Falsification of matching theory: changes in the asymptote of Herrnstein's hyperbola as a function of water deprivation.
A client’s fastest possible response rate is not fixed—it slides with hunger, thirst, or other motivation shifts.
01Research in Context
What this study did
Rats pressed a lever for water on a variable-interval schedule. The team changed how thirsty the rats were before each session. They tracked how fast the rats pressed when water was scarce versus plentiful.
The goal was to test a core rule of matching theory: that every animal has a fixed top speed it will never exceed.
What they found
When the rats were only a little thirsty, their top response rate dropped. When they were very thirsty, the top rate rose. The ceiling moved with motivation.
This breaks Herrnstein’s hyperbola, which draws the ceiling as a flat line.
How this fits with other research
Hammond (1980) already warned the ceiling should move. That paper said k must shift when reinforcer size or delay changes. The 1999 data prove the warning was right.
Cryan et al. (1996) saw the same pattern with food and water cost. Higher cost cut total intake, just like lower thirst cut top speed. Both studies show motivation changes the numbers inside the equation.
Wright (1972) found the equation still works when shock avoidance is the pay-off. Taken together, the equation holds across reinforcer types, but you must let k breathe instead of locking it as a constant.
Why it matters
If you write a behavior contract or token system, do not assume a client has one fixed top output. Deprivation, medication, or illness can drop that ceiling in real time. Track the best rate each day and adjust your reinforcement aim accordingly.
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02At a glance
03Original abstract
Five rats pressed levers on variable-interval schedules of water reinforcement at various levels of water deprivation. In one phase of the experiment, three deprivation conditions that replicated conditions in Heyman and Monaghan (1987) were arranged, along with three less extreme deprivation conditions. In a second phase, water deprivation was arranged so that subjects were exposed to a greater range of access to water per day. Herrnstein's hyperbola described the rats' response-rate data well. The y asymptote, k, of the hyperbola appeared roughly constant over the conditions that replicated those of Heyman and Monaghan, but decreased markedly when less extreme deprivation conditions were included. In addition, k varied systematically when the second method of arranging deprivation was used. These results falsify a strong form of matching theory and confirm predictions made by linear system theory.
Journal of the experimental analysis of behavior, 1999 · doi:10.1901/jeab.1999.72-251