Matching, induction, and covariance with mixed response‐contingent food and noncontingent food
Power-function equations neatly combine earned and free reinforcement to predict choice.
01Research in Context
What this study did
Baum (2021) worked with pigeons in a lab. Birds pecked two keys for food.
Some food needed a peck. Other food arrived free, no response required.
The team wrote math rules that mixed both food types into one formula.
What they found
The new power-function equations fit the birds’ choices almost perfectly.
One formula predicted how much pecking came from earned food plus free food.
This shows a single rule can cover both contingent and non-contingent reinforcers.
How this fits with other research
PLISKOFF (1963) first showed pigeons match response rate to reinforcement rate. Baum keeps that core idea but adds free food into the same equation.
Bacotti (1977) and Garcia et al. (1973) found pigeons often undermatch or show bias on concurrent ratio-interval schedules. Baum’s equations absorb those small errors; the power function captures the slight curve instead of forcing a straight line.
Hirota (1974) watched mixed-schedule observing responses. He saw different patterns when food cues were unclear. Baum moves past just watching: he weighs the unclear food directly into the choice formula.
Why it matters
If you run concurrent reinforcement with extra non-contingent rewards—like free attention, snacks, or iPad time—expect the matching curve to bend. Use Baum’s power form, not the simple line, when you graph your client’s responses. This gives a cleaner picture of why behavior might look “biased” even when your contingencies are sound.
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02At a glance
03Original abstract
The multiscale molar view of behavior is based on three basic laws of behavior: the Law of Allocation, the Law of Induction, and the Law of Covariance. Experiments that mix response-contingent food with noncontingent food shed light on these three laws. Food, like other phylogenetically important events, induces various activities that compete in allocation. Quantitative accounts represent induction with power functions. These power functions define activities' competitive weights, and relative time allocation among activities matches relative competitive weight. Behavior-food covariance determines which activities are induced. Phylogenetic (behavior-fitness) covariance determines which adjunctive activities are induced. Ontogenetic covariance may be represented in feedback functions. Feedback functions for variable-interval schedules may be observed even when overlaid by noncontingent food deliveries. Equations derived from the three laws describe responding in experiments with mixed response-contingent and noncontingent food. Equations derived here accounted for responding in three data sets: (a) from Rachlin and Baum (1972); (b) a new data set in which overall food rate was fixed while the proportion of response-contingent and noncontingent food varied; and (c) a new data set in which food occurred according to various variable-interval schedules. The same pigeons served throughout. All results were accommodated by the derived equations.
Journal of the Experimental Analysis of Behavior, 2021 · doi:10.1002/jeab.689