Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude.

The team tested eight adults with no disabilities. Each adult pressed a button for liquid reinforcers on a variable-interval schedule.

They changed the size of the liquid payoff across conditions. Then they tracked how fast the adults pressed the button.

Seven of eight adults showed the same pattern. Bigger payoffs lifted the top line of Herrnstein’s hyperbola.

In plain words, larger reinforcers pushed the maximum response rate higher. Linear system theory predicted this climb and the data matched it.

Tyrer et al. (2009) later saw the same climb on progressive-ratio schedules. Bigger sucrose pellets made rats work harder and break later.

Levin et al. (2014) added a new twist. They showed that larger reinforcers also protect behavior against extinction and pre-feeding.

Harzem et al. (1978) seems to disagree at first glance. They found that bigger payoffs lengthen the pause right after reinforcement. The two papers differ because P watched the quiet moment after delivery while J watched the overall rate across the whole session.

You now have a dial to turn. Increase reinforcer size when you want faster, more persistent responding. Watch for the brief pause that may follow; it is normal and does not cancel the rate boost. Use this when shaping new skills or when thin schedules start to drag.