Psychological distance to reward: Segmentation of aperiodic schedules of reinforcement

College students responded for monetary rewards in two experiments on choice between differentially segmented aperiodic schedules of reinforcement. On a microcomputer, the concurrent chains were simulated as an air-defense video game in which subjects used two radars for detecting and destroying enemy aircraft. To earn more cash-exchangeable points, subjects had to shoot down as many planes as possible within a given period of time. For both experiments, access to one of two radar systems (terminal link) was controlled by a pair of independent concurrent variable-interval 60-s schedules (initial link) with a 4-s changeover delay always in effect. In Experiment 1, the appearance of an enemy aircraft in the terminal link was determined by a variable-interval (15 s or 60 s) schedule or a two-component chained variable-interval schedule of equal duration. Experiment 2 was similar to Experiment 1 except for the segmented schedule, which had three components. Subjects preferred the unsegmented schedule over its segmented counterpart in the conditions with variable-interval 60 s, and preference tended to be more pronounced with more components in the segmented schedule. These findings are compatible with those from previous studies of periodic and aperiodic schedules with pigeons or humans as subjects.     

Preference for less segmented fixed-time components in concurrent-chain schedules of reinforcement

A concurrent-chain procedure was used to examine choice between segmented and less segmented response-independent schedules of reinforcement. A pair of independent, concurrent variable-interval 60-s schedules were presented in the initial link, along with a 1.5-s changeover delay. A chained fixed-interval fixed-time and its corresponding tandem schedule constituted the terminal links. The length of the fixed-interval schedule in the terminal link was varied between 5 s and 30 s while that of the fixed-time schedule was kept at 5 s over conditions. The first components of both terminal-link schedules were accompanied by the same stimulus. Except in the baseline condition, the onset of the second component of the terminal-link chained schedule was accompanied by either a localized (key color) or a nonlocalized (dark houselight) stimulus change. Stimulus conditions were constant during the terminal-link tandem schedule. With three exceptions, pigeons demonstrated a slight preference for the tandem over the chained schedule in the terminal link. Furthermore, this preference varied inversely with the length of the first component. In general, these results are consistent with previous studies that reported an adverse effect on choice by segmenting an interval schedule into two or more components, but they are inconsistent with studies that reported preference for signaled over unsignaled delay of reinforcement.     

Resistance to change produced by access to fixed-delay versus variable-delay terminal links

Pigeons' responding was reinforced on a multiple schedule consisting of two two-link chain schedules presented in regular alternation. Responding in initial links (always variable-interval 60-s) produced a key-color change and access to a terminal link. The terminal link for one chain provided food after a fixed delay (fixed-interval or fixed-time); the terminal link for the other provided food after a variable delay (variable-interval or variable-time). The average duration of the terminal-link schedules was varied across conditions, but in every condition the arithmetic mean of the variable-delay terminal-link schedule was equal to the duration of the fixed delay. Response rates were higher in the initial links of the chains with the variable-delay terminal links. Response-decreasing operations (satiation, extinction) were used after performances reached asymptote. Response rates maintained by access to variable-delay terminal links tended to be more resistant to change than were rates maintained by access to fixed-delay terminal links. These results are consistent with the preference for variable- over fixed-interval terminal links observed with concurrent-chains schedules, suggesting (1) that immediacy of reinforcement influences the conditioned reinforcing potency of access to a terminal link and (2) that choice in concurrent chains and resistance of responding to change may be manifestations of the same effect of reinforcement.     

Psychological distance to reward: A human replication

Choice behavior in college students was examined in two experiments using the concurrent-chains procedure. In both experiments, the concurrent chains were presented on a microcomputer in the form of an air-defense game in which subjects used two radar systems to detect and subsequently destroy enemy aircraft. Access to one of two radar systems was controlled by a pair of independent concurrent variable-interval 60-s schedules with a 4-s changeover delay always in effect. In the terminal link, the appearance of an enemy aircraft was determined by a pair of differentially segmented fixed-time schedules (Experiment 1) or fixed-interval schedules (Experiment 2) of equal overall duration. In Experiment 1, the terminal-link duration was either 20 s or 40 s, and subjects preferred the unsegmented to the segmented intervals. In Experiment 2, the duration was either 10 s or 60 s, and the reinforcement contingencies required responding during the terminal link. Prior to the reinstatement of the initial link, subjects estimated the duration of the terminal-link schedule. Segmentation affected choice in the 60-s conditions but not in the 10-s ones. Preference for the unsegmented schedule was correlated with an overestimation of the durations for the segmented schedules. These results replicated those found in animal experiments and support the notion of increasing the psychological distance to reward by segmenting a time-based schedule of reinforcement.     

Preference for unsegmented interreinforcement intervals in concurrent chains

Five pigeons were trained under concurrent-chain schedules in which a pair of independent, concurrent variable-interval 60-s schedules were presented in the initial link and either both variable-interval or both fixed-interval schedules were presented in the terminal link. Except for the baseline, one of the terminal-link schedules was always a two-component chained schedule and the other was either a simple or a tandem schedule of equal mean interreinforcement interval. The values of the fixed-interval schedules were either 15 s or 60 s; that of the variable-interval schedules was always 60 s. A 1.5-s changeover delay operated during the initial link in some conditions. The pigeons preferred a simple or a tandem schedule to a chain. For the fixed-interval schedules, this preference was greater when the fixed interval was 60 s than when it was 15 s. For the variable-interval schedules, the preferences were less pronounced and occurred only when the changeover delay was in effect. For a given type of schedule and interreinforcement interval, similar preferences were obtained whether the nonchained schedule was a tandem or simple schedule. The changeover delay generally inflated preference and lowered the changeover rate, especially when the terminal-link schedules were either short (15 s) or aperiodic (variable-interval). The results were consistent with the notion that segmenting the interreinforcement interval of a schedule into a chain lowers the preference for it.     

Homogeneous chains, heterogeneous chains, and delay of reinforcement

Three pigeons responded on two-component chain schedules in which the required response topography in the initial and terminal links was similar (a homogeneous chain) or dissimilar (a heterogeneous chain). Key-peck responding in the initial link under a variable-interval 60-second (VI 60) schedule produced a terminal link in which, in different conditions, either key pecking or foot treadling was reinforced according to a VI 60 schedule. Multiple VI 60 VI 60 schedules, in which the responses required in the chain schedules were maintained by primary reinforcement in the two components, preceded and followed each type of chain. These multiple schedules were used to ensure that both responses occurred reliably prior to introducing the chain schedule. Key-peck response rates in the initial link of the chain consistently were higher during the homogeneous chain than during the heterogeneous chain. These results illustrate that intervening events during a period separating an operant response from primary reinforcement influence that operant, independently of the delay between the response and reinforcement.     

Dual effects on choice of conditioned reinforcement frequency and conditioned reinforcement value

Pigeons were presented with a concurrent‐chains schedule in which the total time to primary reinforcement was equated for the two alternatives (VI 30 s VI 60 s vs. VI 60 s VI 30 s). In one set of conditions, the terminal links were signaled by the same stimulus, and in another set of conditions they were signaled by different stimuli. Choice was in favor of the shorter terminal link when the terminal links were differentially signaled but in favor of the shorter initial link (and longer terminal link) when the terminal links shared the same stimulus. Preference reversed regularly with reversals of the stimulus condition and was unrelated to the discrimination between the two terminal links during the nondifferential stimulus condition. The present results suggest that the relative value of the terminal‐link stimuli and the relative rate of conditioned reinforcer presentation are important influences on choice behavior, and that models of conditioned reinforcement need to include both factors.     

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.     

Effects of free food deliveries and temporal contiguity on choice under concurrent-chain schedules

Eight pigeons responded in a concurrent chain with variable-interval (VI) 10-sec and VI 20-sec terminal links. Free food deliveries were then added to the initial links according to a variable-time (VT) 20-sec schedule in two conditions that differed in terms of whether a differential reinforcement of other (DRO) contingency was also arranged, which ensured that those deliveries could not occur within 2-sec of a response. Preference for the VI 10-sec terminal link increased when VT food was added, but not when the DRO contingency was operative, showing that free food deliveries affected preference only when those deliveries could be temporally contiguous with choice responding. This finding suggests that Mazur’s (2003) report of increased preference with added VT food, replicated here, was due to adventitious reinforcement. Current models for behavioral choice are limited because they are based entirely on temporal relations between stimuli and reinforcers and fail to take into account response-reinforcer contiguity.     

The schedule dependency of the signaled reinforcement effect

In Experiment 1, rats leverpressed for food reinforcement on either a variable ratio (VR) 30 schedule or a variable interval (VI) 15-s schedule. One group in each condition received a signal filling a 500-ms delay of reinforcement. This treatment enhanced rates on the VR schedule, and attenuated rates on the VI schedule, relative to the rate seen in an unsignaled control condition. In Experiment 2 there was no delay of reinforcement and the signal and food were presented simultaneously. Attenuated rates of responding were observed on VI schedules with a range of mean interval values (15 to 300 s). Experiment 3 used a range of VR schedules (10 to 150) with simultaneous presentations of signal and food. A signal-induced enhancement of response rate was found at all VR values. In Experiment 4, a signal elevated response rates on a tandem VI VR schedule, but depressed rates on a tandem VR VI schedule, compared to control conditions receiving unsignaled delayed reinforcement. These results are taken to show that the effect of a signal accompanying reinforcement depends upon the nature of the behavior that is reinforced during exposure to a given schedule.     

Arousal, changeover responses, and preference in concurrent schedules

Pigeons were trained on multiple schedules that provided concurrent reinforcement in each of two components. In Experiment 1, one component consisted of a variable-interval (VI) 40-s schedule presented with a VI 20-s schedule, and the other a VI 40-s schedule presented with a VI 80-s schedule. After extended training, probe tests measured preference between the stimuli associated with the two 40-s schedules. Probe tests replicated the results of Belke (1992) that showed preference for the 40-s schedule that had been paired with the 80-s schedule. In a second condition, the overall reinforcer rate provided by the two components was equated by adding a signaled VI schedule to the component with the lower reinforcer rate. Probe results were unchanged. In Experiment 2, pigeons were trained on alternating concurrent VI 30-s VI 60-s schedules. One schedule provided 2-s access to food and the other provided 6-s access. The larger reinforcer magnitude produced higher response rates and was preferred on probe trials. Rate of changeover responding, however, did not differ as a function of reinforcer magnitude. The present results demonstrate that preference on probe trials is not a simple reflection of the pattern of changeover behavior established during training.     

Preference for simple interval schedules of reinforcement in concurrent chains: Effects of segmentation ratio

A concurrent-chains procedure was used to examine pigeons' preferences between segmented and unsegmented terminal-link schedules of reinforcement. During the initial link, a pair of independent, concurrent variable-interval 60-s schedules was in effect. In the terminal link, reinforcement was provided by a chain fixed-interval fixed-interval schedule on one key and by a simple fixed-interval schedule with an equal interreinforcement interval in the other. The relative duration between the first and second components (segmentation ratio) in the terminal-link chained schedule was systematically varied while the terminal-link duration was kept constant at either 15 s or 30 s in two sets of conditions. With few exceptions, the simple schedule was preferred to the chained schedule. Furthermore, this preference was inversely related to the size of the segmentation ratio in the segmented schedule. When the segmentation ratio was smaller than 1:1, preference was more extreme for a 30-s condition than for a 15-s condition. However, preference decreased more rapidly in conditions with the longer terminal-link duration when the ratio increased. Taken together, these results were consistent with previous findings concerning the effect of the terminal-link duration on choice between segmented and unsegmented schedules. In addition, the data suggested that segmentation ratio in a segmented schedule constitutes another potent factor influencing preference for the unsegmented schedule.     

Conditioned reinforcement by conditional discriminative stimuli.

A concurrent-chains schedule was used to examine how a delay to conditional discriminative stimuli affects conditioned reinforcement strength. Pigeons' key-peck responses in the initial link produced either of two terminal links according to independent variable-interval 30-s schedules. Each terminal link involved an identical successive conditional discrimination and was segmented into three links: a delay interval (green), a color conditional discriminative stimulus (blue or red), and a line conditional discriminative stimulus (vertical or horizontal lines). Food delivery occurred 45 s after entering the terminal link with a probability of .5, but its conditional probability (1.0 or 0) depended on the combination of the color and the line stimuli. One of the color stimuli occurred independently of further responding, 5 s after entry into the right terminal link, but it occurred 35 s after entry into the left terminal link. One of the line stimuli occurred independently of responding 40 s after entry into either terminal link, synchronized with the offset of the color stimulus. The initial-link relative response rate for the right was consistently higher in comparison with a control condition in which the color stimuli occurred 20 s after entry into either terminal link. The preference for the short delay to the color conditional discriminative stimuli suggests the possibility of conditioned reinforcement by information about the relation between the line conditional discriminative stimuli and the outcomes.     

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.     

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.     

The generality of selective observing

Four rats obtained food pellets by poking a key and 5-s presentations of the discriminative stimuli by pressing a lever. Every 1 or 2 min, the prevailing schedule of reinforcement for key poking alternated between rich (either variable-interval [VI] 30 s or VI 60 s) and lean (either VI 240 s, VI 480 s, or extinction) components. While the key was dark (mixed-schedule stimulus), no exteroceptive stimulus indicated the prevailing schedule. A lever press (i.e., an observing response), however, illuminated the key for 5 s with either a steady light (S+), signaling the rich reinforcement schedule, or a blinking light (S-), signaling the lean reinforcement schedule. One goal was to determine whether rats would engage in selective observing (i.e., a pattern of responding that maintains contact with S+ and decreases contact with S-). Such a pattern was found, in that a 5-s presentation of S+ was followed relatively quickly by another observing response (which likely produced another 5-s period of S+), whereas exposure to S- resulted in extended breaks from observing. Additional conditions demonstrated that the rate of observing remained high when lever presses were effective only when the rich reinforcement schedule was in effect (S+ only condition), but decreased to a low level when lever presses were effective only during the lean reinforcement component (S- only condition) or when lever presses had no effect (in removing the mixed stimulus or presenting the multiple-schedule stimuli). These findings are consistent with relativistic conceptualizations of conditioned reinforcement and extend the generality of selective observing to procedures in which the experimenter controls the duration of stimulus presentations, the schedule components both offer intermittent food reinforcement, and rats serve as subjects.     

Value of conditioned reinforcers as a function of temporal context

In two experiments, pigeons were trained on a multiple-chain schedule, in which the initial link for one chain was a variable-interval (VI) 100 s schedule and for the other chain a VI 10 s schedule. The terminal links were both fixed-time 30 s schedules signaled by differently colored stimuli. Following training, the pigeons had their preference for the terminal-link stimuli tested either by presenting these stimuli in concurrent probes or by presenting these stimuli as reinforcement for completing novel initial links. In Experiment 1, pigeons significantly preferred the terminal-link stimulus that followed the long initial link in three of the five conditions. This preference was observed across all three testing procedures (concurrent chains, concurrent chains probes, and concurrent probes). Experiment 2 was a replication of this effect in one of the conditions from Experiment 1. The results demonstrate that temporal context does impact the value of a conditioned reinforcer in a manner consistent with delay-reduction theory, and inconsistent with other choice theories, such as the contextual choice model and scalar expectancy theory.     

Key pecking of pigeons under variable-interval schedules of briefly signaled delayed reinforcement: effects of variable-interval value.

Key pecking of 4 pigeons was maintained under a multiple variable-interval 20-s variable-interval 120-s schedule of food reinforcement. When rates of key pecking were stable, a 5-s unsignaled, nonresetting delay to reinforcement separated the first peck after an interval elapsed from reinforcement in both components. Rates of pecking decreased substantially in both components. When rates were stable, the situation was changed such that the peck that began the 5-s delay also changed the color of the keylight for 0.5 s (i.e., the delay was briefly signaled). Rates increased to near-immediate reinforcement levels. In subsequent conditions, delays of 10 and 20 s, still briefly signaled, were tested. Although rates of key pecking during the component with the variable-interval 120-s schedule did not change appreciably across conditions, rates during the variable-interval 20-s component decreased greatly in 1 pigeon at the 10-s delay and decreased in all pigeons at the 20-s delay. In a control condition, the variable-interval 20-s schedule with 20-s delays was changed to a variable-interval 35-s schedule with 5-s delays, thus equating nominal rates of reinforcement. Rates of pecking increased to baseline levels. Rates of pecking, then, depended on the value of the briefly signaled delay relative to the programmed interfood times, rather than on the absolute delay value. These results are discussed in terms of similar findings in the literature on conditioned reinforcement, delayed matching to sample, and classical conditioning.     

Responding of pigeons under variable-interval schedules of unsignaled, briefly signaled, and completely signaled delays to reinforcement

In Experiment 1, three pigeons' key pecking was maintained under a variable-interval 60-s schedule of food reinforcement. A 1-s unsignaled nonresetting delay to reinforcement was then added. Rates decreased and stabilized at values below those observed under immediate-reinforcement conditions. A brief stimulus change (key lit red for 0.5 s) was then arranged to follow immediately the peck that began the delay. Response rates quickly returned to baseline levels. Subsequently, rates near baseline levels were maintained with briefly signaled delays of 3 and 9 s. When a 27-s briefly signaled delay was instituted, response rates decreased to low levels. In Experiment 2, four pigeons' responding was first maintained under a multiple variable-interval 60-s (green key) variable-interval 60-s (red key) schedule. Response rates in both components fell to low levels when a 3-s unsignaled delay was added. In the first component delays were then briefly signaled in the same manner as Experiment 1, and in the second component they were signaled with a change in key color that remained until food was delivered. Response rates increased to near baseline levels in both components, and remained near baseline when the delays in both components were lengthened to 9 s. When delays were lengthened to 27 s, response rates fell to low levels in the briefly signaled delay component for three of four pigeons while remaining at or near baseline in the completely signaled delay component. In Experiment 3, low response rates under a 9-s unsignaled delay to reinforcement (tandem variable-interval 60 s fixed-time 9 s) increased when the delay was briefly signaled. The role of the brief stimulus as conditioned reinforcement may be a function of its temporal relation to food, and thus may be related to the eliciting function of the stimulus.     

Preference for fixed-interval schedules: effects of unequal initial links

Six homing pigeons were trained on concurrent chain schedules in which the terminal links were fixed-interval schedules of 5 sec or 15 sec. One initial-link schedule was always VI 27-sec; the other was varied over conditions from VI 27-sec to VI 181-sec. Preference measured in the initial links varied as a joint function of the initial- and terminal-link schedules. When the initial links were varied with constant, but unequal, terminal links, the slope of the function relating the logarithm of the initial-link response ratio to the logarithm of the terminal-link entry ratio differed from that obtained with equal terminal links. This result indicates that biases attributable to the terminal-link schedules were not constant. The rate of change of preference, or degree of undermatching, in the initial links depended on whether the shorter initial link led to the shorter or the longer terminal link. These results raise the question of whether bias and undermatching in concurrent schedule performance are independent measures.