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.     

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.     

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.     

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.     

The relative value of two options for pigeons depends on their context

It is well known that when humans are given a choice between two options, their preference is affected by the presence of a third. Generally, there is an increase in preference for the option closer to the third. We show that a shift in preference in the direction away from the third option can occur in animals. We gave pigeons a choice between A, reinforcement following 10 pecks and a 0.5‐s delay, and B, reinforcement following 5 pecks and a 1.5‐s delay. Once stable preferences were established, we introduced a third stimulus, less preferred than the other two: C, reinforcement following 20 pecks and a 0.5‐s delay or D, reinforcement following 5 pecks and a 4.5‐s delay. We found that pigeons presented with C showed an increased preference for B, whereas pigeons presented with D showed an increased preference for A. Our results were consistent with the similarity or attentional hypothesis, which suggests that the third option should interfere with the option more similar to it or would draw attention to the less preferred component of the third option and generalize to the option more similar to it. Possible accounts for the differences in outcomes are suggested.     

Effects of time between trials on rats' and pigeons' choices with probabilistic delayed reinforcers

Parallel experiments with rats and pigeons examined reasons for previous findings that in choices with probabilistic delayed reinforcers, rats' choices were affected by the time between trials whereas pigeons' choices were not. In both experiments, the animals chose between a standard alternative and an adjusting alternative. A choice of the standard alternative led to a short delay (1 s or 3 s), and then food might or might not be delivered. If food was not delivered, there was an "interlink interval," and then the animal was forced to continue to select the standard alternative until food was delivered. A choice of the adjusting alternative always led to food after a delay that was systematically increased and decreased over trials to estimate an indifference point--a delay at which the two alternatives were chosen about equally often. Under these conditions, the indifference points for both rats and pigeons increased as the interlink interval increased from 0 s to 20 s, indicating decreased preference for the probabilistic reinforcer with longer time between trials. The indifference points from both rats and pigeons were well described by the hyperbolic-decay model. In the last phase of each experiment, the animals were not forced to continue selecting the standard alternative if food was not delivered. Under these conditions, rats' choices were affected by the time between trials whereas pigeons' choices were not, replicating results of previous studies. The differences between the behavior of rats and pigeons appears to be the result of procedural details, not a fundamental difference in how these two species make choices with probabilistic delayed reinforcers.     

Commitment, choice and self-control

When offered a choice (Choice Y) between a small immediate reward (2-sec exposure to grain) and a large reward (4-sec exposure to grain) delayed by 4 sec, pigeons invariably preferred the small, immediate reward. However, when offered a choice (Choice X) between a delay of T seconds followed by Choice Y and a delay of T seconds followed by restriction to the large delayed reward only, the pigeon's choice depended on T. When T was small, the pigeons chose the alternative leading to Choice Y (and then chose the small, immediate reward). When T was large, the pigeons chose the alternative leading to the large delayed reward only. The reversal of preference as T increases is predicted by several recent models for choice between various amounts and delays of reward. The preference for the large delayed alternative with long durations of T parallels everyday instances of advance commitment to a given course of action. Such commitment may be seen as a prototype for self-control.     

Effects of reinforcer probability, delay, and response requirements on the choices of rats and pigeons: possible species differences

In Experiment 1 with rats, a left lever press led to a 5-s delay and then a possible reinforcer. A right lever press led to an adjusting delay and then a certain reinforcer. This delay was adjusted over trials to estimate an indifference point, or a delay at which the two alternatives were chosen about equally often. Indifference points increased as the probability of reinforcement for the left lever decreased. In some conditions with a 20% chance of food, a light above the left lever was lit during the 5-s delay on all trials, but in other conditions, the light was only lit on those trials that ended with food. Unlike previous results with pigeons, the presence or absence of the delay light on no-food trials had no effect on the rats' indifference points. In other conditions, the rats showed less preference for the 20% alternative when the time between trials was longer. In Experiment 2 with rats, fixed-interval schedules were used instead of simple delays, and the presence or absence of the fixed-interval requirement on no-food trials had no effect on the indifference points. In Experiment 3 with rats and Experiment 4 with pigeons, the animals chose between a fixed-ratio 8 schedule that led to food on 33% of the trials and an adjusting-ratio schedule with food on 100% of the trials. Surprisingly, the rats showed less preference for the 33% alternative in conditions in which the ratio requirement was omitted on no-food trials. For the pigeons, the presence or absence of the ratio requirement on no-food trials had little effect. The results suggest that there may be differences between rats and pigeons in how they respond in choice situations involving delayed and probabilistic reinforcers.     

Preference for free or forced choice in Sumatran orangutans (Pongo abelii)

Empirical investigations of humans, pigeons, rats, and monkeys have indicated that these species will select free over forced choice, even when faced with identical outcomes. However, the same has yet to be quantitatively confirmed in nonhuman great apes. This experiment is the first systematic investigation of preference for free or forced choice in great apes using a paradigm in which extraneous variables are highly controlled. Three orangutans were given a choice of one of two virtual routes, one that provided a choice and one that did not via a touchscreen computer program. Choice of either route was rewarded with the same type and quantity of food. Initial results indicated a preference for free choice across all three participants. However, in two control conditions, orangutans' preferences varied, suggesting a weaker tendency to exercise choice than species previously tested. We suggest further investigation of preference for free and forced choice in orangutans and other great apes through alternative experimental paradigms that focus on increasing the fidelity of free and forced choice options.     

Hungry pigeons make suboptimal choices, less hungry pigeons do not

Hungry animals will often choose suboptimally by being attracted to reliable signals for food that occur infrequently (they gamble) over less reliable signals for food that occur more often. That is, pigeons prefer an option that 50?% of the time provides them with a reliable signal for the appearance of food but 50?% of the time provides them with a reliable signal for the absence of food (overall 50?% reinforcement) over an alternative that always provides them with a signal for the appearance of food 75?% of the time (overall 75?% reinforcement). The pigeons appear to choose impulsively for the possibility of obtaining the reliable signal for reinforcement. There is evidence that greater hunger is associated with greater impulsivity. We tested the hypothesis that if the pigeons were less hungry, they would be less impulsive and, thus, would choose more optimally (i.e., on the basis of the overall probability of reinforcement). We found that hungry pigeons choose the 50?% reinforcement alternative suboptimally but less hungry pigeons prefer the more optimal 75?% reinforcement. Paradoxically, pigeons that needed the food more received less of it. These findings have implications for how level of motivation may also affect human suboptimal choice (e.g., purchase of lottery tickets and playing slot machines).     

Conditioned reinforcement and choice with delayed and uncertain primary reinforcers.

In an adjusting-delay choice procedure, pigeons could peck on either a red key or a green key. A peck on the red key always led to a delay associated with red houselights and then food. The delay was adjusted over trials to estimate an indifference point--a delay at which the two keys were chosen about equally often. In some conditions, a peck on the green key led to food on all trials after delays of either 10 s or 30 s, and green houselights were lit during the delays. In other conditions, food was presented on only half of the green-key trials. If the green houselights continued to occur on both reinforcement and nonreinforcement trials, preference for the green key always decreased. Preference for the green key also decreased if half of the trials had 30-s houselights followed by food and the other half had no green houselights and no food. However, preference for the green key actually increased if half of the trials had 10-s green houselights followed by food and the other half had no green houselights followed by no food. The latter condition therefore demonstrated a case in which preference for an alternative increased when food was removed from half of the trials. The results suggest that the red and green houselights served as conditioned reinforcers. A hyperbolic decay model (Mazur, 1989) provided good predictions for all conditions by assuming that the strength of a conditioned reinforcer is inversely related to the total time spent in its presence before food is delivered.     

Response rate correlates with indifference points in a delay‐discounting procedure

To study how effort affects reward value, we replicated Fortes, Vasconcelos and Machado's (2015) study using an adjusting‐delay task. Nine pigeons chose between a standard alternative that gave access to 4 s of food, after a 10 s delay, and an adjusting‐delay alternative that gave access to 12 s of food after a delay that changed dynamically with the pigeons' choices, decreasing when they preferred the standard alternative, and increasing when they preferred the adjusting alternative. The delay value at which preference stabilized defined the indifference point, a measure of reward value. To manipulate effort across phases, we varied the response rate required during the delay of the standard alternative. Results showed that a) the indifference point increased in the higher‐response‐rate phases, suggesting that reward value decreased with effort, and b) in the higher‐response‐rate phases, response rate in the standard alternative was linearly related to the indifference point. We advance several conceptions of how effort may change perceived delay or amount and thereby affect reward value.     

Sub-Optimal Choice by Pigeons: Failure to Support The Allais Paradox

Pigeons show a preference for an alternative that provides them with discriminative stimuli (sometimes a stimulus that predicts reinforcement and at other times a stimulus that predicts the absence of reinforcement) over an alternative that provides them with nondiscriminative stimuli, even if the nondiscriminative stimulus alternative is associated with 2.5 times as much reinforcement (Stagner & Zentall, 2010). In Experiment 1 we found that the delay to reinforcement associated with the nondiscriminative stimuli could be reduced by almost one half before the pigeons were indifferent between the two alternatives. In Experiment 2 we tested the hypothesis that the preference for the discriminative stimulus alternative resulted from the fact that, like humans, the pigeons were attracted by the stimulus that consistently predicted reinforcement (the Allais paradox). When the probability of reinforcement associated with the discriminative stimulus that predicted reinforcement was reduced from 100% to 80% the pigeons still showed a strong preference for the discriminative stimulus alternative. Thus, under these conditions, the Allais paradox cannot account for the sub-optimal choice behavior shown by pigeons. Instead we propose that sub-optimal choice results from positive contrast between the low expectation of reinforcement associated with the discriminative stimulus alternative and the much higher obtained reinforcement when the stimulus associated with reinforcement appears. We propose that similar processes can account for sub-optimal gambling behavior by humans.     

Commitment using punishment.

Experimental parameters were adjusted so that pigeons' pairwise choices among three alternatives reflected the following order of preference: (a) a smaller-sooner reinforcer, (b) a larger-later reinforcer, and (c) the smaller-sooner reinforcer followed by a punishment (consisting of an extended blackout period). After this order of preference was established, the pigeons were exposed to a two-link, concurrent-chain-like choice procedure. One terminal link consisted of a choice between the smaller-sooner and the larger-later reinforcer; the other terminal link was identical to the first except that the smaller-sooner reinforcer was followed by blackout punishment. The pigeons' preference (in their initial-link choice) for the terminal link with the punished smaller-sooner alternative increased as the delay between the initial and terminal links increased. By choosing this terminal link, the pigeons are said to have "committed" themselves to obtaining the larger-later reinforcer. However, unlike prior studies of commitment (e.g., Rachlin & Green, 1972), it was still possible after making the commitment for the pigeons to choose the smaller-sooner reinforcer and undergo the punishment. The pigeons did in fact occasionally make this highly deleterious choice.     

Effects of intertrial reinforcers on self-control choice.

In three experiments, pigeons chose between a small amount of food delivered after a short delay and a larger amount delivered after a longer delay. A discrete-trial adjusting-delay procedure was used to estimate indifference points--pairs of delay-amount combinations that were chosen about equally often. In Experiment 1, when additional reinforcers were available during intertrial intervals on a variable-interval schedule, preference for the smaller, more immediate reinforcer increased. Experiment 2 found that this shift in preference occurred partly because the variable-interval schedule started sooner after the smaller, more immediate reinforcer, but there was still a small shift in preference when the durations and temporal locations of the variable-interval schedules were identical for both alternatives. Experiment 3 found greater increases in preference for the smaller, more immediate reinforcer with a variable-interval 15-s schedule than with a variable-interval 90-s schedule. The results were generally consistent with a model that states that the impact of any event that follows a choice response declines according to a hyperbolic function with increasing time since the moment of choice.     

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.     

Choice between reliable and unreliable reinforcement alternatives revisited: Preference for unreliable reinforcement

Pigeons' choices between a reliable alternative that always provided food after a delay (i.e., 100% reinforcement) and an unreliable one that provided food or blackout equally often after a delay (i.e., 50% reinforcement) was studied using a discrete-trials concurrent-chains procedure modified to prevent choice between alternatives following a blackout outcome. Initial links were fixed-ratio 1 schedules, and terminal links were fixed-time schedules. Stimuli presented during the terminal-link delays were correlated with the food and blackout outcomes. In Experiment 1, terminal-link durations were varied. With short terminal links (i.e., 10 s), 6 of 8 subjects showed strong preference for the 50% side. As terminal-link duration increased to 30 s, preference, regardless of direction, became less extreme. In Experiment 2, the side-key location of the 50% and 100% alternatives was reversed for 3 subjects. Preference for the 50% alternative reoccurred following the key reversal. When a 5-s separation was subsequently interposed between the initial and terminal links for both alternatives, all birds reversed to a preference for the 100% side. In general, the strong preference for the 50% side was qualitatively consistent with the expectation that the procedure enhanced the conditioned-reinforcement effectiveness of the food-associated terminal-link stimulus on the 50% side. Implications of the results for various accounts of choice of the 50% alternative are discussed.     

Delay discounting in the pigeon: In search of a magnitude effect

The magnitude effect, where larger outcomes are discounted proportionally less than smaller outcomes, is a well‐established phenomenon in delay discounting by human participants. To this point in the literature magnitude effects have not been reliably evidenced in nonhuman animals. , however, used a concurrent‐chains arrangement with pigeon and found evidence for a magnitude effect. Grace et al. suggested that in many delay discounting experimental arrangements with nonhuman animals (e.g., adjusting amount, adjusting delay) the organism is not given the opportunity to directly compare outcomes of different sizes. They suggest that because of the lack of direct comparison it is difficult for the organism to determine the relative size of each outcome, which in turn mutes the effect of the amount differences between outcomes. As a test of this “comparison hypothesis,” the present experiment was conducted to assess whether the magnitude effect would be evidenced in pigeon when using an adjusting amount procedure where outcomes of different amounts were presented proximally. In the present arrangement, pigeons were presented two choice panels in an operant chamber where each panel was associated with an independent adjusting amount delay discounting task, but with differing outcome amounts (i.e., a 32‐food pellet panel and an 8‐food pellet panel). In this arrangement the choice panels alternated in their availability within a session from trial block to trial block. The present findings indicate no reliable effect of amount, even when the outcomes were proximal and thus readily comparable. This result suggests that the lack of magnitude effect is not driven by the organism's ability to compare the difference in amount between choice alternatives.     

Local effects of delayed food

Five pigeons were trained on a procedure in which seven concurrent variable-interval schedules arranged seven different food-rate ratios in random sequence in each session. Each of these components lasted for 10 response-produced food deliveries, and components were separated by 10-s blackouts. We varied delays to food (signaled by blackout) between the two response alternatives in an experiment with three phases: In Phase 1, the delay on one alternative was 0 s, and the other was varied between 0 and 8 s; in Phase 2, both delays were equal and were varied from 0 to 4 s; in Phase 3, the two delays summed to 8 s, and each was varied from 1 to 7 s. The results showed that increasing delay affected local choice, measured by a pulse in preference, in the same way as decreasing magnitude, but we found also that increasing the delay at the other alternative increased local preference. This result casts doubt on the traditional view that a reinforcer strengthens a response depending only on the reinforcer's value discounted by any response-reinforcer delay. The results suggest that food guides, rather than strengthens, behavior.     

How suboptimal is suboptimal choice?

In a frequently used suboptimal‐choice procedure pigeons choose between an alternative that delivers three food pellets with p = 1.0 and an alternative that delivers ten pellets with p = 0.2. Because pigeons reliably choose the probabilistic (suboptimal) alternative, the procedure has been proposed as a nonhuman analog of human gambling. The present experiments were conducted to evaluate two potential threats to the validity of this procedure. Experiments 1 and 2 evaluated if pigeons obtained food at a lower unit price (i.e., pecks per pellet) on the suboptimal alternative than on the optimal alternative. When pigeons worked under this suboptimal procedure they all preferred the suboptimal alternative despite some pigeons paying a higher price for food on that alternative. In Experiment 2, when the unit price ratio more closely approximated the inverse of the expected value ratio, pigeons continued to prefer the suboptimal alternative despite its economic suboptimality. Experiment 3 evaluated if, in accord with the string‐theory of gambling, the valuation of the suboptimal alternative was increased when pigeons misattributed a subset of the suboptimal no‐food trials to the optimal alternative. When trial sequences were arranged to minimize these possible attribution errors, pigeons still preferred the suboptimal alternative. These data remove two threats to the validity of the suboptimal choice procedure; threats that would have suggested that suboptimal choice reflects economic maximization.