People discount the value of delayed and uncertain outcomes, and how steeply individuals discount is thought to reflect how impulsive they are. From this perspective, steep discounting of delayed outcomes (which fails to maximize long-term welfare) and shallow discounting of probabilistic outcomes (which fails to adequately take risk into account)…

In a temporal double bisection task, animals learn two discriminations. In the presence of Red and Green keys, responses to Red are reinforced after 1-s samples and responses to Green are reinforced after 4-s samples; in the presence of Blue and Yellow keys, responses to Blue are reinforced after 4-s samples and responses to Yellow are reinforced…

In Experiment 1, food-deprived rats responded to one of two schedules that were, with equal probability, associated with a sample lever. One schedule was always variable ratio, while the other schedule, depending on the trial within a session, was: (a) a variable-interval schedule; (b) a tandem variable-interval,…

David Thorne's (2010) article, "The Identities Hidden In The Matching Laws, And Their Uses" performs a valuable service in pointing out alternative expressions of matching. However, some identities tend to obscure rather than illuminate empirical relationships. Three such problematic instances are discussed: interresponse time as a function of…

Some of the differences between Rachlin & Locey (2010) and Thorne (2010) are due to what assumptions are taken as givens versus questionable. Most of the other apparent differences are largely linguistic and can be resolved by agreeing on terminology. The identity combining both rate and probability of reinforcement is general, has already…

Eight pigeons responded in a three-component concurrent-chains procedure, with either independent or dependent initial links. Relative probability and immediacy of reinforcement in the terminal links were both varied, and outcomes on individual trials (reinforcement or nonreinforcement) were either signaled or unsignaled. Terminal-link fixed-time…

Pigeons responded in a perceptual categorization task with six different stimuli (shades of gray), three of which were to be classified as "light" or "dark", respectively. Reinforcement probability for correct responses was varied from 0.2 to 0.6 across blocks of sessions and was unequal for correct light and dark responses. Introduction of a new…

Reinforcers may increase operant responding via a response-strengthening mechanism whereby the probability of the preceding response increases, or via some discriminative process whereby the response more likely to provide subsequent reinforcement becomes, itself, more likely. We tested these two accounts. Six pigeons responded for food…

The effects of a history of differential reinforcement for selecting a free-choice versus a restricted-choice stimulus arrangement on the subsequent responding of 7 undergraduates in a computer-based game of chance were examined using a concurrent-chains arrangement and a multiple-baseline-across-participants design. In the free-choice…

The present study with college students examined the effect of amount on the discounting of probabilistic monetary rewards. A hyperboloid function accurately described the discounting of hypothetical rewards ranging in amount from $20 to $10,000,000. The degree of discounting increased continuously with amount of probabilistic reward. This effect…

The utility of a quantitative model depends on the extent to which its fitted parameters vary systematically with environmental events of interest. Professional football statistics were analyzed to determine whether play selection (passing versus rushing plays) could be accounted for with the generalized matching equation, and in particular…

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…

Various theoretical equations have been proposed to predict response rate as a function of the rate of reinforcement. If both the rate and probability of reinforcement are considered, a simple identity, defining equation, or "law" holds. This identity places algebraic constraints on the allowable forms of our mathematical models and can help…

Preference for working on variable schedules and temporal discrimination were simultaneously examined in two experiments using a discrete-trial, concurrent-chains arrangement with fixed interval (FI) and random interval (RI) terminal links. The random schedule was generated by first sampling a probability distribution after the programmed delay to…

In this article, we describe a test of the active time model for concurrent variable interval (VI) choice. The active time model (ATM) suggests that the time since the most recent response is one of the variables controlling choice in concurrent VI VI schedules of reinforcement. In our experiment, pigeons were trained in a multiple concurrent…