Reinforcer magnitude (sucrose concentration) and the matching law theory of response strength.
Save your best reinforcer for lean schedules; on dense ones it adds no extra punch.
01Research in Context
What this study did
The team gave rats tiny sips of sugar water while they pressed a lever on a VI schedule.
They changed only one thing: how sweet the water was.
Then they watched how fast the rats pressed when rewards came slowly or quickly.
What they found
Stronger sugar only helped when rewards were rare.
At slow reinforcement rates, the rats worked harder for the sweeter sip.
When rewards were already frequent, sugar strength no longer mattered.
How this fits with other research
Bradshaw et al. (1978) saw the same rats slow down with weak sugar, but they blamed a lower top speed.
The new data say the top speed stays the same; only the low-rate end moves.
Rose et al. (2000) went further and proved the "k" number in Herrnstein’s equation is not fixed—it climbs with sweeter water.
Together the three papers rewrite the matching law: reinforcer size tweaks the equation, it does not just lift the ceiling.
Why it matters
If you run a thin schedule—like a sparse DRL or a lean VR—check your reinforcer size. A stronger edible, a bigger piece, or a richer token can wake the behavior up. On dense schedules you can save the calories; rate is already maxed. Test one magnitude, then a stronger one, and watch the low-rate end move. That quick probe tells you if you are on the left or right side of the curve.
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Run a two-minute probe: keep the schedule lean, swap in a higher-magnitude reinforcer, and count if the rate jumps.
02At a glance
03Original abstract
This experiment investigated the relationship between reinforcer magnitude (sucrose concentration) and response rate. The purpose was to evaluate the behavior of two parameters of an equation that predicts absolute response rate as a function of reinforcement rate and two free parameters. According to Herrnstein's (1970) theory of reinforced behavior, one parameter of this "response-strength equation" measures the efficacy of the reinforcer maintaining responding and the other parameter measures motoric components of response rate, such as response duration. Seven rats served as subjects. Experimental sessions consisted of a series of five different variable-interval schedules of reinforcement, each in effect for 5 minutes. Within each session, obtained reinforcement rates varied over more than a 30-fold range, from about 20 per hour to 700 per hour. The reinforcer was sucrose solution, and, between sessions, its concentration was varied from 0.0 to 0.64 molar (0 to 21.9%). For sucrose concentrations of 0.16 to 0.64 m, response rate was a negatively accelerated function of reinforcement rate. Increases in sucrose concentration increased response rates maintained by low but not high reinforcement rates. This pattern of changes corresponds to a change in the reinforcement-efficacy parameter of the response-strength equation. In contrast, the motor-performance parameter did not change as a function of sucrose concentration. These findings are inconsistent with the results of a similar study (Bradshaw, Szabadi, & Bevan, 1978) but support Herrnstein's theory of reinforced behavior.
Journal of the experimental analysis of behavior, 1994 · doi:10.1901/jeab.1994.61-505