Author's School

Graduate School of Arts & Sciences

Author's Department/Program



English (en)

Date of Award

Summer 9-1-2014

Degree Type


Degree Name

Doctor of Philosophy (PhD)

Chair and Committee

Leonard Green


The phenomenon of probability discounting - the decrease in the subjective value of an outcome as the likelihood of its receipt decreases - has been an increasingly explored area of research with human participants, but has received little attention with nonhuman animals. The few studies that have attempted to obtain probability discounting functions with animals have serious limitations. For example, in Wilhelm and Mitchell's (2008) study with rats, the experienced probabilities often differed markedly from the programmed probabilities. Green, Myerson, and Calvert's study with pigeons (2010) used repeated gambles rather than one-shot choices, which is the typical situation studied with humans, and the time to reinforcement, rather than the probability of reinforcement, may well have determined the animals' behavior.

The current work developed an innovative procedure, one that combined the concurrent-chains and the adjusting-amount procedures, to study probability discounting in pigeons. The concurrent-chains procedure included a non-independent VI 30-second schedule in the initial link, during which pigeons revealed their preference between a smaller, more likely reinforcer and a larger, but less likely reinforcer. The adjusting-amount procedure allowed for the estimation of the subjective value of the probabilistic reinforcer.

In Experiment 1, pigeons were presented choices between a smaller, certain amount and a larger, probabilistic amount at each of five probabilities (10%, 25%, 50%, 75%, and 90%). In Experiment 2, the probabilities associated with each reinforcer were multiplied by three different values (1.0, 0.75, and 0.25) in order to determine subjective values when both reinforcers were probabilistic while the ratio of the probabilities between the smaller and larger reinforcers was held constant. Finally, in Experiment 3 the same concurrent-chains procedure was used but with delay to rather than probability of reinforcement manipulated. Specifically, the pigeons chose between a smaller, immediate reinforcer and a larger, delayed reinforcer. The purpose of Experiment 3 was to determine whether the new procedure, which combines a concurrent-chains procedure with an adjusting-amount procedure, would produce results similar to those with standard adjusting-amount procedures. An amount manipulation (in which the larger reinforcer was 16 food pellets and 32 food pellets in different phases) was included in all three experiments to test for an amount effect in discounting.

The discounting of the larger reinforcer increased as the odds against (Experiments 1 and 2) or delay to (Experiment 3) its receipt increased. Data were well described by the hyperbolic discounting model. Consistent with most animal discounting studies, no amount effect was observed (i.e., degree of discounting did not vary as a function of the amount of the larger reinforcer).

To our knowledge, this study is the first to demonstrate probability discounting in nonhuman animals that ensures that the probabilities the animals actually experienced matched those programmed. Furthermore, the procedure provides an alternative technique that may allow one to directly compare delay and probability discounting mechanisms in animals.


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