We present the mathematical description of feedback functions of variable interval and variable differential reinforcement of low rates as functions of schedule size only. These results were obtained using an R script named Beak, which was built to simulate rates of behavior interacting with simple schedules of reinforcement. Using Beak, we have simulated data that allow an assessment of different reinforcement feedback functions. This was made with unparalleled precision, as simulations provide huge samples of data and, more importantly, simulated behavior is not changed by the reinforcement it produces. Therefore, we can vary response rates systematically. We've compared different reinforcement feedback functions for random interval schedules, using the following criteria: meaning, precision, parsimony, and generality. Our results indicate that the best feedback function for the random interval schedule was published by Baum (1981). We also propose that the model used by Killeen (1975) is a viable feedback function for the random differential reinforcement of low rates schedule. We argue that Beak paves the way for greater understanding of schedules of reinforcement, addressing still open questions about quantitative features of simple schedules. Also, Beak could guide future experiments that use schedules as theoretical and methodological tools.
We pay tribute to Rachlin's work stating that researching and writing for posterity is an act of selfcontrol and altruism. We show how Rachlin's work influenced a series of seminars at the University of São Paulo (Brazil) based on his book from 1989, Judgment, Decision, and Choice. This influence is illustrated through two empirical exercises conducted during our seminars, where students were actively involved in data collection and analysis. The first exercise is about judgment of randomness involving coin tossing. The second is a replication of a procedure by Jones and Rachlin ( 2006) about social discounting of monetary quantities. We use these empirical examples to highlight some of Rachlin's major contributions to the science of behavior and their implications to our seminars and to ourselves as researchers.
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