Consumer choices with variations in item price, delay, and opportunity cost.

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.

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.

Human choices between variable and fixed rewards in hypothetical variable-delay and double-reward discounting procedures.

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.

Rats' choices with token stimuli in concurrent variable-interval schedules.

Four rats responded on concurrent variable-interval schedules that delivered token stimuli (stimulus lights arranged vertically above each of two side levers). During exchange periods, each token could be exchanged for one food pellet by responding on a center lever, with one response required for each pellet delivery. In different conditions, the exchange requirements (number of tokens that had to be earned before they could be exchanged for food) varied between one and four for the two response levers.

Pigeons' choices with token stimuli in concurrent variable-interval schedules.

Twelve pigeons responded on concurrent variable-interval schedules that delivered token stimuli (stimulus lights for some pigeons, and white circles on the response keys for others). During exchange periods, each token could be exchanged for food on a fixed-ratio 1 schedule. Across conditions, the exchange requirements (number of tokens that had to be earned before they could be exchanged for food) varied between one and four for the two response keys.

Choice behavior of pigeons (Columba livia), college students, and preschool children (Homo sapiens) in the Monty Hall dilemma.

In the Monty Hall dilemma, an individual chooses between three options, only one of which will deliver a prize. After the initial choice, one of the nonchosen options is revealed as a losing option, and the individual can choose to stay with the original choice or switch to the other remaining option. Previous studies have found that most adults stay with their initial choice, although the chances of winning are 2/3 for switching and 1/3 for staying.

Effects of pre-trial response requirements on self-control choices by rats and pigeons.

Parallel experiments with rats and pigeons examined whether the size of a pre-trial ratio requirement would affect choices in a self-control situation. In different conditions, either 1 response or 40 responses were required before each trial. In the first half of each experiment, an adjusting-ratio schedule was used, in which subjects could choose a fixed-ratio schedule leading to a small reinforcer, or an adjusting-ratio schedule leading to a larger reinforcer.

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.

Distributed versus exclusive preference in discrete-trial choice.

Two experiments on discrete-trial choice examined the conditions under which pigeons would exhibit exclusive preference for the better of two alternatives as opposed to distributed preference (making some choices for each alternative). In Experiment 1, pigeons chose between red and green response keys that delivered food after delays of different durations, and in Experiment 2 they chose between red and green keys that delivered food with different probabilities. Some conditions of Experiment 1 had fixed delays to food and other conditions had variable delays.

Delay-amount tradeoffs in choices by pigeons and rats: hyperbolic versus exponential discounting.

An adjusting-delay procedure was used to study the choices of pigeons and rats when both delay and amount of reinforcement were varied. In different conditions, the choice alternatives included one versus two reinforcers, one versus three reinforcers, and three versus two reinforcers. The delay to one alternative (the standard alternative) was kept constant in a condition, and the delay to the other (the adjusting alternative) was increased or decreased many times a session so as to estimate an indifference point--a delay at which the two alternatives were chosen about equally often.

Effects of reinforcer delay and variability in a successive-encounters procedure.

Pigeons responded in a successive-encounters procedure that consisted of a search period, a choice period, and a handling period. The search period was either a fixed-interval or a mixed-interval schedule presented on the center key of a three-key chamber. Upon completion of the search period, the center key was turned off and the two side keys were lit.

Rats' choices between one and two delayed reinforcers.

Rats chose between alternatives that differed in the number of reinforcers and in the delay to each reinforcer. A left leverpress led to two reinforcers, each delivered after a fixed delay. A right leverpress led to one reinforcer after an adjusting delay.

Choice in a successive-encounters procedure and hyperbolic decay of reinforcement.

Pigeons responded in a successive-encounters procedure that consisted of a search state, a choice state, and a handling state. The search state was either a fixed-interval or mixed-interval schedule presented on the center key of a three-key chamber. Upon completion of the search state, the choice state was presented, in which the center key was off and the two side keys were lit.

Species differences between rats and pigeons in choices with probabilistic and delayed reinforcers.

An adjusting-delay procedure was used to study rats' choices with probabilistic and delayed reinforcers, and to compare them with previous results from pigeons. A left lever press led to a 5-s delay signaled by a light and a tone, followed by a food pellet on 50% of the trials. A right lever press led to an adjusting delay signaled by a light followed by a food pellet on 100% of the trials.

Choice between single and multiple reinforcers in concurrent-chains schedules.

Pigeons responded on concurrent-chains schedules with equal variable-interval schedules as initial links. One terminal link delivered a single reinforcer after a fixed delay, and the other terminal link delivered either three or five reinforcers, each preceded by a fixed delay. Some conditions included a postreinforcer delay after the single reinforcer to equate the total durations of the two terminal links, but other conditions did not include such a postreinforcer delay.

Mathematical models and the experimental analysis of behavior.

The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make equally accurate predictions for a large body of data.

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.

Heuristics and general principles of learning.

This research on decision-making heuristics is similar to research on animal learning in at least two ways. First, optimality modeling has not proven to be very useful for either research area. Second, both of these research areas seek to find general principles (or heuristics) that are applicable to different species in different settings.

Exploring a concurrent-chains paradox: decreasing preference as an initial link is shortened.

Experiments with pigeons and rats on concurrent-chains schedules examined a paradoxical effect reported by R. A. Preston and E.

Varying initial-link and terminal-link durations in concurrent-chains schedules: a comparison of three models.

In Experiment 1, pigeons responded on concurrent-chains schedules with equal variable-interval schedules as initial links and fixed delays to food as terminal links. One terminal-link delay was always three times as long as the other. As terminal-link delays increased, response percentages on the key with the shorter terminal link increased according to a curvilinear function.

Effects of free-food deliveries and delays on choice under concurrent-chains schedules.

Pigeons responded on a concurrent-chains schedule with two equal variable-interval (VI) schedules as initial links and delays to food of 3 and 12s as the two terminal links. In even-numbered sessions, no other reinforcement schedule was present, and all pigeons showed a strong preference for the response key that had the shorter, 3-s terminal-link delay. In odd-numbered sessions, the initial links were interrupted at random times by one of three different types of events.

Concurrent-chain performance in transition: effects of terminal-link duration and individual reinforcers.

Pigeons responded on concurrent-chain schedules with variable-interval initial links and equal delays as terminal links. The terminal-link delays were 1 sec in some conditions and 20 sec in other conditions. The percentages of reinforcers delivered for responses on the left key were 10%, 30%, 70%, or 90%, and this percentage was switched every five to nine sessions.

Evidence against a constant-difference effect in concurrent-chains schedules.

Savastano and Fantino (1996) reported that in concurrent-chains schedules, initial-link choice proportions remained constant as terminal-link durations increased as long as the subtractive difference between the two terminal-link schedules remained constant. Two experiments with pigeons were conducted to examine this constant-difference effect. Both experiments used equal variable-interval schedules as initial links.