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 discounting of monetary gains and losses in adolescents with ADHD: Contribution of delay aversion to choice

Adolescents with attention-deficit/hyperactivity disorder (ADHD) are known to have stronger preferences for smaller immediate rewards over larger delayed rewards in delay discounting tasks than their peers, which has been argued to reflect delay aversion. Here, participants performed a delay discounting task with gains and losses. In this latter condition, participants were asked whether they were willing to wait in order to lose less money. Following the core assumption of the delay aversion model that individuals with ADHD have a general aversion to delay, one would predict adolescents with ADHD to avoid waiting in both conditions. Adolescents (12–17 years) with ADHD (n = 29) and controls (n = 28) made choices between smaller immediate and larger delayed gains, and between larger immediate and smaller delayed losses. All delays (5–25 s) and gains/losses (2–10 cents) were experienced. In addition to an area under the curve approach, a mixed-model analysis was conducted to disentangle the contributions of delay duration and immediate gain/delayed loss amount to choice. The ADHD group chose the immediate option more often than controls in the gain condition, but not in the loss condition. The contribution of delay duration to immediate choices was stronger for the ADHD group than the control group in the gain condition only. In addition, the ADHD group scored higher on self-reported delay aversion, and delay aversion was associated with delay sensitivity in the gain condition, but not in the loss condition. In sum, we found no clear evidence for a general aversion to delay in adolescents with ADHD.     

The rich get richer: Students’ discounting of hypothetical delayed rewards and real effortful extra credit

The present research compared choices among students with higher or lower grades for rewards that were devalued by imposing a delay to their receipt (Study 1) or by requiring more work for a larger reward (Study 2). In Study 1, students chose between hypothetical and noncontingent smaller immediate or larger delayed monetary rewards. In Study 2, students chose from among different amounts of real, response-contingent academic rewards (extra credit) that required different amounts of work. The results of both studies were similar: The highest scoring students discounted the value of the delayed money less than did their lower scoring counterparts, and the highest scoring students also chose to do and actually did more extra-credit work than lower scoring students did. Differences in the discounting of devalued rewards might represent a fundamental difference between the highest and lower scoring students.     

“金钱-环境”复合收益的风险决策:价值取向的影响

现实中的环境决策,往往要在多个由"金钱-环境"复合而成的结果间做选择。人们如何对异质复合结果进行评估与选择,是决策研究面临的新课题。本研究着重考察个体金钱取向和环境取向的相对强度对复合收益风险决策的影响。结果表明,无论是采用自陈量表(实验1)或内隐联想测验(实验2)来测量价值取向,还是采用混词造句任务(实验3)来启动价值取向,均发现价值取向相对强度对复合风险决策有显著影响。(1)相比于金钱取向占优的个体,环境取向占优的个体在进行复合风险决策时更偏好环境风险较小的复合选项;(2)在复合选项等价匹配任务中,环境取向占优的个体会赋予复合选项中的环境收益以更高权重,倾向于用更多的金钱收益来弥补环境收益的风险折扣;(3)在复合收益风险概率匹配任务中,环境取向占优的个体更倾向于为获取倍增的环境收益而承担更大的复合收益风险。作为对复合结果风险决策的首次探索,本研究初步回答了不同价值取向的个体在金钱-环境复合风险决策中更倾向于规避什么风险、拿什么冒险以及为什么冒险等问题,为今后进一步开展复合决策研究打下了理论和方法基础。     

Gambling for Gatorade: risk-sensitive decision making for fluid rewards in humans

Determining how both humans and animals make decisions in risky situations is a central problem in economics, experimental psychology, behavioral economics, and neurobiology. Typically, humans are risk seeking for gains and risk averse for losses, while animals may display a variety of preferences under risk depending on, amongst other factors, internal state. Such differences in behavior may reflect major cognitive and cultural differences or they may reflect differences in the way risk sensitivity is probed in humans and animals. Notably, in most studies humans make one or a few choices amongst hypothetical or real monetary options, while animals make dozens of repeated choices amongst options offering primary rewards like food or drink. To address this issue, we probed risk-sensitive decision making in human participants using a paradigm modeled on animal studies, in which rewards were either small squirts of Gatorade or small amounts of real money. Possible outcomes and their probabilities were not made explicit in either case. We found that individual patterns of decision making were strikingly similar for both juice and for money, both in overall risk preferences and in trial-to-trial effects of reward outcome on choice. Comparison with decisions made by monkeys for juice in a similar task revealed highly similar gambling styles. These results unite known patterns of risk-sensitive decision making in human and nonhuman primates and suggest that factors such as the way a decision is framed or internal state may underlie observed variation in risk preferences between and within species.     

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.     

Stimulus Equivalence: Effects Of A Default-response Option On Emergence Of Untrained Stimulus Relations

Human subjects were exposed to a concurrent-chains schedule in which reinforcer amounts, delays, or both were varied in the terminal links, and consummatory responses were required to receive points that were later exchangeable for money. Two independent variable-interval 30-s schedules were in effect during the initial links, and delay periods were defined by fixed-time schedules. In Experiment 1, subjects were exposed to three different pairs of reinforcer amounts and delays, and sensitivity to reinforcer amount and delay was determined based on the generalized matching law. The relative responding (choice) of most subjects was more sensitive to reinforcer amount than to reinforcer delay. In Experiment 2, subjects chose between immediate smaller reinforcers and delayed larger reinforcers in five conditions with and without timeout periods that followed a shorter delay, in which reinforcer amounts and delays were combined to make different predictions based on local reinforcement density (i.e., points per delay) or overall reinforcement density (i.e., points per total time). In most conditions, subjects' choices were qualitatively in accord with the predictions from the overall reinforcement density calculated by the ratio of reinforcer amount and total time. Therefore, the overall reinforcement density appears to influence the preference of humans in the present self-control choice situation.     

Delay-discounting probabilistic rewards: Rates decrease as amounts increase

The independence of delay-discounting rate and monetary reward size was tested by offering subjects (N = 621) a series of choices between immediate rewards and larger, delayed rewards. In contrast to previous studies, in which hypothetical rewards have typically been employed, subjects in the present study were entered into a lottery in which they had a chance of actually receiving one of their choices. The delayed rewards were grouped into small ($30–$35), medium ($55–$65), and large amounts ($70–$85). Using a novel parameter estimation procedure, we estimated discounting rates for all three reward sizes for each subject on the basis of his/her pattern of choices. The data indicated that the discounting rate is a decreasing function of the size of the delayed reward (p < .0001), whether hyperbolic or exponential discounting functions are assumed. In addition, a reliable gender difference was found (p = .005), with males discounting at higher rates than females, on average.     

The absence of numbers to express the amount may affect delay discounting with humans

Human delay discounting is usually studied with experimental protocols that use symbols to express delay and amount. In order to further understand discounting, we evaluated whether the absence of numbers to represent reward amounts affects discount rate in general, and whether the magnitude effect is generalized to nonsymbolic situations in particular. In Experiment 1, human participants were exposed to a delay‐discounting task in which rewards were presented using dots to represent monetary rewards (nonsymbolic); under this condition the magnitude effect did not occur. Nevertheless, the magnitude effect was observed when equivalent reward amounts were presented using numbers (symbolic). Moreover, in estimation tasks, magnitude increments produced underestimation of large amounts. In Experiment 2, participants were exposed only to the nonsymbolic discounting task and were required to estimate reward amounts in each trial. Consistent with Experiment 1, the absence of numbers representing reward amounts produced similar discount rates of small and large rewards. These results suggest that value of nonsymbolic rewards is a nonlinear function of amount and that value attribution depends on perceived difference between the immediate and the delayed nonsymbolic rewards.     

更优更耐心：质量结果对跨期选择的影响

跨期选择以往的研究集中于金钱数量结果。基于维度加工的模型,本文探究了在跨期选择中,人们面对质量差异的结果(如,今天的低配版手机还是六个月后的高配版手机)vs.相对应的金钱结果(如,今天的5000元还是六个月后的6000元)的选择偏好差异。3个实验结果表明：人们面对质量结果(相比于金钱结果)的跨期选择表现得更耐心,而这种现象是由于人们面对选择时在结果维度差异感知不同所致。与金钱结果跨期选择相同,质量结果跨期选择的心理加工过程同样遵循维度间差异比较。本研究为基于维度的跨期选择模型提供了新的证据。     

Delay discounting by pathological gamblers

Discounting of delayed rewards by pathological gamblers was compared to discounting of delayed rewards by matched control nongambling participants. All participants completed a hypothetical choice task in which they made repeated choices between dollars 1,000 available after a delay and an equal or lesser amount of money available immediately. The delay to the large amount of money was varied from 1 week to 10 years across conditions. Indifference points between immediate money and delayed money were identified at each delay condition by varying the amount of immediate money across choice trials. For the majority of participants, indifference points decreased monotonically across delays. Overall, gamblers discounted the delayed rewards more steeply than did control participants.     

Does betrayal aversion really guide trust decisions towards strangers?

Trust is a double-edged sword. When warranted, it leads to positive and rewarding interactions. When not, it leads to disappointment and anger. Therefore, it has been argued that people will display “betrayal aversion” in trust situations (i.e., avoid trusting to avoid betrayal). Yet, people also feel tense and uneasy when they signal distrust to another person and thus show signs of “principled trustfulness” (i.e., choosing to trust others although being skeptical of their trustworthiness). These two theoretical orientations imply directly opposite influences on trust behavior. Thus, we conducted two laboratory studies (with a total of 841 participants) with binary trust games (implying a risk of being betrayed) and extended lottery games (implying no such risk). In both studies, we varied the payoff structures of both games. Further, we made sure that the average perceived likelihood of winning or losing money when choosing the risky option was identical in both games, as was the distribution of these likelihoods. Neither study showed any sign of betrayal aversion. Rather, participants were more willing to risk their money in the trust game than they were to invest their money in a lottery, supporting the principled trustfulness view. We discuss possible explanations why, unlike previous studies, we did not find any indication of betrayal aversion.     

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.     

The influence of mortality and socioeconomic status on risk and delayed rewards: a life history theory approach

Why do some people take risks and live for the present, whereas others avoid risks and save for the future? The evolutionary framework of life history theory predicts that preferences for risk and delay in gratification should be influenced by mortality and resource scarcity. A series of experiments examined how mortality cues influenced decisions involving risk preference (e.g., $10 for sure vs. 50% chance of $20) and temporal discounting (e.g., $5 now vs. $10 later). The effect of mortality depended critically on whether people grew up in a relatively resource-scarce or resource-plentiful environment. For individuals who grew up relatively poor, mortality cues led them to value the present and gamble for big immediate rewards. Conversely, for individuals who grew up relatively wealthy, mortality cues led them to value the future and avoid risky gambles. Overall, mortality cues appear to propel individuals toward diverging life history strategies as a function of childhood socioeconomic status, suggesting important implications for how environmental factors influence economic decisions and risky behaviors.     

The magnitude effect: Temporal discount rates and restaurant tips

Decision makers show a larger subjective temporal discount rate for small magnitudes than for large ones. That is, they demand a larger percent increase in value to compensate for a delay when they are waiting for a small amount of money than for a large amount. Prelec and Loewenstein (1991; see also Loewenstein & Prelec, 1992) proposed an increasing proportional sensitivity account of this magnitude effect. This account surmises that the magnitude effect stems from the utility function for money and is consequently not unique to intertemporal choice. One study tested this prediction by demonstrating the magnitude effect in two domains: intertemporal choice and tipping for restaurant meals, haircuts, and taxi rides. In intertemporal choice, subjects showed a larger discount rate for smaller monetary amounts. They also tipped a larger percentage on small bills than on large bills. Thus, both domains showed the magnitude effect; however, the size of the effect was not well correlated between domains.     

Temporal discounting for monetary and close relationship outcomes

The present study extended research on intertemporal choice—in which individuals choose between outcomes that may be received immediately or after a delay—to close relationships. In Experiment 1, New Zealand university students aged 18 to 25 made decisions about hypothetical monetary and relationship outcomes, and in Experiment 2, about relationship outcomes which emphasized companionate or sexual aspects (Ns = 64). Both experiments found effects of delay and magnitude on temporal discounting rates, and domain independence for choices about close relationships, similar to previous studies with monetary outcomes. There were no significant gender differences. Overall, results suggest that people make intertemporal choices about relationships according to a similar process used to make decisions involving other types of outcomes.     

Decision biases in intertemporal choice and choice under uncertainty: Testing a common account

Two experiments were performed to test a psychophysical account of parallels between biases in risky choice and intertemporal choice. Experiment 1 demonstrated the common difference effect in intertemporal choice and the common ratio effect in risky choice. As was predicted, these two biases were uncorrelated with each other, although each was correlated across monetary/health domains. This result is consistent with the supposition that these two biases result from psychophysical properties of two different dimensions (time and probability, respectively). Experiment 2 examined the magnitude effect in intertemporal choice and the peanuts effect in risky choice. These two biases were correlated with each other but were uncorrelated across monetary/health domains. This result is consistent with the supposition that these two biases result from psychophysical properties of the same dimension (utility of money or health).     

LOTTERIES AND THE TIME HORIZON

Abstract— People chose between hypothetical alternatives of (a) a million-dollar lottery prize and (b) a much smaller but certain amount of money When probabilities of winning the lottery were above about 1/100,000, subjects avoided risk, for example, a 1/100,000 probability of the million-dollar prize was chosen about as often as $700 for sure But at probabilities below 1/100,000, subjects sought risk, for example, a 1/1,000,000 probability of the million-dollar prize was chosen about as often as $9 for sure This crossover from risk aversion to risk seeking is predicted by Mazur's (1987) hyperbolic delay discount function with probability expressed as average delay due to strings of losses followed by a win, together with a time horizon limiting subjective delay     

Effects of mindful eating training on delay and probability discounting for food and money in obese and healthy-weight individuals

Obese individuals tend to behave more impulsively than healthy weight individuals across a variety of measures, but it is unclear whether this pattern can be altered. The present study examined the effects of a mindful eating behavioral strategy on impulsive and risky choice patterns for hypothetical food and money. In Experiment 1, 304 participants completed computerized delay and probability discounting tasks for food-related and monetary outcomes. High percent body fat (PBF) predicted more impulsive choice for food, but not small-value money, replicating previous work. In Experiment 2, 102 randomly selected participants from Experiment 1 were assigned to participate in a 50-min workshop on mindful eating or to watch an educational video. They then completed the discounting tasks again. Participants who completed the mindful eating session showed more self-controlled and less risk-averse discounting patterns for food compared to baseline; those in the control condition discounted similarly to baseline rates. There were no changes in discounting for money for either group, suggesting stimulus specificity for food for the mindful eating condition.     

心理距离对跨期选择和风险选择的影响

通过考察时间距离、社会距离和概率距离对跨期选择和风险选择的影响, 探究跨期选择和风险选择心理过程的相似性, 并检验不同心理距离影响决策的相似性。结果发现, 无论是时间距离(实验1)、社会距离(实验2)、还是概率距离(实验3), 心理距离越远, 被试在跨期选择中越倾向于延迟选项, 在风险选择中越倾向于风险选项。研究认为, 在跨期选择和风险选择中, 选项的表征结构和选项整体评价时不同选项特征的相对权重具有相似性。随着心理距离增加, 与高识解相联系的金额特征的相对权重增加, 与低识解相联系的时间和概率特征的相对权重降低, 这使得被试更倾向于选择金额较大的延迟和风险选项。同时, 研究发现三类心理距离对两类决策有相似影响, 进一步验证了不同心理距离的本质相似性。