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.

When offered a choice (Choice Y) between a smiiall immediate reward (2-sec exposure to grain) and a large rewvard (4-sec exposure to grain) delayed by 4 sec, pigeons invariably preferred the small, immnediate 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 lea(ling to Choice Y (and then chose the small, immediate reward). When T was large, the pigeons chose the alternative leading to the large delayed rewvard 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 commitmiient to a given course of action. Such coullmitment may be seen as a prototype for self-control.Commitment to a course of action is a form of self-control (Skinner, 1953) the utility of which depends on reversals of preference from time to time. Consider, for instance, a popular form of commitment, payroll savings. When a man signs a payroll savings agreement he prefers saving a certain portion of his paycheck to spending it. The utility of making this commitment rests on the fact that, when the man actually receives the money, he prefers to spend it rather than save it. Were it not for the reversal, there would be no reason to sign the payroll deduction agreement in the first place.A similar reversal of preference underlies the effectiveness of a device invented by Azrin and Powell (1968)

When pigeons' standing on one or the other side of a chamber was reinforced on two concurrent variable-interval schedules, the ratio of time spent on the left to time spent on the right was directly proportional to the ratio of reinforcements produced by standing on the left to reinforcements produced by standing on the right. The constant of proportionality was less than unity for all pigeons, indicating a bias toward the right side of the chamber. The biased matching relation obtained here is comparable to the matching relation obtained with concurrent reinforcement of key pecks. The present results, together with related research, suggest that the ratio of time spent in two activities equals the ratio of the "values" of the activities. The value of an activity is the product of several parameters, such as rate and amount of reinforcement, contingent on that activity.