Experiments on single, multiple, and concurrent schedules of reinforcement find various correlations between the rate of responding and the rate or magnitude of reinforcement. For concurrent schedules (i.e., simultaneous choice procedures), there is matching between the relative frequencies of responding and reinforcement; for multiple schedules (i.e., successive discrimination procedures), there are contrast effects between responding in each component and reinforcement in the others; and for single schedules, there are a host of increasing monotonic relations between the rate of responding and the rate of reinforcement. All these results, plus several others, can be accounted for by a coherent system of equations, the most general of which states that the absolute rate of any response is proportional to its associated relative reinforcement.

A previous paper (Herrnstein, 1958) reported how pigeons behave on a concurrent schedule under which they peck at either of two response-keys. The significant finding of this investigation was that the relative frequency of responding to each of the keys may be controlled within narrow limits by adjustments in an independent variable. In brief, the requirement for reinforcement in this procedure is the emission of a minimum number of pecks to each of the keys. The pigeon receives food when it completes the requirement on both keys. The frequency of responding to each key was a close approximation to the minimum requirement.The present experiment explores the relative frequency of responding further. In the earlier study it was shown that the output of behavior to each of two keys may be controlled by specific requirements of outputs. Now we are investigating output as a function of frequency of reinforcement. The earlier experiment may be considered a study of differential reinforcement; the present one, a study of strength of response. Both experiments are attempts to elucidate the properties of rdlative frequency of responding as a dependent variable. MI,THOD SubjectsThree adult, male, White Carneaux pigeons, maintained at 80% of free-feeding weights, and experimentally naive at the start of the study, were used. ApparatusA conventional experimental chamber for pigeons (Ferster & Skinner, 1957)

Pigeons were trained to peck either of two response keys for food reinforcement on equated aperiodic schedules. The distribution of responding at the two keys was studied as reinforcement was delayed for various durations. The relative frequency of responding at each key was shown to match the relative immediacy of reinforcement, immediacy defined as the reciprocal of the delay of reinforcement.The present experiment extends the investigation of reinforcement delay described by Chung (1965 auditory feedback to the pigeon. The chamber was illuminated by a white bulb, and, except when the magazine was operated, each response key was transilluminated by a 7-w red bulb. A continuous white masking noise was delivered during sessions. ProcedurePecks on either of the two response keys were, at first, reinforced on a variable-interval schedule with an average interval of 1 min. Two independent programmers arranged reinforcements for responses on the two response keys, with the restriction that a switch from one response key to the other prevented reinforcement for 1 sec (changeover delay or COD l-sec). When the rate of pecking on the two keys became stable and approximately equal, delays of reinforcement were initiated. For subjects 237, 236, 415, and 416, responses on the left key were reinforced after an 8-sec delay (standard key). Reinforcements for responses on the right key were delayed for various durations ranging from 1 to 30 sec (experimental key). The intervals of delay imposed on the experimental key, in-irregular order, were: 1, 2, 4, 6, 8, 12, 16, 20, 24, and Between the response-to-be-reinforced and delivery of the reinforcement, the chamber 67 1967, 10,[67][68][69][70][71][72][73][74] NUMBER I (JANUARY)

A basic stationarity axiom of economic theory assumes stable preference between two deferred goods separated by a fixed time To test this assumption, we offered subjects choices between delayed rewards, while manipulating the delays to those rewards Preferences typically reversed with changes in delay, as predicted by hyperbolic discounting models of impulsiveness Of 36 subjects, 34 reversed preference from a larger, later reward to a smaller, earlier reward as the delays to both rewards decreased We conclude that the stationarity axiom is not appropriate in models of human choice

The matching law implies that any form of behavior approaches an asymptotic frequency as its reinforcement approaches 100 per cent of the total reinforcement being obtained at a given time. This asymptote is formally independent of the kind or quantity of drive or reinforcement associated with the response in question or with any competing response.It has been repeatedly shown that animals (including human beings) distribute their behavior across alternatives according to the matching principle (Herrnstein, 1970(Herrnstein, , 1971