Falsification of matching theory's account of single-alternative responding: Herrnstein's k varies with sucrose concentration.

The team tested four rats on a single lever that paid off with sweet water. They kept the schedule the same but changed how strong the sucrose tasted.

Each session used one concentration: 5, 10, 20, or 40 percent. They counted lever presses and fit the data to Herrnstein’s hyperbola.

The curve still fit, but the top line (k) moved. Stronger sucrose made k rise; weaker made it drop.

Matching theory says k should stay put. The data broke that rule.

Wilkie et al. (1981) saw the same right-shift when they cut sucrose volume, yet they kept k fixed. The two papers seem to clash, but they tested different things: volume versus strength. Volume slides the curve sideways; concentration lifts the ceiling.

Davis et al. (1972) showed that extra rewards anywhere lower the baseline rate. Their work and this one both chip away at the idea that k is a stable trait.

Innis (1978) found birds undermatched in concurrent schedules. Together, these studies show every part of the matching equation—k, a, and bias—can move when conditions change.

If you assume a client’s maximum response rate is fixed, you may pick the wrong schedule or set the wrong goal. This paper tells you that richer reinforcers can raise the ceiling itself. When you fade edibles or dilute juice, expect the top rate to drop too—plan extra training trials or bump the quality back up.