Preference for multiple versus mixed schedules of reinforcement

Five pigeons were trained in a concurrent-chain procedure. In the initial links, equal nonindependent variable-interval schedules were available concurrently on two keys. Completing the schedule on either key led to exclusive presentation of one of two further variable-interval schedules for a fixed period of time. During these terminal links, as many reinforcers as were scheduled could be obtained. If the response producing this terminal link occurred on one key, differential stimuli signaled which variable-interval schedule had been produced. If the response producing the terminal link occurred on the other key, no such differential stimuli were available. Once the fixed period of time elapsed, the initial links were reinstated. In Experiment 1, the period of time for which the terminal links were available was always 10 s and the absolute duration of the initial links was varied. Subjects preferred the alternative leading to the multiple schedule when the initial-link duration was short, but preferred the alternative leading to the mixed schedule when the initial-link durations were longer. In Experiment 2, both the initial-link duration and the duration of the terminal links were varied. The effect of initial-link duration was identical to that in Experiment 1 and there was no systematic effect of varying the terminal-link duration.     

Bias and sensitivity to reinforcement in a concurrent-chain schedule

Six pigeons were trained on concurrent-chain schedules in which the initial links were either dependent (Experiment 1) or independent (Experiment 2) concurrent variable-interval schedules and the terminal links were fixed-duration delays to reinforcement in blackout. A changeover delay of three seconds operated in the initial links. Both the initial- and terminal-link schedule values were varied over 61 experimental conditions. An analysis of the data using the generalized matching law showed that the sensitivity of initial-link response allocation to the frequency of terminal-link production was independent of both the duration of the terminal-link delays and, though less clearly, of the duration of the initial-link schedules. Sensitivity of initial-link response allocation to terminal-link reinforcer-rate ratios was a joint function of the terminal-link durations and the smaller average initial-link duration. The results showed that the generalized matching law is useful in analyzing concurrent-chain schedule performance and that a changeover delay in the initial links eliminates some terminal- to initial-link interactions that have made quantitative predictions for concurrent-chain performances difficult.     

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 delay of reinforcement: Effects of terminal-link stimulus and response conditions

In two experiments, pigeons were exposed to concurrent-chains schedules in which a single initial-link variable-interval schedule led to access to terminal links composed of fixed-interval or fixed-delay schedules. In Experiment 1, an 8-s (or 16-s) delay to reinforcement was associated with the standard key, while reinforcer delay values associated with the experimental key were varied from 4 to 32 s. The results of Experiment 1 showed undermatching of response ratios to delay ratios with terminal-link fixed-delay schedules, whereas in some pigeons matching or overmatching was evident with the fixed-interval schedules. In Experiment 2, one pair of reinforcer delay values, either 8 versus 16 s or 16 versus 32 s, was used. In the first condition of Experiment 2, different delays were associated with different keylight stimuli (cued condition). In the second condition, different terminal-link delays were associated with the same stimulus, either a blackout (uncued-blackout condition) or a white key (uncued-white condition). To examine the role of responses emitted during delays, the keys were retracted during a delay (key-absent condition) in the third condition and responses were required by a fixed-interval schedule in the fourth condition. Experiment 2 demonstrated that the choice proportions for the shorter delay were more extreme in the cued condition than in the uncued-blackout condition, and that the response requirement imposed by the fixed-interval schedules did not affect choice of the shorter delay, nor did the key-absent and key-present conditions. These results indicate that the keylight-stimulus conditions affected preference for the shorter of two delays and that the findings obtained in Experiment 1 depended mainly on the keylight-stimulus conditions of the terminal links (i.e., the conditioned reinforcing value of the terminal-link stimuli).     

Effects on preference of reinforcement delay, number of reinforcers, and terminal-link duration

Three experiments used concurrent-chains procedures to examine the effects of reinforcement delay, number of reinforcers, and terminal-link duration on preference. In Condition 30 of Experiment 1, food was delivered after 30 seconds in each 150-second terminal link, with four additional food deliveries occurring at 30-second intervals in one of the links. In Condition 5, food was delivered after 5 seconds in each 25-second terminal link, and the four additional reinforcers were delivered at 5-second intervals. Preferences for the multiple-food chain were greater in Condition 30. In Experiment 2, the terminal link(s) providing only one reinforcer terminated immediately after delivery of the reinforcer. Preferences for the multiple-food chain were smaller than in Experiment 1. In Condition 5 of Experiment 3, food was delivered after 5, 75, 100, 125, and 150 seconds in one 150-second link and after 5 seconds in the other. Condition 50 differed only in that the first (or only) reinforcer in each link was delivered after 50 seconds instead of after 5 seconds. Preferences for the multiple-food chain were greater in Condition 50. Results of Experiments 1 and 2 do not correspond to results obtained by Moore (1979).     

DOES SENSITIVITY TO MAGNITUDE DEPEND ON THE TEMPORAL DISTRIBUTION OF REINFORCEMENT?

Our research addressed the question of whether sensitivity to relative reinforcer magnitude in concurrent chains depends on the distribution of reinforcer delays when the terminal-link schedules are equal. In Experiment 1, 12 pigeons responded in a two-component procedure. In both components, the initial links were concurrent variable-interval 40-s variable-interval 40-s, and the terminal links were both 20-s interval schedules in which responses were reinforced by either 4-s of grain in one, or 2-s of grain in the other. The only difference between the components was whether the terminal-link schedules were fixed interval or variable intervals. For all subjects, the relative rate of responding in the initial links for the terminal link that produced the 4-s reinforcer was greater when the terminal links were fixed-interval schedules than when they were variable-interval schedules. This result is contrary to the prediction of Grace's (1994) contextual choice model, but is consistent with both Mazur's (2001) hyperbolic value-added model and Killeen's (1985) incentive theory. In Experiment 2, 4 pigeons responded in a concurrent-chains procedure in which 4-s or 2-s reinforcers were provided independently of responding according to equal fixed-time or mixed-time schedules. Preference for the 4-s reinforcer increased as the variability of the intervals comprising the mixed-time schedules was decreased. Generalized-matching sensitivity of initial-link response allocation to relative reinforcer magnitude was proportional to the geometric mean of the terminal-link delays.     

Children's choice: Sensitivity to changes in reinforcer density

Two experiments were carried out in which children's sensitivity to changes in reinforcer density (number of reinforcers per session) was measured in a choice paradigm. In Experiment 1, 24 girls (ages 6, 9, and 12 years) performed on concurrent-chain schedules of reinforcement. The initial links were variable-interval 10-s schedules. One terminal link always gave three tokens after 30 s, but the parameters associated with the other were varied. Independent manipulations of reinforcer size (two tokens or four tokens) and prereinforcement delay (25 s or 65 s) led to equal changes in the relative density of tokens that could be earned on the schedules. Subjects at all ages were sensitive to changes in reinforcer density brought about by changes in reinforcer size, whereas only 3 12-year-olds showed sensitivity to the changes brought about by manipulation of prereinforcer delay. In Experiment 2, titration procedures were used to test the extent of this insensitivity to delay in 32 6- and 12-year-old children. In these procedures, a repeated choice of the large reinforcer increased the delay to its delivery, and a repeated choice of the small reinforcer reduced the delay to the delivery of the large reinforcer. Whereas 6-year-old boys and girls tended to maintain a strong preference for the large reinforcer, so increasing the delay to its delivery, 12-year-olds tended to distribute their responses to both alternatives, thus producing a stable level of delay to the large reinforcer. The results from the two experiments support the idea of two stages in the development of adaptive intertemporal choice.     

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.     

Stimulus Equivalence: Effects Of A Default-response Option On Emergence Of Untrained Stimulus Relations

Human subjects were exposed to a concurrent-chains schedule in which reinforcer amounts, delays, or both were varied in the terminal links, and consummatory responses were required to receive points that were later exchangeable for money. Two independent variable-interval 30-s schedules were in effect during the initial links, and delay periods were defined by fixed-time schedules. In Experiment 1, subjects were exposed to three different pairs of reinforcer amounts and delays, and sensitivity to reinforcer amount and delay was determined based on the generalized matching law. The relative responding (choice) of most subjects was more sensitive to reinforcer amount than to reinforcer delay. In Experiment 2, subjects chose between immediate smaller reinforcers and delayed larger reinforcers in five conditions with and without timeout periods that followed a shorter delay, in which reinforcer amounts and delays were combined to make different predictions based on local reinforcement density (i.e., points per delay) or overall reinforcement density (i.e., points per total time). In most conditions, subjects' choices were qualitatively in accord with the predictions from the overall reinforcement density calculated by the ratio of reinforcer amount and total time. Therefore, the overall reinforcement density appears to influence the preference of humans in the present self-control choice situation.     

Choice in the time-left procedure and in concurrent chains with a time-left terminal link.

In two experiments, rats chose between a standard fixed-duration food-associated stimulus and a stimulus whose duration was the time remaining to reinforcement in an elapsing comparison interval. In Experiment 1, 4 rats responded in a time-left procedure wherein a single initial-link variable-interval schedule set up two potential terminal links simultaneously. As time elapsed in the initial-link schedule, the choice was between a standard fixed-interval 30-s terminal link and a time-left terminal link whose programmed interval requirement equaled 90 s minus the elapsed time in the initial link. Rats generally responded more on the lever with the shortest programmed terminal-link duration, but the temporal parameters of the procedure were found to vary with response distributions. Contrary to previous reports, therefore, time-left data were well predicted by choice models that make no assumptions about animal timing. In Experiment 2, 8 rats responded on a concurrent-chains schedule with independent variable-interval initial links and a time-left terminal link in one of the choice schedules. On the time-left lever, the programmed terminal-link delay equaled 90 s minus the elapsed time in the time-left initial link. On the standard lever, terminal-link responses were reinforced according to a variable-interval schedule whose average value varied over four conditions. Relative time-left initial-link responses increased in the elapsing time-left initial-link schedule as the time-left terminal link became shorter relative to the standard terminal link. Scalar expectancy theory failed to predict the resultant data, but a modified version of the delay-reduction model made good predictions. An analysis of the elaboration of scalar expectancy theory for variable delays demonstrated that the model is poorly formulated for arithmetically distributed delays.     

Concurrent-chain performance in transition: effects of terminal-link duration and individual reinforcers

Pigeons responded on concurrent-chain schedules with variable-interval initial links and equal delays as terminal links. The terminal-link delays were 1 sec in some conditions and 20 sec in other conditions. The percentages of reinforcers delivered for responses on the left key were 10%, 30%, 70%, or 90%, and this percentage was switched every five to nine sessions. The rate of change in the pigeons' response percentages after a switch was the same whether the terminal-link delays were 1 sec or 20 sec. Analysis of the effects of individual reinforcers showed that after a response on one key had been reinforced, response percentages on that key were higher for at least the next 100 responses. Small effects of individual reinforcers were evident after eight or nine additional reinforcers had been delivered. The effects of individual reinforcers were about equally large during times of transition and during periods in which overall response percentages were relatively stable.     

Two- versus three-alternative concurrent-chain schedules: a test of three models

Two experiments with pigeons used concurrent-chain procedures with variable-interval schedules as initial links and different delays to food as terminal links. Two schedules were present in all sessions, but a 3rd schedule was alternately present and absent in successive sessions. When the 3rd schedule delivered food with no terminal-link delay, the presence of this schedule led to an increase in preference for the schedule with the shorter terminal link of the 2 unchanged schedules. When the terminal-link delay for the 3rd schedule was 30 s, the presence of this schedule led to a decrease in preference for the schedule with the shorter terminal link of the 2 unchanged schedules. These results are inconsistent with the predictions of R. Grace's (1994) contextual-choice model, but they are consistent with 2 other mathematical models--delay-reduction theory and the hyperbolic value-added model.     

Concurrent-chain performance: Effects of absolute and relative terminal-link entry frequency

Six pigeons were trained in a concurrent-chain procedure with constant variable-interval 6-s variable-interval 12-s terminal links. Five groups of conditions were arranged. Within a group of conditions, the duration of one initial-link schedule was held constant and the duration of the other initial link was varied. The duration of the varied initial link was always longer than, or equal to, the constant initial-link duration. The duration of the shorter initial link was varied across groups of conditions from 5 s to 70 s. The data from each group were well described by the generalized matching law. Sensitivity (a) to the terminal-link entry ratio increased as the shorter initial-link duration increased, but appeared to reach an asymptote at shorter initial-link durations greater than 32 s. Terminal-link bias did not change with changes in shorter initial-link duration for the response-allocation data, but showed a small increase with increasing shorter initial-link duration for the time-allocation data.     

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.     

Effects of experience on preference between forced and free choice

Preference between forced choice and free choice in concurrent-chain schedules of reinforcement was investigated in pigeons after exposure to particular combinations of terminal links. In Experiment 1, in which terminal links always ended with reinforcers, one of three pairs of terminal links was arranged as preexposure: (a) both terminal links had only one key (forced choice), (b) both terminal links had two keys (free choice), or (c) a combination of forced and free choice was arranged across sessions. In test sessions following the preexposure, pigeons' preferences rapidly shifted to the terminal links with which they had no recent experience. In Experiment 2, the same procedure was repeated except that each terminal link ended intermittently with reinforcers with a probability of .5 and there was no terminal-link arrangement with a combination of free and forced choice. Pigeons showed the same preference changes as in Experiment 1, but the preference changes did not appear immediately at the beginning of test sessions. These data suggest that recent previous experience was a more important determinant of preference than the difference between forced-choice and free-choice terminal links.     

Transfer tests of stimulus value in concurrent chains

We report two experiments that use transfer tests to investigate whether in concurrent chains the value of a terminal-link stimulus is affected by the alternate terminal link. In Experiment 1, two groups of pigeons were trained on multiple concurrent-chains schedules in which switching between the schedules was via pecking a changeover key. For one group, the terminal links were fixed-interval 8 s versus fixed-interval 16 s in one component and fixed-interval 16 s versus fixed-interval 32 s in the other component. For a second group, the terminal links were variable-interval 10 s versus variable-interval 20 s in one component and variable-interval 20 s versus variable-interval 40 s in the other. After sufficient baseline training had been given so that performances had stabilized, transfer tests were conducted in which the two chains with equal terminal-link schedules were presented together as a new concurrent pair. For 6 of the 7 subjects, initial-link responding changed fairly rapidly during the test in the manner predicted if the values of the terminal links were equal. In Experiment 2, pigeons were trained on multiple concurrent chains using a two-key procedure, and the terminal links were the same variable-interval schedules as in Experiment 1. After baseline training, transfer tests were conducted that assessed (a) the relative reinforcing strength of the terminal-link stimuli in a novel initial-link situation and (b) the relative ability of those stimuli to evoke responding. The data from the reinforcing strength test were consistent with those from Experiment 1, but those from the evocation strength test were not. Although this discrepancy shows that responding in transfer tests is not solely a function of stimulus value, the results from both experiments suggest, overall, that value is determined by the stimulus—reinforcer relation independently of the alternative terminal link.     

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.     

Evidence against a constant-difference effect in concurrent-chains schedules

Savastano and Fantino (1996) reported that in concurrent-chains schedules, initial-link choice proportions remained constant as terminal-link durations increased as long as the subtractive difference between the two terminal-link schedules remained constant. Two experiments with pigeons were conducted to examine this constant-difference effect. Both experiments used equal variable-interval schedules as initial links. The terminal links were fixed delays to reinforcement in Experiment 1 and variable delays to reinforcement in Experiment 2. The durations of the terminal links were varied across conditions, but the difference between pairs of terminal links was always 10 s. In both experiments, preference for the shorter terminal link became less extreme as terminal-link durations increased, so a constant-difference effect was not found. It is argued, however, that this choice situation does not provide clear evidence for or against delay-reduction theory versus other theories of choice.     

The effect of shock intensity on concurrent and single-key responding in concurrent-chain schedules

Pigeons were trained to respond in a two-link, concurrent-chain schedule. Pecks on each key during the concurrent initial links occasionally produced a 5-min terminal link, during which only that key was operative. Food reinforcement and various intensities of shock were scheduled during the terminal links. When shock was contingent on response, the effect of shock was greater on terminal-link responding than on initial-link responding. When shock was independent of response, the effect was reversed, with larger changes in initial-link responding than terminal-link responding. In general, shock was found to affect behavior most drastically when behavior could, in turn, affect the rate of shock.