In a choice between an immediate, small reward and a delayed, large reward, an organism may be said to exhibit "self-control" if it chooses the large reward. Given an opportunity in advance to avoid this choice, pigeons may commit themselves to the large reward, but if the choice is encountered they will almost always select the immediate, small reward. This preference reversal as a function of temporal distance from reinforcement is compatible with some general theories of choice. The present study tested one such model, developed by Rachlin and his co-workers, which assumes that (a) relative choice responses "match" the relative values of the outcomes; and (b) outcome values equal the product of rate and amount of reinforcement. Pigeons chose between 4.5 and 1.5 sec access to grain with equal or unequal delays of reinforcement. When delays consisted of unequal fixed-interval schedules the shorter delay terminated with the smaller reward, and preference for the large reward tended to increase with the absolute size of the delays (consistent with the matching model). However, preference for the large reward increased with delay size even when the delays were equal, a violation of the model. It is shown that both findings are derivable from either models of choice (developed by Logan and by Rachlin and Ainslie) based on gradients of reinforcing value, or from a more general model, previously applied to other choice situations, which assumes preference to depend on the reduction in time to reinforcement correlated with the alternatives.

Pigeons' pecks in the presence of two concurrently available initial-link stimuli occasionally produced one of two stimuli associated with mutually exclusive terminal links. Pecks during either terminal link produced food according to aperiodic (variable-interval and variable-ratio) or periodic (fixed-interval and fixed-ratio) schedules of reinforcement. Aperiodic and periodic schedules to which the pigeons were indifferent, in the sense that these schedules maintained equal responding in the initial links, often yielded different preferences in separate choice tests with a third schedule. Conversely, aperiodic and periodic schedules that were equally preferred to a third schedule often failed to generate indifference. These intransitivities imply that (1) aperiodic and periodic schedules are not functionally equivalent in their effects upon choice, and (2) efforts to find a simple method for transforming aperiodic schedules into their periodic equivalents will fail.

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The ability of a reinforcer to maintain behavior decreases as a hyperbolic function of its delay. This discounted value can help explain impulsivity defined as the choice of an immediate, small reinforcer over a delayed, large reinforcer. Human operant studies using consumable reinforcers such as videos have found impulsivity with delays under 1 min . However, measures of discounting rates using questionnaires that dElscribe hypothetical amounts of monetary reinforcers and delays of days, months, or years have found discounting rates that are much too low to explain impulsive choice in operant procedures. A comparison of discounting rates across questionnaire and operant studies indicates that questionnaires produce slower discounting because of the absence of both reinforcement and consumption processes. Combining reinforcement with questions about future reinforcers could facilitate the integration of questionnaire research into a behavioral framework.The ability of a reinforcer to maintain behavior generally decreases the longer the reinforcer is withheld after thEl behavior occurs. This decrease in reinforcer value over time is known as delay (or temporal) discounting. The precise form of the relationship and the methodology for investigating it have received considerable attention in connection with behavioral theories of impulsivity. In contrast to psychiatric theories, which view impulsivity as a predisposition toward a pattern of behavior (Moeller, Barrat, Dougherty, Schmitz, & Swann, 2001), behavioral theories view impulsivity as a specific choice response in a situation defined mainly by two parameters, amount and delay of reinforcement (Ainslie, 1975;Navarick & Fantino, 1976). Consistent choice of an immediate, small reinforcer over a delayed, large reinforcer represents impulsivity; the opposite preference represents self-control. A behavioral analysis implies that the same individual may exhibit impulsivity or selfcontrol depending on the precise amounts and delays of reinforcement Requests for reprints should be sent to Douglas J. Navarick,