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Two experiments measured pigeons' choices between probabilistic reinforcers and certain but delayed reinforcers. In Experiment 1, a peck on a red key led to a 5-s delay and then a possible reinforcer (with a probability of .2). A peck on a green key led to a certain reinforcer after an adjusting delay. This delay was adjusted over trials so as to estimate an indifference point, or a duration at which the two alternatives were chosen about equally often. In all conditions, red houselights were present during the 5-s delay on reinforced trials with the probabilistic alternative, but the houselight colors on nonreinforced trials differed across conditions. Subjects showed a stronger preference for the probabilistic alternative when the houselights were a different color (white or blue) during the delay on nonreinforced trials than when they were red on both reinforced and nonreinforced trials. These results supported the hypothesis that the value or effectiveness of a probabilistic reinforcer is inversely related to the cumulative time per reinforcer spent in the presence of stimuli associated with the probabilistic alternative. Experiment 2 tested some quantitative versions of this hypothesis by varying the delay for the probabilistic alternative (either 0 s or 2 s) and the probability of reinforcement (from .1 to 1.0). The results were best described by an equation that took into account both the cumulative durations of stimuli associated with the probabilistic reinforcer and the variability in these durations from one reinforcer to the next.
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Twenty acquisition curves were obtained from each of 8 pigeons in a free-operant choice procedure. Every condition began with a phase in which two response keys had equal probabilities of reinforcement, and, as a result, subjects' responses were divided fairly evenly between the two keys. This was followed by a phase in which one key had a higher probability of reinforcement than the other, and the development of preference was observed. In all but a few cases, response proportions increased for the key with the higher probability of reinforcement. In most conditions, the two probabilities differed by .06, but the actual probabilities varied (from .16 and .10 in one condition to .07 and .01 in another). Development of preference for the key with the higher probability of reinforcement was slower when the ratio of the two reinforcement probabilities was small (.16/.10) than when it was large (.07/.01). This finding is inconsistent with the predictions of several different quantitative models of acquisition, including the kinetic model (Myerson & Miezin, 1980) and the ratio-invariance model (Horner & Staddon, 1987). However, the finding is consistent with a hypothesis based on Weber's law, which states that the two alternatives are more discriminable when the ratio of their reinforcement probabilities is larger, and, as a result, the acquisition of preference is faster.