Choice between rewards differing in amount and delay: Toward a choice model of self control

A concurrent-chain procedure was used to study pigeons' choices between rewards differing in both amount and delay. The shorter delay terminated with a 2-second access to grain whereas the longer delay terminated with a 6-second access to grain. The ratio of the delays was constant within a given condition while their absolute values were varied. Over conditions, ratios of 6:1, 3:1, and 3:2 were studied. As the absolute values of the delays to reinforcement increased, preference for the longer-delayed but larger reward decreased under both the 6:1 and 3:1 ratios, but increased under the 3:2 ratio. These results are inconsistent with choice models predicting no change in preference when the ratios of delays and amounts are held constant. In addition, the change in preference under the 3:1 ratio is inconsistent with a simple multiplicative interaction of the trade off between reinforcer amount and delay, and suggests that delay is a more potent determinant of choice than is amount. These results have implications for models that view choice between small immediate rewards and large but delayed rewards as underlying the behavior commonly called self control.     

Modeling Myopic Decisions: Evidence for Hyperbolic Delay-Discounting within Subjects and Amounts

Hyperbolic and exponential discounting functions were compared as models of subjects′ present valuations of delayed rewards. Previous comparisons have been limited by relying on the assumption that discounting rate is independent of reward size; we avoided this limitation by making all comparisons within reward sizes. In Experiment 1, using real rewards in a simulated auction, and in Experiment 2, using hypothetical rewards, we offered subjects five monetary rewards at six delays each and asked them to indicate the smallest amount that they would accept immediately in exchange for those rewards. Both discounting functions were then fit to the six reported amounts for each reward using nonlinear regressions. In both experiments, although both functions fit the data very well, the hyperbolic function fit better for all of the delayed rewards. Furthermore, the hyperbolic function better described the data for 20 of 21 and 14 of 18 subjects in Experiments 1 and 2, respectively.     

Introduction to the special issue on comparative cognition

Prior research has shown that nonhumans show an extreme preference for variable‐ over fixed‐delays to reinforcement. This well‐established preference for variability occurs because a reinforcer's strength or “value” decreases according to a curvilinear function as its delay increases. The purpose of the present experiments was to investigate whether this preference for variability occurs with human participants making hypothetical choices. In three experiments, participants recruited from Amazon Mechanical Turk made choices between variable and fixed monetary rewards. In a variable‐delay procedure, participants repeatedly chose between a reward delivered either immediately or after a delay (with equal probability) and a reward after a fixed delay (Experiments 1 and 2). In a double‐reward procedure, participants made choices between an alternative consisting of two rewards, one delivered immediately and one after a delay, and a second alternative consisting of a single reward delivered after a delay (Experiments 1 and 3). Finally, all participants completed a standard delay‐discounting task. Although we observed both curvilinear discounting and magnitude effects in the standard discounting task, we found no consistent evidence of a preference for variability—as predicted by two prominent models of curvilinear discounting (i.e., a simple hyperbola and a hyperboloid)—in our variable‐delay and double‐reward procedures. This failure to observe a preference for variability may be attributed to the hypothetical, rule‐governed nature of choices in the present study. In such contexts, participants may adopt relatively simple strategies for making more complex choices.     

Choosing schedules of signaled appetitive events over schedules of unsignaled ones

Two experiments were completed allowing albino rats to choose between signaled and unsignaled reward conditions. These experiments examined the effects on preference of (1) response dependent versus response-independent reward and, (2) food pellets versus chocolate milk as the reward. All subjects preferred the signaled condition over the unsignaled condition, whether exposed to response-dependent, or to response-independent delivery of rewards. Preference was controlled most effectively by presenting both the signal itself and the correlated stimulus identifying the signaled condition. The signal presented alone (Extinction 3) controlled preference more effectively than did the stimulus correlated with the signaled condition (Extinction 2). The second experiment showed that the quality of the reinforcer (pellets and chocolate milk) did not affect preference for signaled reward since all subjects preferred the signaled condition at levels comparable to those observed in Experiment 1, with food pellets. These results, along with others, argue against species differences, response-dependency, and reinforcer quality as variables affecting the direction of preference.     

Waiting for more: the performance of domestic dogs (Canis familiaris) on exchange tasks

Five domestic dogs (Canis familiaris) were tested in a cooperative exchange task with an experimenter, as previously tested in non-human primates. In the first task, the dogs exchanged to maximise payoffs when presented with food items of differing quality. All consistently exchanged lower-value for higher-value rewards, as determined by their individual food preference, and exchanges corresponded significantly with the spontaneous preferences of three dogs. Next, all subjects demonstrated an ability to perform two and three exchanges in succession, to gain both qualitative and quantitatively increased rewards (group mean = 72 and 92% successful triple exchanges, respectively). Finally, the ability to delay gratification over increasing intervals was tested; the dogs kept one food item to exchange later for a larger item. As previously reported in non-human primates, there was considerable individual variation in the tolerance of delays, between 10 s and 10 min for the largest rewards. For those who reached longer time lags (>40 s), the dogs gave up the chance to exchange earlier than expected by each subject’s general waiting capacity; the dogs anticipated delay duration and made decisions according to the relative reward values offered. Compared to primates, dogs tolerated relatively long delays for smaller value rewards, suggesting that the socio-ecological history of domestic dogs facilitates their performance on decision-making and delay of gratification tasks.     

Preference for Different Sequences of Increasing or Decreasing Rewards

Preference for different increasing (or decreasing) sequences of rewards has been found to depend both on the magnitude of increase or decrease from step-to-step in the sequence and on the rate of change with which rewards increase or decrease. This experiment examined the effects on preference of different magnitudes and rates of change of reward. Using rewards for actual task performance, four increasing and four decreasing sequences were studied, each consisting of 24 rewards of varying magnitude. Sequences differed according to four possible models of rate change: linear, exponential, logarithmic, and step function. Preferences for given reward sequences obtained prior to extensive task and reward experience (decision utility) were not closely related to preferences after such experience (predicted utility). In the increasing reward sequences, subjects preferred the step sequence (with its single large increase at the end) prior to experience, but after experience they preferred the exponential, linear, and logarithmic sequences which entailed continuous reward-to-reward improvement throughout the sequence. In the decreasing sequences, subjects were less definite in their preferences. Prior to experience they most preferred the logarithmic sequence with its decelerating decline in magnitude of rewards, while after experience they least preferred the step function, with its huge loss at the end of the sequence.     

Making choices in anticipation of similar future choices can increase self-control

Two experiments tested the efficacy of linking a current choice with similar future choices as a means of increasing self-control. Participants were offered choices between smaller and sooner vs. larger and later amounts of money (Experiment 1, n = 60) or food (Experiment 2, n = 34). After a small-large pair for which the participant preferred the smaller reward was found, a choice between the same pair was offered as the 1st of 5 such choices to be offered over a period of weeks. The majority of participants in both experiments who chose between all 5 smaller and all 5 larger rewards chose the larger rewards. One third of participants in Experiment 1 who could choose independently on each pair in the series reversed their previous preference and chose the larger reward in the context of the series. These results suggest that self-control can be enhanced by viewing one's current choice as predictive of future choices.     

Subjective probability and delay.

Human subjects indicated their preference between a hypothetical $1,000 reward available with various probabilities or delays and a certain reward of variable amount available immediately. The function relating the amount of the certain-immediate reward subjectively equivalent to the delayed $1,000 reward had the same general shape (hyperbolic) as the function found by Mazur (1987) to describe pigeons' delay discounting. The function relating the certain-immediate amount of money subjectively equivalent to the probabilistic $1,000 reward was also hyperbolic, provided that the stated probability was transformed to odds against winning. In a second experiment, when human subjects chose between a delayed $1,000 reward and a probabilistic $1,000 reward, delay was proportional to the same odds-against transformation of the probability to which it was subjectively equivalent.     

Evidence for a magnitude effect in temporal discounting with pigeons

A magnitude effect in human intertemporal choice is well established-larger rewards or outcomes are discounted over time at a lower rate than are smaller rewards. However, many recent studies have failed to find a corresponding effect in nonhuman animals. Here we report a magnitude effect in temporal discounting for pigeons' choices involving a tradeoff between reward delay and amount. Pigeons chose between a small reward (1-s access to food) after a 2-s delay, and a large reward (4.5-s access to food) after a 28-s delay. Across conditions, the delays to the small and large rewards were increased or decreased, respectively. Temporal discounting functions obtained through a value-estimation procedure showed clear evidence of a magnitude effect: The value of the large reward decreased more slowly with increasing delay than the value of the small reward. We linked this result to a nonlinear relationship between choice and the delays associated with the small and large rewards. The nonlinearity was contrary to the generalized matching law but was predicted by the contextual choice model. Our results confirm the existence of a magnitude effect in nonhuman temporal discounting, showing that this adaptation is not unique to humans.     

Preference reversals with food and water reinforcers in rats

Rats were given a choice between a smaller, immediately available reward and a larger reward available after a delay. In one phase, the reward was food and in another phase, the reward was water. Constant delays were added between the choice presentation and the delivery of the reward alternatives. As the time between choice and reward delivery increased from 0 to 25 s, all rats (except one in the water phase) reversed their preference from the smaller, sooner alternative to the larger, later alternative. These findings extend the generality of the preference-reversal animal model to qualitatively different reinforcers. Furthermore, the presence of both impulsive and self-control choices within the same animal is consistent with the view that self-control may be understood as choice behavior, and that species differences in self-control may be differences in degree, not kind.     

Temporal discounting when the choice is between two delayed rewards

The present experiments extend the temporal discounting paradigm from choice between an immediate and a delayed reward to choice between 2 delayed rewards: a smaller amount of money available sooner and a larger amount available later. Across different amounts and delays, the data were consistently well described by a hyperbola-like discounting function, and the degree of discounting decreased systematically as the delay to the sooner reward increased. Three theoretical models (the elimination-by-aspects, present-value comparison, and common-aspect attenuation hypotheses) were evaluated. The best account of the data was provided by the common-aspect attenuation hypothesis, according to which the common aspect of the choice alternatives (i.e., the time until the sooner reward is available) receives less weight in the decision-making process.     

Temporal discounting and preference reversals in choice between delayed outcomes

Subjects chose between pairs of hypothetical amounts of money available after different delays. When smaller, more immediate amounts were selected over larger, more delayed amounts, the addition of a constant delay to both outcomes resulted in reversals of preference, contrary to the standard discounted utility model of economics. The delays at which preference reversed were determined for three pairs of amounts ($20 vs. $50, $100 vs. $250, and $500 vs. $1,250). The relation between the delay to the larger amount and the delay to the smaller amount at preference reversal was well fit by both linear and quadratic functions. Intercepts increased with amount, strongly suggesting that rate of discounting decreases with amount. The presence of significant negative curvature in the data from the majority of individual subjects poses problems for exponential and hyperbolic models of temporal discounting in self-control, both of which predict a linear relation between the delays to the larger and smaller amounts.     

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.     

The Influence of Time Estimation and Time‐Saving Preferences on Learning to Make Temporally Dependent Decisions from Experience

In this paper, we merge research related to experiential learning, temporal perception, and the value of time and money by examining decisions where the timing of action (response) determines the outcome received. We predicted that time‐saving preferences and impatience would decrease maximization (i.e., taking action when it returned the largest reward), and that the constraints of temporal perception would compound their effects. Across three studies, participants undershot on average (i.e., responded earlier than the period of time during which a response would return the maximal reward) showed a preference for shorter‐delay options and often did not find the maximal reward. In addition, participants' reliance on temporal perception increased undershooting, increased preferences for shorter‐delay options, and reduced maximization. Nevertheless, participants who found the maximal reward continued to maximize at a high rate rather than opting for shorter delays and smaller rewards. Thus, while most participants appeared to have a preference for saving time, most behaved as reward maximizers rather than temporal discounters. Copyright © 2017 John Wiley & Sons, Ltd.     

DISCOUNTING OF DELAYED REWARDS:

Abstract— In this study, children, young adults, and older adults chose between immediate and delayed hypothetical monetary rewards The amount of the delayed reward was held constant while its delay was varied All three age groups showed delay discounting, that is, the amount of an immediate reward judged to be of equal value to the delayed reward decreased as a function of delay The rate of discounting was highest for children and lowest for older adults, predicting a life-span developmental trend toward increased selfcontrol Discounting of delayed rewards by all three age groups was well described by a single function with agesensitive parameters (all R²s>94) Thus, even though there are quantitative age differences in delay discounting, the existence of an age-invanant form of discount function suggests that the process of choosing between rewards of different amounts and delays is qualitatively similar across the life span     

Are people really more patient than other animals? Evidence from human discounting of real liquid rewards

In previous studies, researchers have found that humans discount delayed rewards orders of magnitude less steeply than do other animals. Humans also discount smaller delayed reward amounts more steeply than larger amounts, whereas animals apparently do not. These differences between humans and animals might reflect differences in the types of rewards studied and/or the fact that animals actually had to wait for their rewards. In the present article, we report the results of three experiments in which people made choices involving liquid rewards delivered and consumed after actual delays, thereby bridging the gap between animal and human studies. Under these circumstances, humans, like animals, discounted the value of rewards delayed by seconds; however, unlike animals, they still showed an effect of reward amount. Human discounting was well described by the same hyperboloid function that has previously been shown to describe animal discounting of delayed food and water rewards, as well as human discounting of real and hypothetical monetary rewards.     

Exchange delays and impulsive choice in adult humans.

Choice responding by adult humans in a discrete-trial task was examined as a function of conditions that manipulated either the delay to point delivery or the delay between points and their exchange for money. In point-delay conditions, subjects chose between an "impulsive" alternative that provided a small amount of points immediately and a "self-control" alternative that provided a larger amount of points delayed by 15, 30, or 60 s. Points were exchanged for money immediately following the session. Subjects preferred the self-control alternative. In exchange-delay conditions, subjects chose between a small amount of points exchangeable for money immediately following the session and a larger amount of points exchangeable for money after 1 day, 3 weeks, or 6 weeks. A self-control preference observed for all subjects in the 1-day exchange-delay condition reversed to exclusive impulsive preference for 4 of the 6 subjects when choice conditions involved exchange delays of 3 or 6 weeks. These results show that human choice is sensitive to the manipulation of exchange delays and that impulsive preference can be obtained with exchange delays on the order of weeks.     

Tests of an indifference rule in variable‐delay and double‐reward choice procedures with humans

Four hundred and fifty participants were recruited from Amazon Mechanical Turk across 3 experiments to test the predictions of a hyperbolic discounting equation in accounting for human choices involving variable delays or multiple rewards (Mazur, 1984, 1986). In Experiment 1, participants made hypothetical choices between 2 monetary alternatives, 1 consisting of a fixed delay and another consisting of 2 delays of equal probability (i.e., a variable‐delay procedure). In Experiment 2, participants made hypothetical monetary choices between a single, immediate reward and 2 rewards, 1 immediate and 1 delayed (i.e., a double‐reward procedure). Experiment 3 also used a double‐reward procedure, but with 2 delayed rewards. Participants in all 3 experiments also completed a standard delay‐discounting task. Finally, 3 reward amounts were tested in each type of task ($100, $1000, and $5000). In the double‐reward conditions (Experiments 2 and 3), the results were in good qualitative and quantitative agreement with Mazur's model (1984, 1986). In contrast, when participants made choices involving variable delays (Experiment 1), there was relatively poor qualitative and quantitative agreement with this model. These results, along with our previous findings, suggest the structure of questions in hypothetical tasks with humans can be a strong determinant of the choice pattern.     

Delay and amount of reward in a concurrent chain

Eight pigeons responded under a concurrent-chain schedule for rewards differing in both delay and amount, the larger reward being associated with the longer delay. Preference was examined as the absolute durations of the terminal-link delays were increased at four different delay ratios. Difficulties with other experiments of this type were controlled for by the use of (a) a single-tape initial link to equalize terminal-link entries, (b) a blackout following the more immediate reward to equalize terminal-link length, and (c) a photocell to measure reinforcer duration more accurately. Preference for the larger reward changed systematically as delays increased in all conditions, decreasing for the 6:1, 3:1, and 3:2 ratios, and increasing for the 1:1 ratio. These results were similar to, but significantly different from, those of previous investigations. The implications of these results for various models of concurrent-chain behavior are discussed.