Choice and reinforcement delay

Previous studies of choice between two delayed reinforcers have indicated that the relative immediacy of the reinforcer is a major determinant of the relative frequency of responding. Parallel studies of choice between two interresponse times have found exceptions to this generality. The present study looked at the choice by pigeons between two delays, one of which was always four times longer than the other, but whose absolute durations were varied across conditions. The results indicated that choice is not uniquely determined by the relative immediacy of reinforcement, but that absolute delays are also involved. Models for concurrent chained schedules appear to be more applicable to the present data than the matching relation; however, these too failed to predict choice for long delays.     

Choice and conditioned reinforcement.

A potential weakness of one formulation of delay-reduction theory is its failure to include a term for rate of conditioned reinforcement, that is, the rate at which the terminal-link stimuli occur in concurrent-chains schedules. The present studies assessed whether or not rate of conditioned reinforcement has an independent effect upon choice. Pigeons responded on either modified concurrent-chains schedules or on comparable concurrent-tandem schedules. The initial link was shortened on only one of two concurrent-chains schedules and on only one of two corresponding concurrent-tandem schedules. This manipulation increased rate of conditioned reinforcement sharply in the chain but not in the tandem schedule. According to a formulation of delay-reduction theory, when the outcomes chosen (the terminal links) are equal, as in Experiment 1, choice should depend only on rate of primary reinforcement; thus, choice should be equivalent for the tandem and chain schedules despite a large difference in rate of conditioned reinforcement. When the outcomes chosen are unequal, however, as in Experiment 2, choice should depend upon both rate of primary reinforcement and relative signaled delay reduction; thus, larger preferences should occur in the chain than in the tandem schedules. These predictions were confirmed, suggesting that increasing the rate of conditioned reinforcement on concurrent-chains schedules may have no independent effect on choice.     

Unsignalled delay of reinforcement in variable-interval schedules

Three pigeons responded on several tandem variable-interval fixed-time schedules in which the value of the fixed-time component was varied to assess the effects of different unsignalled delays of reinforcement. Actual (obtained) delays between the last key peck in an interval and reinforcement were consistently shorter than the nominal (programmed) delay. When nominal delays were relatively short, response rates were higher during the delay condition than during the corresponding nondelay condition. At longer nominal delay intervals, response rates decreased monotonically with increasing delays. The results were consistent with those obtained from delay-of-reinforcement procedures that impose either a stimulus change (signal) or a no-response requirement during the delay interval.     

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).     

A quantitative analysis of sensitivity to the conditioned reinforcing value of terminal-link stimuli in a concurrent-chains schedule.

Pigeons were exposed to a concurrent-chains schedule in which a single variable-interval 30-s schedule was used in the initial links and fixed-time schedules were used in the terminal links. Three types of keylight conditions were used in the terminal links. In the first condition, different delays were associated with different keylight stimuli (cued condition). In the second condition, different delays were associated with the same stimulus, either a blackout (uncued blackout condition) or a white key (uncued white condition). Paired values of terminal-link fixed-time schedules differed by a constant ratio of 3:1, while the absolute value of delays was varied from 3 s to 54 s. The results showed that choice proportions for the shorter of two delays increased when the absolute size of the delays was increased for all keylight conditions. Further, the choice proportions for the shorter delay increased from the uncued blackout condition, to the uncued white condition, to the cued condition. A modified version of Fantino's (1969) delay-reduction model (expressed as a function relating the response ratio to the delay-reduction ratio) can be applied to these data by showing that sensitivity to delay reduction increased from the uncued blackout condition, to the uncued white condition, to the cued condition. Thus, the present study demonstrated that a modified version of the delay-reduction model can be used to assess quantitative differences in the terminal-link keylight condition in terms of sensitivity to delay reduction (i.e., the conditioned reinforcing value of the terminal-link keylight stimuli).     

Effects on choice of reinforcement delay and conditioned reinforcement

Pigeons chose between fixed-interval schedules of different durations presented in the terminal links of concurrent-chains schedules. The pair of schedules was always in the ratio of 2:1, but the absolute duration of the fixed intervals varied. In one set of conditions, the different terminal-link schedules were associated with different keylight stimuli (cued conditions). In a second set of conditions, the different terminal-link schedules were associated with the same stimulus (uncued conditions). Results from the cued conditions replicated previous findings that preference for the shorter fixed-interval schedule increased with fixed-interval duration. Preferences in the uncued conditions were lower than in the corresponding cued conditions but also increased with fixed-interval length. In addition, the degree of control under the uncued conditions was correlated with the extent to which the schedule during the terminal link was discriminated immediately upon entry into the terminal link. The pattern of results in both conditions was inconsistent with the notion that choice behavior matches relative immediacy of reinforcement. Reanalysis of previous evidence for matching (Chung and Herrnstein, 1967) showed that matching in fact did not occur, as the preferences of their subjects for the shorter of two delays also increased with the absolute size of the delays.     

Choice and the relative immediacy of reinforcement

The relative immediacy of reinforcement in concurrent-chain schedules was varied while the relative reduction in the overall average time to reinforcement associated with terminal-link entry was held constant. For each of four pigeons, choice did not vary with relative immediacy of reinforcement. Subsequently, choice by the same subjects was shown to be sensitive to relative reduction in average time to reinforcement.     

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.     

Effects of delayed conditioned reinforcement in chain schedules.

The contingency between responding and stimulus change on a chain variable-interval 33-s, variable-interval 33-s, variable-interval 33-s schedule was weakened by interposing 3-s delays between either the first and second or the second and third links. No stimulus change signaled the delay interval and responses could occur during it, so the obtained delays were often shorter than the scheduled delay. When the delay occurred after the initial link, initial-link response rates decreased by an average of 77% with no systematic change in response rates in the second or third links. Response rates in the second link decreased an average of 59% when the delay followed that link, again with little effect on response rates in the first or third links. Because the effect of delaying stimulus change was comparable to the effect of delaying primary reinforcement in a simple variable-interval schedule, and the effect of the unsignaled delay was specific to the link in which the delay occurred, the results provide strong evidence for the concept of conditioned reinforcement.     

Conditioned reinforcement versus time to reinforcement in chain schedules.

Pigeons were trained on three-component chain schedules in which the initial component was either a fixed-interval or variable-interval schedule. The middle and terminal components were varied among fixed-interval fixed-interval, variable-interval variable-interval, and an interdependent variable-interval variable-interval schedule in which the sum of the durations of the two variable-interval components was always equal to the sum of the fixed-interval fixed-interval components. At issue was whether the response rate in the initial component was controlled by its time to primary reinforcement or by the temporal parameters of the stimulus correlated with the middle terminal link. The fixed-interval initial-link schedule maintained much lower response rates than the variable-interval initial-link schedule regardless of the schedules in the middle and terminal links. Nevertheless, the intervening schedules played some role: With fixed-interval schedules in the initial links, response rates were consistently highest with independent variable-interval schedules in the middle and terminal links and intermediate with the interdependent variable-interval schedules; these initial-link differences were predicted by the response rates in the middle link of the chain. With variable-interval schedules in the initial links, response rates were lowest with the fixed-interval fixed-interval schedules following the initial link and were not systematically different for the two types of variable-interval variable-interval schedules. The results suggest that time to reinforcement itself accounts for little if any variance in initial-link responding.     

Choice, changing over, and reinforcement delays

In three experiments, pigeons were used to examine the independent effects of two normally confounded delays to reinforcement associated with changing between concurrently available variable-interval schedules of reinforcement. In Experiments 1 and 2, combinations of changeover-delay durations and fixed-interval travel requirements were arranged in a changeover-key procedure. The delay from a changeover-produced stimulus change to a reinforcer was varied while the delay between the last response on one alternative and a reinforcer on the other (the total obtained delay) was held constant. Changeover rates decreased as a negative power function of the total obtained delay. The delay between a changeover-produced stimulus change had a small and inconsistent effect on changeover rates. In Experiment 3, changeover delays and fixed-interval travel requirements were arranged independently. Changeover rates decreased as a negative power function of the total obtained delay despite variations in the delay from a change in stimulus conditions to a reinforcer. Periods of high-rate responding following a changeover, however, were higher near the end of the delay from a change in stimulus conditions to a reinforcer. The results of these experiments suggest that the effects of changeover delays and travel requirements primarily result from changes in the delay between a response at one alternative and a reinforcer at the other, but the pattern of responding immediately after a changeover depends on the delay from a changeover-produced change in stimulus conditions to a reinforcer.     

Choice with probabilistic reinforcement: effects of delay and conditioned reinforcers.

Two experiments measured pigeons' choices between probabilistic reinforcers and certain but delayed reinforcers. In Experiment 1, a peck on a red key led to a 5-s delay and then a possible reinforcer (with a probability of .2). A peck on a green key led to a certain reinforcer after an adjusting delay. This delay was adjusted over trials so as to estimate an indifference point, or a duration at which the two alternatives were chosen about equally often. In all conditions, red houselights were present during the 5-s delay on reinforced trials with the probabilistic alternative, but the houselight colors on nonreinforced trials differed across conditions. Subjects showed a stronger preference for the probabilistic alternative when the houselights were a different color (white or blue) during the delay on nonreinforced trials than when they were red on both reinforced and nonreinforced trials. These results supported the hypothesis that the value or effectiveness of a probabilistic reinforcer is inversely related to the cumulative time per reinforcer spent in the presence of stimuli associated with the probabilistic alternative. Experiment 2 tested some quantitative versions of this hypothesis by varying the delay for the probabilistic alternative (either 0 s or 2 s) and the probability of reinforcement (from .1 to 1.0). The results were best described by an equation that took into account both the cumulative durations of stimuli associated with the probabilistic reinforcer and the variability in these durations from one reinforcer to the next.     

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.     

Choice and foraging

In Experiment 1, six naive pigeons were trained on a foraging schedule characterized by different states beginning with a search state in which completion of a fixed-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 of reinforcement that was offered (either a variable-interval five-second or a variable-interval 20-second). If the subject accepted the schedule, it entered a “handling state” in which the appropriate variable-interval schedule was presented. Completion of the variable-interval schedule produced food. The independent variable was the fixed-interval value in the search state, and the dependent variable was the rate of acceptance of the long variable-interval in the choice state. Experiment 2 was identical except that the search state required completion of a variable-interval, instead of a fixed-interval, schedule. The rate of acceptance of the long variable-interval schedule in both experiments was a direct function of the length of the search state, in accordance with both optimality theory and the delay-reduction hypothesis.     

Effects of unsignaled delay of reinforcement on preference and resistance to change

In Phase 1, pigeons were trained on a concurrent chain in which a 3-s unsignaled delay of reinforcement was imposed on responding in a terminal link in some conditions. Preference for that terminal link was always reduced in comparison with conditions in which there was no delay, substantially so for 3 of the 4 pigeons. In Phase 2, pigeons responded in a two-component multiple schedule. The scheduled rates of reinforcement were equal, but a 3-s unsignaled delay was imposed in one component. Resistance of responding to prefeeding and extinction was reduced in the delay component for the same 3 subjects for which the data had shown strong effects of delay on preference. Systematic observation revealed differences in response topography. In the delay component, subjects oriented more closely to the key and responses were less forceful compared with the no-delay component. Our results give further evidence that preference and resistance to change covary within subjects. However, they challenge the premise that the critical determiners of preference (i.e., terminal-link value) and resistance to change (behavioral mass) may be quantified purely in terms of stimulus—reinforcer relations.     

Independence of reinforcement delay and magnitude in concurrent chains

A three-component concurrent-chains procedure was used to investigate preference between terminal-link schedules that differed in delay and magnitude of reinforcement. Response and time allocation data were well described by a generalized matching model. Sensitivity to delay appeared to be lower when reinforcement magnitudes were unequal than when they were equal, but when obtained rather than programmed time spent responding in the initial links was used in the model, the difference vanished. The results support independence of delay and magnitude as separate dimensions of reinforcement value, as required by the matching law, and the assumption of the contextual choice model (Grace, 1994) that sensitivities to delay and magnitude are affected similarly by temporal context. Although there was statistical evidence for interaction between successive components, the effects were small and transient. The multiple-component concurrent-chains procedure should prove useful in future research on multidimensional preference, although it may be necessary to control obtained initial-link time more precisely.     

Effects of response type on pigeons' sensitivity to variation in reinforcer amount and reinforcer delay

Twelve pigeons, divided into two groups, responded on concurrent nonindependent variable-interval schedules to obtain access to grain by either pecking keys or pressing treadles. Either the amount of grain or the delay to the receipt of grain was varied in separate conditions to determine the sensitivity of relative responding to variation in reinforcer amount (s_A), the sensitivity to variation in reinforcer delay (s_D), and s_A/s_D, a measure related to self-control. There were no significant differences between the two groups in the values of s_A, s_D, and s_A/s_D. These results suggest that the values of s_A, s_D, and s_A/s_D for pigeons may be similar across these two types of responses.