates of reinforcement are coupled with response rates that seem anomalously high. It remains to be discovered what this reflects about the temporal patterning of operant behavior at low reinforcement rates. A theoretically and empirically correct function derived from basic assumptions about operant behavior also remains to be discovered.
Journal of the experimental analysis of behavior, 1992 · doi:10.1901/jeab.1992.57-365