Choice in a self-control paradigm: Quantification of experience-based differences

Previous quantitative models of choice in a self-control paradigm (choice between a larger, more-delayed reinforcer and a smaller, less-delayed reinforcer) have not described individual differences. Two experiments are reported that provide additional quantitative data on experience-based differences in choice between reinforcers of varying sizes and delays. In Experiment 1, seven pigeons in a self-control paradigm were exposed to a fading procedure that increased choices of the larger, more-delayed reinforcer through gradually decreasing the delay to the smaller of two equally delayed reinforcers. Three control subjects, exposed to each of the small-reinforcer delays to which the experimental subjects were exposed, but for fewer sessions, demonstrated that lengthy exposure to each of the conditions in the fading procedure may be necessary in order for the increase to occur. In Experiment 2, pigeons with and without fading-procedure exposure chose between reinforcers of varying sizes and delays scheduled according to a concurrent variable-interval variable-interval schedule. In both experiments, pigeons with fading-procedure exposure were more sensitive to variations in reinforcer size than reinforcer delay when compared with pigeons without this exposure. The data were described by the generalized matching law when the relative size of its exponents, representing subjects' relative sensitivity to reinforcer size and delay, were grouped according to subjects' experience.     

Effects of variable-interval value and amount of training on stimulus generalization.

In Experiment 1 pigeons pecked a key that was illuminated with a 501-nm light and obtained food by doing so according to a variable-interval (VI) schedule of reinforcement, the mean value of which differed across groups: either 30 s, 120 s, or 240 s. The pigeons in all three groups were trained for 10 50-min sessions. Generalization testing was conducted in extinction with different wavelengths of light. Absolute and relative generalization gradients were similar in shape for the three groups. Experiment 2 was a systematic replication of Experiment 1 using line orientation as the stimulus dimension and a mean VI value of either 30 s or 240 s. Again, gradients of generalization were similar for the two groups. In Experiment 3 pigeons pecked a key that was illuminated with a 501-nm light and obtained food reinforcers according to either a VI 30-s or a 240-s schedule. Training continued until response rates stabilized (> 30 sessions). For subjects trained with the 30-s schedule, generalization gradients were virtually identical regardless of whether training was for 10 sessions (Experiment 1) or until response rates stabilized. For subjects trained with the VI 240-s schedule, absolute generalization gradients for subjects trained to stability were displaced upward relative to gradients for subjects trained for only 10 sessions (Experiment 1), and relative generalization gradients were slightly flatter. These results indicate that the shape of a generalization gradient does not necessarily depend on the rate of reinforcement during 10-session single-stimulus training but that the effects of prolonged training on stimulus generalization may be schedule dependent.     

Human variable ratio performance

The generality of the mathematical principles of reinforcement (MPR) was tested with humans. In Experiment 1A, participants’ mouse clicks were reinforced according to a series of variable-ratio (VR) values. In one condition, a situated task was used (searching for treasure on a map presented via a PC monitor); in the other, abstract version of the task, participants clicked on a white screen. Under the “map” condition, response rates increased with increasing ratio value before decreasing with further ratio increases; under the “no-map” condition, response rates decreased linearly from a peak at the smallest ratio. In Experiment 1B, the pattern of responding was confirmed under the “map” conditions using a different set of ratio values. In Experiment 2, reinforcer magnitude was manipulated using the “map” context. Response rates did not differ significantly when large rather than small cash reinforcers were delivered according to a VR 30 but were significantly higher when large rather than small cash reinforcers were delivered according to a VR 120. Together these experiments offer qualified support for extending MPR to the behavior of human participants.     

DELAY‐AMOUNT TRADEOFFS IN CHOICES BY PIGEONS AND RATS: HYPERBOLIC VERSUS EXPONENTIAL DISCOUNTING

An adjusting‐delay procedure was used to study the choices of pigeons and rats when both delay and amount of reinforcement were varied. In different conditions, the choice alternatives included one versus two reinforcers, one versus three reinforcers, and three versus two reinforcers. The delay to one alternative (the standard alternative) was kept constant in a condition, and the delay to the other (the adjusting alternative) was increased or decreased many times a session so as to estimate an indifference point—a delay at which the two alternatives were chosen about equally often. Indifference functions were constructed by plotting the adjusting delay as a function of the standard delay for each pair of reinforcer amounts. The experiments were designed to test the prediction of a hyperbolic decay equation that the slopes of the indifference functions should increase as the ratio of the two reinforcer amounts increased. Consistent with the hyperbolic equation, the slopes of the indifference functions depended on the ratios of the two reinforcer amounts for both pigeons and rats. These results were not compatible with an exponential decay equation, which predicts slopes of 1 regardless of the reinforcer amounts. Combined with other data, these findings provide further evidence that delay discounting is well described by a hyperbolic equation for both species, but not by an exponential equation. Quantitative differences in the y‐intercepts of the indifference functions from the two species suggested that the rate at which reinforcer strength decreases with increasing delay may be four or five times slower for rats than for pigeons.     

RISKY CHOICE IN PIGEONS: PREFERENCE FOR AMOUNT VARIABILITY USING A TOKEN-REINFORCEMENT SYSTEM

Pigeons were given repeated choices between variable and fixed numbers of token reinforcers (stimulus lamps arrayed above the response keys), with each earned token exchangeable for food. The number of tokens provided by the fixed‐amount option remained constant within blocks of sessions, but varied parametrically across phases, assuming values of 2, 4, 6, or 8 tokens per choice. The number of tokens provided by the variable‐amount option varied between 0 and 12 tokens per choice, arranged according to an exponential or rectangular distribution. In general, the pigeons strongly preferred the variable option when the fixed option provided equal or greater numbers of tokens than the variable amount. Preference for the variable amount decreased only when the alternatives provided widely disparate amounts favoring the fixed amount. When tokens were removed from the experimental context, preference for the variable option was reduced or eliminated, suggesting that the token presentation played a key role in maintaining risk‐prone choice patterns. Choice latencies varied inversely with preferences, suggesting that local analyses may provide useful ancillary measures of reinforcer value. Overall, the results indicate that systematic risk sensitivity can be attained with respect to reinforcer amount, and that tokens may be critical in the development of such preferences.     

Effects of pre-trial response requirements on self-control choices by rats and pigeons

Parallel experiments with rats and pigeons examined whether the size of a pre-trial ratio requirement would affect choices in a self-control situation. In different conditions, either 1 response or 40 responses were required before each trial. In the first half of each experiment, an adjusting-ratio schedule was used, in which subjects could choose a fixed-ratio schedule leading to a small reinforcer, or an adjusting-ratio schedule leading to a larger reinforcer. The size of the adjusting ratio requirement was increased and decreased over trials based on the subject's responses, in order to estimate an indifference point-a ratio at which the two alternatives were chosen about equally often. The second half of each experiment used an adjusting-delay procedure-fixed and adjusting delays to the small and large reinforcers were used instead of ratio requirements. In some conditions, particularly with the reinforcer delays, the rats had consistently longer adjusting delays with the larger pre-trial ratios, reflecting a greater tendency to choose the larger, delayed reinforcer when more responding was required to reach the choice point. No consistent effects of the pre-trial ratio were found for the pigeons in any of the conditions. These results may indicate that rats are more sensitive to the long-term reinforcement rates of the two alternatives, or they may result from a shallower temporal discounting rate for rats than for pigeons, a difference that has been observed in previous studies.     

Incentive theory: IV. Magnitude of reward

Incentive theory is successfully applied to data from experiments in which the amount of food reward is varied. This is accomplished by assuming that incentive value is a negatively accelerated function of reward duration. The interaction of the magnitude of a reward with its delay is confirmed, and the causes and implications of this interaction are discussed.     

Choice, foraging, and reinforcer duration.

Pigeons were exposed to a foraging schedule characterized by three different states, beginning with a search state in which completion of a variable interval on a white key led to a choice state. In the choice state the subject could, by appropriate responding on a fixed ratio of three, either accept or reject the schedule offered. If the subject accepted the schedule, it entered a handling state in which the appropriate reinforcer amount was presented according to a variable-interval schedule. In Experiment 1 the shorter duration reinforcer was more likely to be accepted the longer the duration of the search state and the shorter the equal durations of the handling states. In Experiment 2 the shorter duration reinforcer was more likely to be accepted the longer the handling time preceding the longer duration reinforcer. All of the results were in qualitative--and some were in quantitative--agreement with those predicted by the delay-reduction hypothesis and the optimal-diet model.     

Choice between single and multiple delayed reinforcers.

Pigeons chose between alternatives that differed in the number of reinforcers and in the delay to each reinforcer. A peck on a red key produced the same consequences on every trial within a condition, but between conditions the number of reinforcers varied from one to three and the reinforcer delays varied between 5 s and 30 s. A peck on a green key produced a delay of adjustable duration and then a single reinforcer. The green-key delay was increased or decreased many times per session, depending on a subject's previous choices, which permitted estimation of an indifference point, or a delay at which a subject chose each alternative about equally often. The indifference points decreased systematically with more red-key reinforcers and with shorter red-key delays. The results did not support the suggestion of Moore (1979) that multiple delayed reinforcers have no effect on preference unless they are closely grouped. The results were well described in quantitative detail by a simple model stating that each of a series of reinforcers increases preference, but that a reinforcer's effect is inversely related to its delay. The success of this model, which considers only delay of reinforcement, suggested that the overall rate of reinforcement for each alternative had no effect on choice between those alternatives.     

Operant hoarding: a new paradigm for the study of self-control.

In the first of four experiments, rats were exposed to a modified multiple continuous reinforcement-extinction schedule during 15-min daily sessions. In one condition (saves condition) with the cuelight on, a single lever press produced a food pellet, briefly extinguished the cuelight, and started a clock. Saves (additional lever presses with interresponse times less than 1 s) produced an additional food pellet, briefly extinguished the cuelight, and restarted the interresponse time clock. The cuelight was extinguished 1 s after the last lever press and remained off during a 10-s period of extinction, during which no food pellets were delivered. In the other condition (savings account condition), the contingencies were the same except that the cuelight was extinguished and was not reilluminated after the initial lever press, and the delivery of all food pellets in the reinforcement component was delayed until the onset of extinction. In both conditions, rats made saves, but mean saves (total saves divided by the number of reinforcement components) were slightly reduced in the savings account condition. In Experiment 2, using six equally spaced 15-min sessions per day on alternate days, saves were either followed immediately with food and brief cuelight offset (saves condition) or were not reinforced at all. Mean saves were much greater when saves were reinforced. In Experiment 3, during 5-min daily sessions, saves earned a single pellet (savings account condition) or a number of pellets equal to the ordinal number of the lever press (interest condition). Rats made fewer mean saves, with little change in the food rate, when saves earned interest. In Experiment 4, the rats earned all their food in the operant situation during 24 daily 5-min sessions, these separated by 55-min intersession intervals during which no food was available; otherwise, the conditions were the same as in Experiment 3. In Experiment 4, the shift to interest for saves led to an increase in mean daily mean saves (total daily mean saves divided by the number of daily sessions) as well as to an increase in the number of food pellets delivered in each session. The results are discussed in terms of self-control and behavioral economics.