Risky choice in pigeons: preference for amount variability using a token-reinforcement system

Pigeons were given repeated choices between variable and fixed numbers of token reinforcers (stimulus lamps arrayed above the response keys), with each earned token exchangeable for food. The number of tokens provided by the fixed-amount option remained constant within blocks of sessions, but varied parametrically across phases, assuming values of 2, 4, 6, or 8 tokens per choice. The number of tokens provided by the variable-amount option varied between 0 and 12 tokens per choice, arranged according to an exponential or rectangular distribution. In general, the pigeons strongly preferred the variable option when the fixed option provided equal or greater numbers of tokens than the variable amount. Preference for the variable amount decreased only when the alternatives provided widely disparate amounts favoring the fixed amount. When tokens were removed from the experimental context, preference for the variable option was reduced or eliminated, suggesting that the token presentation played a key role in maintaining risk-prone choice patterns. Choice latencies varied inversely with preferences, suggesting that local analyses may provide useful ancillary measures of reinforcer value. Overall, the results indicate that systematic risk sensitivity can be attained with respect to reinforcer amount, and that tokens may be critical in the development of such preferences.

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. The size of the adjusting ratio requirement was increased and decreased over trials based on the subject's responses, in order to estimate an indifference point-a ratio at which the two alternatives were chosen about equally often. The second half of each experiment used an adjusting-delay procedure-fixed and adjusting delays to the small and large reinforcers were used instead of ratio requirements. In some conditions, particularly with the reinforcer delays, the rats had consistently longer adjusting delays with the larger pre-trial ratios, reflecting a greater tendency to choose the larger, delayed reinforcer when more responding was required to reach the choice point. No consistent effects of the pre-trial ratio were found for the pigeons in any of the conditions. These results may indicate that rats are more sensitive to the long-term reinforcement rates of the two alternatives, or they may result from a shallower temporal discounting rate for rats than for pigeons, a difference that has been observed in previous studies.

Delay discounting of qualitatively different reinforcers in rats

Humans discount larger delayed rewards less steeply than smaller rewards, whereas no such magnitude effect has been observed in rats (and pigeons). It remains possible that rats' discounting is sensitive to differences in the quality of the delayed reinforcer even though it is not sensitive to amount. To evaluate this possibility, Experiment 1 examined discounting of qualitatively different food reinforcers: highly preferred versus nonpreferred food pellets. Similarly, Experiment 2 examined discounting of highly preferred versus nonpreferred liquid reinforcers. In both experiments, an adjusting-amount procedure was used to determine the amount of immediate reinforcer that was judged to be of equal subjective value to the delayed reinforcer. The amount and quality of the delayed reinforcer were varied across conditions. Discounting was well described by a hyperbolic function, but no systematic effects of the quantity or the quality of the delayed reinforcer were observed.

Isolating behavioral mechanisms of intertemporal choice: nicotine effects on delay discounting and amount sensitivity

Many drugs of abuse produce changes in impulsive choice, that is, choice for a smaller-sooner reinforcer over a larger-later reinforcer. Because the alternatives differ in both delay and amount, it is not clear whether these drug effects are due to the differences in reinforcer delay or amount. To isolate the effects of delay, we used a titrating delay procedure. In phase 1, 9 rats made discrete choices between variable delays (1 or 19 s, equal probability of each) and a delay to a single food pellet. The computer titrated the delay to a single food pellet until the rats were indifferent between the two options. This indifference delay was used as the starting value for the titrating delay for all future sessions. We next evaluated the acute effects of nicotine (subcutaneous 1.0, 0.3, 0.1, and 0.03 mg/kg) on choice. If nicotine increases delay discounting, it should have increased preference for the variable delay. Instead, nicotine had very little effect on choice. In a second phase, the titrated delay alternative produced three food pellets instead of one, which was again produced by the variable delay (1 s or 19 s) alternative. Under this procedure, nicotine increased preference for the one pellet alternative. Nicotine-induced changes in impulsive choice are therefore likely due to differences in reinforcer amount rather than differences in reinforcer delay. In addition, it may be necessary to include an amount sensitivity parameter in any mathematical model of choice when the alternatives differ in reinforcer amount.

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. Indifference functions were constructed by plotting the adjusting delay as a function of the standard delay for each pair of reinforcer amounts. The experiments were designed to test the prediction of a hyperbolic decay equation that the slopes of the indifference functions should increase as the ratio of the two reinforcer amounts increased. Consistent with the hyperbolic equation, the slopes of the indifference functions depended on the ratios of the two reinforcer amounts for both pigeons and rats. These results were not compatible with an exponential decay equation, which predicts slopes of 1 regardless of the reinforcer amounts. Combined with other data, these findings provide further evidence that delay discounting is well described by a hyperbolic equation for both species, but not by an exponential equation. Quantitative differences in the y-intercepts of the indifference functions from the two species suggested that the rate at which reinforcer strength decreases with increasing delay may be four or five times slower for rats than for pigeons.