Choice and number of reinforcers

Pigeons were exposed to the concurrent-chains procedure in two experiments designed to investigate the effects of unequal numbers of reinforcers on choice. In Experiment 1, the pigeons were indifferent between long and short durations of access to variable-interval schedules of equal reinforcement density, but preferred a short high-density terminal link over a longer, lower density terminal link, even though in both sets of comparisons there were many more reinforcers per cycle in the longer terminal link. In Experiment 2, the pigeons preferred five reinforcers, the first of which was available after 30 sec, over a single reinforcer available at 30 sec, but only when the local interval between successive reinforcers was short. The pigeons were indifferent when this local interval was sufficiently long. The pigeons' behavior appeared to be under the control of local terminal-link variables, such as the intervals to the first reinforcer and between successive reinforcers, and was not well described in terms of transformed delays of reinforcement or reductions in average delay to reinforcement.     

Comparing preference and resistance to change in constant- and variable-duration schedule components

Two experiments explored preference and resistance to change in concurrent chains in which the terminal links were variable-interval schedules that ended either after a single reinforcer had been delivered (variable duration) or after a fixed period of access to the schedule (constant duration). In Experiment 1, pigeons' preference between the same pair of terminal links overmatched relative reinforcement rate when the terminal links were of constant duration, but not when they were of variable duration. Responding during the richer terminal link decreased less, relative to baseline, when response-independent food was presented during the initial links according to a variable-time schedule. In Experiment 2, all subjects consistently preferred a terminal link that consisted of 20-s access to a variable-interval 20-s schedule over a terminal link that ended after one reinforcer had been delivered by the same schedule. Results of resistance-to-change tests corresponded to preference, as responding during the constant-duration terminal link decreased less, relative to baseline, when disrupted by both response-independent food during the initial links and prefeeding. Overall, these data extend the general covariation of preference and resistance to change seen in previous studies. However, they suggest that reinforcement numerosity, including variability in the number of reinforcers per terminal-link entry, may sometimes affect preference and resistance to change in ways that are difficult to explain in terms of current models.     

Choice in a "self-control" paradigm: effects of a fading procedure

Pigeons chose between an immediate 2-second reinforcer (access to grain) and a 6-second reinforcer delayed 6 seconds. The four pigeons in the control group were exposed to this condition initially. The four experimental subjects first received a condition where both reinforcers were delayed 6 seconds. The small reinforcer delay was then gradually reduced to zero over more than 11,000 trials. Control subjects almost never chose the large delayed reinforcer. Experimental subjects chose the large delayed reinforcer significantly more often. Two experimental subjects showed preference for the large reinforcer even when the consequences for pecking the two keys were switched. The results indicate that fading procedures can lead to increased “self-control” in pigeons in a choice between a large delayed reinforcer and a small immediate reinforcer.     

Choice with delayed and probabilistic reinforcers: effects of variability, time between trials, and conditioned reinforcers.

In a discrete-trials procedure with pigeons, a response on a green key led to a 4-s delay (during which green houselights were lit) and then a reinforcer might or might not be delivered. A response on a red key led to a delay of adjustable duration (during which red houselights were lit) and then a certain reinforcer. The delay was adjusted so as to estimate an indifference point--a duration for which the two alternatives were equally preferred. Once the green key was chosen, a subject had to continue to respond on the green key until a reinforcer was delivered. Each response on the green key, plus the 4-s delay that followed every response, was called one "link" of the green-key schedule. Subjects showed much greater preference for the green key when the number of links before reinforcement was variable (averaging four) than when it was fixed (always exactly four). These findings are consistent with the view that probabilistic reinforcers are analogous to reinforcers delivered after variable delays. When successive links were separated by 4-s or 8-s "interlink intervals" with white houselights, preference for the probabilistic alternative decreased somewhat for 2 subjects but was unaffected for the other 2 subjects. When the interlink intervals had the same green houselights that were present during the 4-s delays, preference for the green key decreased substantially for all subjects. These results provided mixed support for the view that preference for a probabilistic reinforcer is inversely related to the duration of conditioned reinforcers that precede the delivery of food.     

Conditioned reinforcement value and choice.

The delay-reduction hypothesis of conditioned reinforcement states that the reinforcing value of a food-associated stimulus is determined by the delay to primary reinforcement signaled by the onset of the stimulus relative to the average delay to primary reinforcement in the conditioning situation. In contrast, most contemporary models of conditioned reinforcement strength posit that the reinforcing strength of a stimulus is some simple function only of the delay to primary reinforcement in the presence of stimulus. The delay-reduction hypothesis diverges from other conditioned reinforcement models in that it predicts that a fixed-duration food-paired stimulus will have different reinforcing values depending on the frequency of its presentation. In Experiment 1, pigeons' key pecks were reinforced according to concurrent-chains schedules with variable-interval 10-second and variable-interval 20-second terminal-link schedules. The initial-link schedule preceding the shorter terminal link was always variable-interval 60 seconds, and the initial-link schedule requirement preceding the longer terminal link was varied between 1 second and 60 seconds across conditions. In Experiment 2, the initial-link schedule preceding the longer of two terminal links was varied for each of three groups of pigeons. The terminal links of the concurrent chains for the three groups were variable-interval 10 seconds and 20 seconds, variable-interval 10 seconds and 30 seconds, and variable-interval 30 seconds and 50 seconds. In both experiments, preference for the shorter terminal link was either a bitonic function or an inverse function of the initial-link schedule preceding the longer terminal-link schedule. Consistent with the predictions of the delay-reduction hypothesis, the relative values of the terminal-link stimuli changed as a function of the overall frequency of primary reinforcement. Vaughan's (1985) melioration model, which was shown to be formally similar to Squires and Fantino's (1971) delay-reduction model, can be modified so as to predict these results without changing its underlying assumptions.     

Choice for conditioned reinforcers in the signaled absence of primary reinforcement

Pigeons responded in a multiple schedule in which concurrent schedules of brief-stimulus presentation alternated with a component in which food was available (concurrent-chains component). In the initial links of the concurrent-chains component subjects chose either of two stimuli each correlated with the terminal link of one chain. The terminal links involved either variable-interval 30-second or variable-interval 60-second schedules. In the brief-stimulus component subjects chose between 0.5-second presentations of the terminal-link stimuli from the concurrent-chains component. Responding was generally maintained in the brief-stimulus component in two subjects for more than 300 sessions, suggesting that brief stimuli were conditioned reinforcers. During the brief-stimulus component, in 17 of 21 cases for which a minimal number of responses occurred, choice proportions above 0.55 were obtained for the brief-stimulus presentations correlated with the higher rate of primary reinforcement in the concurrent-chains component. These results support the suggestion that choice in conventional concurrent-chains procedures is partially controlled by production of the terminal-link stimuli.     

Delay or rate of food delivery as determiners of response rate

Pigeons were confronted with two keys: a green food key and a white changeover key. Food became available for a peck to the green key after variable intervals of time (mean = 113 seconds). A single peck on the changeover key changed the color of the food key to red for a fixed period of time during which the timing of the variable-interval schedule in green was suspended and the switching option eliminated and after which the conditions associated with green were reinstated. In Experiment 1 a single food presentation was obtainable during each red-key period after a minimum delay timed from the switch. This delay and the duration of the red-key period were held constant during a condition but varied between conditions (delay = 2.5, 7.5, 15, or 30 seconds; red-period duration = 30, 60, 120, 240, or 480 seconds). In Experiment 2 additional food presentations were scheduled during a 240-second red-key period with the delay to the first food delivery held constant at 30 seconds, and the delays to later food deliveries varied over conditions. Considering the data from both experiments, the rate of switching to red was a decreasing function of the delay to the first food, the delay to the second food, and perhaps the delay to the third food after a switch. There was no clear evidence that the rate of food in the red-key period made an independent contribution. The ordering of response rates among conditions was consistent with the view that each food presentation after a response adds an incremental effect to the rate of the response and that each food presentation's contribution is a decreasing function of its delay timed from the response.     

Choice between single and multiple reinforcers in concurrent-chains schedules

Pigeons responded on concurrent-chains schedules with equal variable-interval schedules as initial links. One terminal link delivered a single reinforcer after a fixed delay, and the other terminal link delivered either three or five reinforcers, each preceded by a fixed delay. Some conditions included a postreinforcer delay after the single reinforcer to equate the total durations of the two terminal links, but other conditions did not include such a postreinforcer delay. With short initial links, preference for the single-reinforcer alternative decreased when a postreinforcer delay was present, but with long initial links, the postreinforcer delays had no significant effect on preference. In conditions with a postreinforcer delay, preference for the single-reinforcer alternative frequently switched from above 50% to below 50% as the initial links were lengthened. This pattern of results was consistent with delay-reduction theory (Squires & Fantino, 1971), but not with the contextual-choice model (Grace, 1994) or the hyperbolic value-added model (Mazur, 2001) as they have usually been applied. However, the hyperbolic value-added model could account for the results if its calculations were expanded to include reinforcers delivered in later terminal links. The implications of these findings for models of concurrent-chains performance are discussed.     

Choice and amount of reinforcement in rats

Rats were exposed to concurrent-chains schedules in which the terminal links were equal, fixed-interval (FI) schedules terminating in one or a varying number of food pellets. In most rats, choice proportions for the larger reinforcer increased with increases in reinforcer amount (e.g., from one to five food pellets). When log response ratios were plotted against log reinforcer amount ratios, the results indicated that the effects of reinforcer amount depended on the length of fixed-interval terminal links, by showing that rats undermatched their response ratios to reinforcer amount ratios with the shorter terminal links (FI 5 s, Experiment 1), whereas they overmatched with the longer terminal links (FI 20 s, Experiment 2). These results demonstrated that the manipulation of FI terminal-link schedules affected the sensitivity of choice to reinforcer amount, and are consistent with the previous findings that choice proportions for the larger of two reinforcers (one vs three food pellets) increased with increases in the length of FI terminal-link schedules.     

Choice with delayed and probabilistic reinforcers: effects of prereinforcer and postreinforcer stimuli.

In Experiment 1, pigeons' pecks on a green key led to a 5-s delay with green houselights, and then food was delivered on 20% (or, in other conditions, 50%) of the trials. Pecks on a red key led to an adjusting delay with red houselights, and then food was delivered on every trial. The adjusting delay was used to estimate indifference points: delays at which the two alternatives were chosen about equally often. Varying the presence or absence of green houselights during the delays that preceded possible food deliveries had large effects on choice. In contrast, varying the presence of the green or red houselights in the intertrial intervals had no effects on choice. In Experiment 2, pecks on the green key led to delays of either 5 s or 30 s with green houselights, and then food was delivered on 20% of the trials. Varying the duration of the green houselights on nonreinforced trials had no effect on choice. The results suggest that the green houselights served as a conditioned reinforcer at some times but not at others, depending on whether or not there was a possibility that a primary reinforcer might be delivered. Given this interpretation of what constitutes a conditioned reinforcer, most of the results were consistent with the view that the strength of a conditioned reinforcer is inversely related to its duration.     

Motivational control of impulsive behavior interacts with choice opportunities

Impulsive behavior has been investigated through choice between a smaller/immediate reinforcer and a larger/delayed reinforcer, or through performance on a differential reinforcement of low rate (DRL) schedule. In the present study, we investigated a methodological divergence between these two procedures: in the former procedure, delay is a consequence of the subject's own choice, whereas in the later procedure, subjects are explicitly reinforced for delaying a response. In Experiment 1, 7 rats maintained at 80% of their free-feeding weights showed poorer efficiency of lever-pressing responses on a DRL 30-s schedule than when they were maintained at 90% of free-feeding weight. In Experiment 2, 16 rats were subjected to a concurrent chain schedule: the initial link was concurrent fixed ratio 1 fixed ratio 1, and each of these alternatives was followed by a short-DRL requirement with a one pellet reinforcer or a long-DRL requirement with a three pellet reinforcer. In one block of trials, rats were not allowed to choose between the two terminal links (forced-choice), whereas in the other block of trials rats were allowed to choose freely between the two terminal links (free-choice). Compared with rats maintained at 95% of their free-feeding weights, rats maintained at 80% of their free-feeding weights showed poorer efficiency in the terminal links’ DRL schedule performance (just as in Experiment 1), but this difference was shown only in the forced-choice blocks. These results indicate that motivational control of DRL schedule performance interacts with type of choice-making opportunity and highlight the direct comparison of motivational control of impulsive choice and DRL schedule performance.     

Quinine pellets as an inferior good and a Giffen good in rats.

In Experiment 1, 4 rats earned their daily food ration by choosing between two levers. One lever delivered two regular and one quinine-adulterated food pellets, and the other delivered two regular and four quinine pellets. A 20-s intertrial interval separated successive choices. Sessions began with 10 forced trials during which only one lever, selected with p = .5 and cued by a light above it, could deliver its reinforcer. Forced trials were followed by 30 or 150 trials, depending on the condition, during which choices to either lever could be reinforced. Over this range, absolute choice of the four-quinine, two-regular-pellet lever was inversely related to the number of free-choice trials, establishing this reinforcer as an inferior good. In Condition 1 of Experiment 2, the prior design was altered in two ways: (a) one lever delivered four quinine pellets, and the other lever delivered one standard pellet; and (b) sessions ended after 140 free-choice trials. When the number of free-choice trials was reduced to 100 (Condition 2), all 3 rats increased their preference for quinine pellets, confirming their status as an inferior good. In the next several conditions, the number of quinine pellets provided for selecting its associated lever was varied between three and four. Preference for the quinine-pellet alternative was inversely related to the number of pellets it provided, a result defining it as a Giffen good. These findings are not accommodated readily by extant choice models and complicate the search for a unitary model of choice.     

Determination of discount functions in rats with an adjusting-amount procedure.

An adjusting-amount procedure was used to measure discounting of reinforcer value by delay. Eight rats chose between a varying amount of immediate water and a fixed amount of water given after a delay. The amount of immediate water was systematically adjusted as a function of the rats' previous choices. This procedure was used to determine the indifference point at which each rat chose the immediate amount and the delayed amount with equal frequency. The amount of immediate water at this indifference point was used to estimate the value of the delayed amount of water. In Experiment 1, the effects of daily changes in the delay to the fixed reinforcer (100 microliters of water delivered after 0, 2, 4, 8, or 16 s) were tested. Under these conditions, the rats reached indifference points within the first 30 trials of each 60-trial session. In Experiment 2, the effects of water deprivation level on discounting of value by delay were assessed. Altering water deprivation level affected the speed of responding but did not affect delay discounting. In Experiment 3, the effects of varying the magnitude of the delayed water (100, 150, and 200 microliters) were tested. There was some tendency for the discounting function to be steeper for larger than for smaller reinforcers, although this difference did not reach statistical significance. In all three experiments, the obtained discount functions were well described by a hyperbolic function. These experiments demonstrate that the adjusting-amount procedure provides a useful tool for measuring the discounting of reinforcer value by delay.     

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.     

Food deliveries during the pause on fixed-interval schedules

Pigeons were trained on fixed-interval schedules of food delivery. In Experiments I and II, the fixed interval was initiated by the previous fixed-interval reinforcer; in Experiment III, the fixed interval was initiated by the first key peck following the preceding fixed-interval reinforcer (a chain fixed-ratio one, fixed-interval schedule). During the postreinforcement pause, variable-time schedules delivered food independent of any specific response. Rate of food delivery during the pause had only small effects on pause duration in Experiments I and II. In Experiment III, however, pause duration increased systematically with the rate of food delivery during the pause. These data suggest that the momentary proximity to reinforcement delivered via the fixed-interval schedule exerts potent control over pause termination. Additional analysis revealed that pause termination was unaffected by the intermittent delivery of food during the pause. Such data suggest that the temporal control by fixed-interval schedules is highly resistant to interference.     

Preference for signaled versus unsignaled reinforcement delay in concurrent-chain schedules

A concurrent-chain schedule was employed to examine pigeons' preferences for signaled versus unsignaled delay of reinforcement in which the delay durations ranged from zero to ten seconds. In general, pigeons preferred signaled delay over unsignaled delay especially when a variable-interval 30-second schedule operated in each initial link; when a variable-interval 90-second schedule operated in each initial link, these preferences tended toward indifference or were attenuated. In addition, prior training seemed to exert partial control over behavior. Responding in the terminal link was higher under signaled delay than unsignaled delay in a majority of the cases. Moreover, response rates under signaled delay remained fairly constant whereas responding under unsignaled delay was initially high, but decreased systematically with delay durations as short as 2.5 seconds. These results are consistent with a number of other studies demonstrating the significant role of a signal for impending positive stimuli.     

Delay and number of food reinforcers: Effects on choice and latencies

Pigeons were given a choice between two identical-duration situations (terminal links of chain schedules). One terminal link of the choice pair provided two food deliveries, and the other provided five. The exact times of these food deliveries differed between the terminal links and were varied over conditions. A single response during the initial link gave immediate access to the corresponding terminal link. Forced trials, during which only one of the initial-link keys was lighted, were interspersed with choice trials during which both initial-link keys were lighted. Choice tended to favor whichever terminal link was correlated with the higher sum of the immediacies (i.e., the sum of the reciprocals of the delays to each of the reinforcers following the choice, with all delays measured from the choice). Latencies on forced trials and on choice trials also were related (negatively) to the sum of the immediacies. This correlation among response measures (choice and latencies) suggests that both measures are manifestations of the effect of conditioned reinforcement on response tendencies.     

Theories of probabilistic reinforcement.

In three experiments, pigeons chose between two alternatives that differed in the probability of reinforcement and the delay to reinforcement. A peck at a red key led to a delay of 5 s and then a possible reinforcer. A peck at a green key led to an adjusting delay and then a certain reinforcer. 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 Experiments 1 and 2, the intertrial interval was varied across conditions, and these variations had no systematic effects on choice. In Experiment 3, the stimuli that followed a choice of the red key differed across conditions. In some conditions, a red houselight was presented for 5 s after each choice of the red key. In other conditions, the red houselight was present on reinforced trials but not on nonreinforced trials. Subjects exhibited greater preference for the red key in the latter case. The results were used to evaluate four different theories of probabilistic reinforcement. The results were most consistent with the view that the value or effectiveness of a probabilistic reinforcer is determined by the total time per reinforcer spent in the presence of stimuli associated with the probabilistic alternative. According to this view, probabilistic reinforcers are analogous to reinforcers that are delivered after variable delays.