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  • 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.

  • 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.

  • Tversky and Kahneman (1981) told participants to imagine they were at a store about to purchase an item. They were asked if they would be willing to drive 20 min to another store to receive a $5 discount on the item's price. Most participants were willing, but only when the original price of the item was small ($15); when the original price was relatively large ($125), most said they would not drive 20 min for a $5 discount. We examined this framing effect in 296 participants, but instead used a psychophysical-adjustment procedure to obtain quantitative estimates of the discount required with different (a) item prices, (b) delays until the item's receipt, and (c) opportunity costs (in “driving” vs. “delivery” tasks). We systematically replicated Tversky and Kahneman's results, but also extended them by showing a substantial influence of opportunity costs on the consumer discounts required. A behavioral model of delay discounting—additive-utility theory—accounted for 97% of the variance in these consumer discounts.

Last update from database: 3/13/26, 4:15 PM (UTC)

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