Suboptimal choice in a percentage-reinforcement procedure: effects of signal condition and terminal-link length.

Pigeons' choice between reliable (100%) and unreliable (50%) reinforcement was studied using a concurrent-chains procedure. Initial links were fixed-ratio 1 schedules, and terminal links were equal fixed-time schedules. The duration of the terminal links was varied across conditions. The terminal link on the reliable side always ended in food; the terminal link on the unreliable side ended with food 50% of the time and otherwise with blackout. Different stimuli present during the 50% terminal links signaled food or blackout outcomes under signaled conditions but were uncorrelated with outcomes under unsignaled conditions. In signaled conditions, most pigeons displayed a nearly exclusive preference for the 100% alternative when terminal links were short (5 or 10 s), but with terminal links of 30 s or longer, preference for the 100% alternative was sharply reduced (often to below .5). In unsignaled conditions, most pigeons showed extreme preference for the 100% alternative with either short (5 s) or longer (30 s) terminal links. Thus, pigeons' choice between reliable and unreliable reinforcement is influenced by both the signal conditions on the unreliable alternative and the duration of the terminal-link delay. With a long delay and signaled outcomes, many pigeons display a suboptimal tendency to choose the unreliable side.     

Testing the Δ-∑ hypothesis in the suboptimal choice task: Same delta with different probabilities of reinforcement

In a concurrent-chain procedure, pigeons choose between 2 initial-link stimuli; one is followed by terminal link stimuli that signal reliably whether food will be delivered after a delay; the other is followed by terminal link stimuli that do not signal whether food will be delivered after the delay. Pigeons prefer the former alternative even when it yields a lower overall probability of food. Recently, we proposed the Delta-Sigma (∆-∑) hypothesis to explain the effect: Preference depends on the difference (∆) between the reinforcement probabilities associated with the terminal link stimuli, and the overall probability of reinforcement (∑) associated with the alternative. The hypothesis predicts that, for constant ∑, animals should prefer alternatives with greater ∆ values regardless of the specific probabilities of reinforcement that determine ∆. In 2 experiments, we tested this prediction by comparing a ∆ = .5 against a ∆ = 0 alternative, with the former obtained with different pairs of reinforcement probabilities across conditions. The results supported the hypothesis when the 2 probabilities defining ∆ were significantly greater than 0, but not when one of them was close to 0. The results challenge our theoretical accounts of suboptimal choice and the variables considered to determine pigeons’ preference.     

Suboptimal choice and initial‐link requirement

Pigeons (n = 14) were trained in a concurrent‐chains suboptimal choice procedure that tested the effect of an increased ratio requirement in the initial links. Fixed‐ratio 1 and 25 conditions were manipulated within subjects in a counterbalanced order. In all conditions, distinct terminal‐link stimuli on a suboptimal alternative signaled either primary reinforcement (20% of the time) or extinction (80% of the time). On an optimal alternative, two distinct terminal‐link stimuli each signaled a 50% chance of primary reinforcement. Preference for the suboptimal alternative was significantly attenuated, and in some birds completely reversed, by the larger response requirement irrespective of condition order. This larger response requirement also generated a notable increase in between‐subject variability. A measure of cumulative choice responding is introduced to mitigate the problems associated with traditional session averages. Ordinal predictions of some current theories of suboptimal choice are also considered in light of the results.     

Preferences for and against stimuli paired with food.

Pigeons were presented with a concurrent-chains schedule in which terminal-link entries were assigned to two response keys on a percentage basis. The terminal links were fixed delays that sometimes ended with food and sometimes did not. In most conditions, 80% of the terminal links were assigned to one key, but a smaller percentage of the terminal links ended with food for this key, so the number of food reinforcers delivered by the two alternatives was equal. When the same terminal-link stimuli (orange houselights) were used for both alternatives, the pigeons showed a preference for whichever alternative delivered more frequent terminal links. When different terminal-link stimuli (green vs. red houselights) were used for the two alternatives, the pigeons showed a preference for whichever alternative delivered fewer terminal links when terminal-link durations were long, and no systematic preferences when terminal-link durations were short. This pattern of results was consistent with the predictions of Grace's (1994) contextual choice model. Preference for the alternative that delivered more frequent terminal links was usually stronger in the first few sessions of a condition than at the end of a condition, suggesting that the conditioned reinforcing effect of the additional terminal-link presentation was, in part, transitory.     

Conditioned reinforcement dynamics in three-link chained schedules.

In two experiments rats were trained on three-link concurrent-chains schedules of reinforcement. In Experiment 1, additional entries to one terminal link were added during one of the middle links to a baseline schedule that was otherwise equal for the two chains, and, depending on the condition, these additional terminal-link presentations ended either in food or in no food. When food occurred, preference was always in favor of the chain with the additional terminal-link presentations (which also entailed a higher rate of reinforcement). When no food occurred at the end of the additional terminal links, the outcome depended on the nature of the stimuli associated with these additional terminal links. When stimuli different from the reinforced baseline terminal links were used for the no-food terminal links, preference was against the choice alternative that led to the extra periods of extinction. When the same stimulus was used for the two kinds of terminal links, preference was near indifference, that is, significantly greater than when different stimuli were used. In Experiment 2, rats learned repeated reversals of a simultaneous discrimination under a three-link concurrent-chains schedule, in which the food or no-food choice outcomes were delayed until the end of the chain. Different conditions were defined by the point in the chain at which differential stimuli occurred. When the middle and terminal links provided no differential stimuli, discrimination was acquired more slowly than when differential stimuli occurred in both links. When differential stimuli occurred in the middle but not the terminal links, acquisition rates were intermediate. Both experiments together show that the effects of stimuli in a chain schedule are due partly to the time to food correlated with the stimuli and partly to the time to the next conditioned reinforcer in the sequence.     

Contiguity and conditioned reinforcement in probabilistic choice

In a baseline condition, pigeons chose between an alternative that always provided food following a 30-s delay (100% reinforcement) and an alternative that provided food half of the time and blackout half of the time following 30-s delays (50% reinforcement). The different outcomes were signaled by different-colored keylights. On average, each alternative was chosen approximately equally often, replicating the finding of suboptimal choice in probabilistic reinforcement procedures. The efficacy of the delay stimuli (keylights) as conditioned reinforcers was assessed in other conditions by interposing a 5-s gap (keylights darkened) between the choice response and one or more of the delay stimuli. The strength of conditioned reinforcement was measured by the decrease in choice of an alternative when the alternative contained a gap. Preference for the 50% alternative decreased in conditions in which the gap preceded either all delay stimuli, both delay stimuli for the 50% alternative, or the food stimulus for the 50% alternative, but preference was not consistently affected in conditions in which the gap preceded only the 100% delay stimulus or the blackout stimulus for the 50% alternative. These results support the notion that conditioned reinforcement underlies the finding of suboptimal preference in probabilistic reinforcement procedures, and that the signal for food on the 50% reinforcement alternative functions as a stronger conditioned reinforcer than the signal for food on the 100% reinforcement alternative. In addition, the results fail to provide evidence that the signal for blackout functions as a conditioned punisher.     

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.     

When good news leads to bad choices

Pigeons and other animals sometimes deviate from optimal choice behavior when given informative signals for delayed outcomes. For example, when pigeons are given a choice between an alternative that always leads to food after a delay and an alternative that leads to food only half of the time after a delay, preference changes dramatically depending on whether the stimuli during the delays are correlated with (signal) the outcomes or not. With signaled outcomes, pigeons show a much greater preference for the suboptimal alternative than with unsignaled outcomes. Key variables and research findings related to this phenomenon are reviewed, including the effects of durations of the choice and delay periods, probability of reinforcement, and gaps in the signal. We interpret the available evidence as reflecting a preference induced by signals for good news in a context of uncertainty. Other explanations are briefly summarized and compared.     

SOME EFFECTS OF PROCEDURAL VARIATIONS ON CHOICE RESPONDING IN CONCURRENT CHAINS

The present research used pigeons in a three‐key operant chamber and varied procedural features pertaining to both initial and terminal links of concurrent chains. The initial links randomly alternated on the side keys during a session, while the terminal links always appeared on the center key. Both equal and unequal initial‐link schedules were employed, with either differential or nondifferential terminal‐link stimuli across conditions. The research was designed to neutralize initial‐ and terminal‐link spatial cues in order to gain a clearer understanding of the roles of conditioned reinforcement and delayed primary reinforcement in choice. With both equal and unequal initial links and with differential terminal‐link stimuli, all pigeons reliably preferred the chain with the shorter terminal link. However, with equal initial links and nondifferential stimuli, all pigeons were indifferent. With unequal initial links and nondifferential stimuli, some pigeons were also indifferent, while others actually reversed and preferred the chain with the shorter initial link, even though it was followed by the longer terminal link. The decrease if not reversal of the previous preferences implies that preferences in concurrent chains are a function of the conditioned reinforcement afforded by terminal‐link stimuli, rather than delayed primary 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.     

Choice with uncertain outcomes: conditioned reinforcement effects.

Pigeons responded on concurrent chains with equal initial- and terminal-link durations. In all conditions, the terminal links of one chain ended reliably in reinforcement; the terminal links on the alternative chain ended in either food or blackout. In Experiment 1, the terminal-link stimuli were correlated with (signaled) the outcome, and the durations of the initial and terminal links were varied across conditions. Preference did not vary systematically across conditions. In Experiment 2, terminal-link durations were varied under different stimulus conditions. The initial links were variable-interval 80-s schedules. Preference for the reliable alternative was generally higher in unsignaled than in signaled conditions. Preference increased with terminal-link durations only in the unsignaled conditions. There were no consistent differences between conditions with and without a common signal for reinforcement on the two chains. In the first series of conditions in Experiment 3, a single response was required in the initial links, and the stimulus conditions during 50-s terminal links were varied. Preference for the reliable outcome approached 1.0 in unsignaled conditions and was considerably lower (below .50 for 3 of 5 subjects) in signaled conditions. In a final series of signaled conditions with relatively long terminal links, preference varied with duration of the initial links. The results extend previous findings and are discussed in terms of the delay reduction signaled by terminal-link stimuli.     

Pigeons' preferences for stimulus information: effects of amount of information

A concurrent-chain procedure was used to study pigeons' preferences as a function of amount of information. Pigeons chose between two terminal links. Both terminal links ended in food reinforcement with probability (p) and in blackout with probability (1–p). One terminal link (noninformative link) was signalled by a stimulus uncorrelated with either food or blackout. The other terminal link (informative link) was signalled by stimuli correlated with these outcomes. Amount of information conveyed by these stimuli was varied across conditions by changing the probability of reinforcement (p) and blackout (1–p). The pigeons strongly preferred the informative link, and preferences were greater at p values above 0.50 than for their complements. The pigeons engaged in different behaviors during the stimulus periods, suggesting that the value of informative stimuli may be in their function as discriminative stimuli for interim activities and terminal responses.     

The Δ–∑ hypothesis: How contrast and reinforcement rate combine to generate suboptimal choice

When given a choice between two alternatives, each offering food after the same delay with different but signaled probabilities, pigeons often prefer the low probability alternative. This preference is surprising because pigeons fail to maximize the rate of food intake; they exhibit a suboptimal preference. We advance a new explanation, the Δ–∑ hypothesis, in which the difference in probability of reinforcement within terminal links (Δ) and the overall reinforcement probability rate of each alternative (∑) are the key variables responsible for such suboptimal preference. We tested the Δ–∑ hypothesis in two experiments. In Experiment 1, we manipulated the Δs while maintaining constant all other parameters of the task, in particular the ∑s. We predicted a preference for the alternative with the larger Δ. In Experiment 2, we examined the effect of the overall reinforcement probabilities, the ∑s, while maintaining constant all other parameters of the task, in particular the Δs. We predicted a preference for the larger ∑. The results of both experiments support the Δ–∑ hypothesis.     

Behavioral ephemera,difficult discriminations,and behavioral stability

Every species possesses abilities for successfully interacting with its environment. These result from phylogeny. In the laboratory, one may arrange artificial conditions that thwart an organism's abilities. The result may be a “phenomenon.” With sufficient training, however, the phenomenon may prove to be ephemeral, as the organism's basic abilities reassert themselves. Pigeons respond extremely well to differences and nondifferences in rate of obtaining food. This ability may be thwarted in a variety of ways, but the results tend to be ephemeral. An example is an experiment that pitted pigeons' preference for unimpeded responding against their ability to respond to food rate. In a concurrent-chains procedure, the terminal links were identical variable-interval schedules, but in one terminal link, every response produced a timeout. The duration of the timeout varied, and preference varied with it, but the relation vanished with training, in keeping with the equality of food rate across the 2 terminal links. Some other examples of “phenomena” that tend to disappear with sufficient training and sufficient variation in experimental parameters are behavioral contrast, conditioned reinforcement, resistance to extinction, and suboptimal choice. These “phenomena” depend on pigeons' failing to make difficult discriminations. They appear to be behavioral ephemera.     

The effect of conditioned reinforcement rate on choice: a review

We review the nature of conditioned reinforcement, including evidence that conditioned reinforcers maintain choice behavior in concurrent schedules and that they elevate responding in the terminal links of concurrent‐chains schedules. A question has resurfaced recently: Do theories of choice in concurrent‐chains schedules need to include a term reflecting greater preference for higher rates of conditioned reinforcement? The review of several studies addressing this point suggests that such a term is inappropriate. Elevated rates of conditioned reinforcement (and responding) in the terminal links of concurrent‐chains schedules do not lead to greater preference in the initial link leading to the higher rate of conditioned reinforcement. If anything, the opposite preference is likely to occur. This result is not surprising, since the additional putative conditioned reinforcers in the terminal link are not correlated with a reduction in time to primary reinforcement nor with an increase in value.     

Effects of primary reinforcement on pigeons' initial-link responding under a concurrent chains schedule with nondifferntial terminal links

The effect of primary reinforcement on initial-link responding under concurrent-chains schedules with nondifferential terminal links was assessed in 12 pigeons. The iniitial and terminal links were variable-interval schedules (always the same for both alternatives). The positions (left or right key) of the initial-link stimuli (red or green) were randomized while the correlation between color and food amount remained constant within each condition. The terminal-link stimuli were always presented on the center key. Except in two control groups and conditions, the terminal-link stimuli were the same color (nondifferential, blue or yellow). Over six conditions, the differences in food amont and the durations of the initial- and terminal-link schedules were manipulated. In 57 of 60 cases, birds generated choice proportions above .50 in favor of the initial-link stimlus that was correlated with the larger reinforcer. There was some indication that preference increased with shortened terminal-link durations. Because the terminal-link stimuli were nondifferential, differential responding in the initial links cannot be explained easily by conditioned reinforcement represented by the terminal-link stimuli. Thus, primiary reinforcement has a direct effect on initial-link responding in concurrent-chains schedules.     

Reinforcement: Food Signals the Time and Location of Future Food

It has long been understood that food deliveries may act as signals of future food location, and not only as strengtheners of prefood responding as the law of effect suggests. Recent research has taken this idea further—the main effect of food deliveries, or other “reinforcers”, may be signaling rather than strengthening. The present experiment investigated the ability of food deliveries to signal food contingencies across time after food. In Phase 1, the next food delivery was always equally likely to be arranged for a left‐ or a right‐key response. Conditions were arranged such that the next food delivery was likely to occur either sooner on the left (or right) key, or sooner on the just‐productive (or not‐just‐productive) key. In Phase 2, similar contingencies were arranged, but the last‐food location was signaled by a red keylight. Preference, measured in 2‐s bins across interfood intervals, was jointly controlled by the likely time and location of the next food delivery. In Phase 1, when any food delivery signaled a likely sooner next food delivery on a particular key, postfood preference was strongly toward that key, and moved toward the other key across the interreinforcer interval. In other conditions in which food delivery on the two keys signaled different subsequent contingencies, postfood preference was less extreme, and quickly moved toward indifference. In Phase 2, in all three conditions, initial preference was strongly toward the likely‐sooner food key, and moved to the other key across the interfood interval. In both phases, at a more extended level of analysis, sequences of same‐key food deliveries caused a small increase in preference for the just‐productive key, suggesting the presence of a “reinforcement effect”, albeit one that was very small.     

Effects of signaled versus unsignaled delay of reinforcement on choice

Pigeons chose between 5-s and 15-s delay-of-reinforcement alternatives. The first key peck to satisfy the choice schedule began a delay timer, and food was delivered at the end of the interval. Key pecks during the delay interval were measured, but had no scheduled effect. In Experiment 1, signal conditions and choice schedules were varied across conditions. During unsignaled conditions, no stimulus change signaled the beginning of a delay interval. During differential and nondifferential signal conditions, offset of the choice stimuli and onset of a delay stimulus signaled the beginning of a delay interval. During differential signal conditions, different stimuli were correlated with the 5-s and 15-s delays, whereas the same stimulus appeared during both delay durations during nondifferential signal conditions. Pigeons showed similar, extreme levels of preference for the 5-s delay alternative during unsignaled and differentially signaled conditions. Preference levels were reliably lower with nondifferential signals. Experiment 2 assessed preference with two pairs of unsignaled delays in which the ratio of delays was held constant but the absolute duration was increased fourfold. No effect of absolute duration was found. The results highlight the importance of delayed primary reinforcement effects and challenge models of choice that focus solely on conditioned reinforcement.     

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.     

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).