Matching since Baum (1979).

Data from recent studies employing concurrent variable-interval schedules are reviewed. Subject species employed in different experiments have included rats, pigeons, and humans, and reinforcers have varied from food and shock avoidance to points exchangeable for money. Undermatching (a greater preference for the schedule of the concurrent pair that delivers the lower rate of reinforcement than the Matching Law predicts) has been preponderant in recent studies, irrespective of whether behavior has been measured in terms of response ratios or time allocation, with the possible exception of data produced by human subjects. Little difference in the degree of undermatching exhibited by response and time measures has been found, except in the results from a single laboratory, in which time-allocation measures have tended to undermatch less than response measures. Procedural features, such as type of manipulandum used and changeover delay, seem to have little effect on the degree of undermatching exhibited, but asymmetrical response manipulanda (such as lever and key) for the different concurrent schedules, or other asymmetries in the experimental situation, show up clearly in bias measures, in a manner consistent with previous analyses.     

Pigeons' spatial memory: factors affecting delayed matching of key location.

The delayed-matching-to-sample procedure was modified to study pigeons' spatial memory. Nine pecking keys, arranged as a three-by-three matrix, served as the spatial cues. Trials began with a brief "ready" stimulus (dimming of the houselight). Then a randomly chosen key was lit briefly as a sample. After a short delay the sample key was lit again along with one of the other eight keys. A peck at the key that had served as the sample produced grain reinforcement, where as a peck to the other key produced only the intertrial interval. After delayed matching of key location was learned, the effects of sample and delay duration, number of keys illuminated as sample and comparisons, and organization of three-key samples were studied. Matching accuracy decreased as sample duration decreased, delay increased, the number of locations serving as samples increased, the number and proximity of comparisons increased, and when the three-key samples were "discontinuous" rather than "lines".     

A search for symmetry in the conditional discriminations of rhesus monkeys, baboons, and children.

Procedures for generating arbitrary matching-to-sample performances may generate only conditional discriminations. Rational grounds for this distinction are proposed, based on the properties that any equivalence relation must possess. Empirical tests are described for determining whether subjects trained on conditional discriminations are also engaged in true matching to sample. A series of studies than leads to the conclusion that proof of true matching to sample by monkeys, pigeons, or baboons is yet to be provided. Whether the absence of such proof reflects experiential factors or species-defined limitations is not presently clear.     

Changeover ratio effects on concurrent variable-interval performance

Rats' bar-pressing was maintained by concurrent variable-interval schedules of reinforcement. A fixed-ratio of pulls on a chain (the changeover ratio) was required for switching between schedules. The first experiment employed equal variable-interval schedules and symmetrical changeover ratios. Increasing these ratios resulted in a decrease in the rate of switching between schedules and an increase in local response rate. In the second experiment, a range of asymmetrical changeover ratios was used with equal variable-interval schedules, and a preference was found for the schedule associated with the larger switching-into ratio. Both the distributions of responses and time between the two schedules deviated from those expected on the basis of obtained reinforcers. In the third experiment, the switching-out-of ratio was dependent on the amount of time spent in a variable-interval 2-minute schedule; a constant ratio permitted switching out of the alternative variable-interval 1-minute schedule. A strong preference was shown for the variable-interval 2-minute schedule. The fourth experiment used equal variable-interval schedules; one changeover ratio was varied while the second remained constant. The results failed to show systematic differences in local response rates immediately after a changeover.     

The effect of punishment on free-operant choice behavior in humans

During Phase I, three female human subjects pressed a button for monetary reinforcement in five variable-interval schedules specifying different frequencies of reinforcement. On alternate days, responding was also punished (by subtracting money) according to a variable-ratio 34 schedule. In the absence of punishment, response rates conformed to Herrnstein's equation for single variable-interval schedules. Punishment suppressed responding at all frequencies of reinforcement. This was reflected in a change in the values of both constants in Herrnstein's equation: the value of the theoretical maximum response-rate parameter was reduced, and the parameter describing the reinforcement frequency corresponding to the half-maximal response rate was elevated. During Phase II, the same five schedules (A) were in operation (without punishment), but in addition, a concurrent variable-interval schedule (B) of standard reinforcement frequency was introduced. On alternate days, responding in Component B was punished according to a variable-ratio 34 schedule. In the absence of punishment, absolute response rates conformed to equations proposed by Herrnstein to describe performance in concurrent schedules; the ratios of the response rates in the two components and the ratios of the times spent in the two components conformed to the Matching Law. When responding in Component B was punished, response rates in Component B were reduced and those in Component A were elevated, these changes being reflected in distortions of the matching relationship.     

Psychophysics of remembering

We present a new model of remembering in the context of conditional discrimination. For procedures such as delayed matching to sample, the effect of the sample stimuli at the time of remembering is represented by a pair of Thurstonian (normal) distributions of effective stimulus values. The critical assumption of the model is that, based on prior experience, each effective stimulus value is associated with a ratio of reinforcers obtained for previous correct choices of the comparison stimuli. That ratio determines the choice that is made on the basis of the matching law. The standard deviations of the distributions are assumed to increase with increasing retention-interval duration, and the distance between their means is assumed to be a function of other factors that influence overall difficulty of the discrimination. It is a behavioral model in that choice is determined by its reinforcement history. The model predicts that the biasing effects of the reinforcer differential increase with decreasing discriminability and with increasing retention-interval duration. Data from several conditions using a delayed matching-to-sample procedure with pigeons support the predictions.     

The Matching Law And Amount-dependent Exponential Discounting As Accounts Of Self-control Choice

Studies with humans have found evidence for amount-dependent temporal discounting, that is, that the sensitivity of choice to reinforcer delay varies inversely with reinforcer magnitude. To test whether similar results could be obtained with nonhumans, pigeons were trained on a two-component concurrent-chains procedure in which the durations of food reinforcement in the terminal links were equal within components but unequal between components. Terminal-link schedules were varied over four conditions to allow separate estimates of sensitivity to delay to be obtained for the large and small reinforcer-magnitude components. Although sensitivity to delay was greater in the small-magnitude component for all subjects, the effect was quite small. The difference in sensitivity was generally less than one standard error, and t tests on parameter differences failed to reach significance. Several models for temporal discounting, including an amount-dependent exponential function, were fitted to the data from the first four conditions. The resulting parameter estimates were used to make predictions for a self-control condition in which one terminal link arranged a smaller, less delayed reinforcer and the other arranged a larger, more delayed reinforcer. For all models, predictions were considerably more accurate when sensitivity to delay was the same regardless of reinforcer magnitude. The results support the independence of delay and magnitude as required by a version of the matching law, and provide strong evidence against amount-dependent exponential discounting as an account of self-control choice. A new two-parameter discounting function, consistent with the matching law, is proposed that has wide empirical generality for both human and nonhuman data.     

Increasing and signaling background reinforcement: effect on the foreground response-reinforcer relation.

Herrnstein's (1970) hyperbolic matching equation describes the relationship between response rate and reinforcement rate. It has two estimated parameters, k and Re. According to one interpretation, k measures motor performance and Re measures the efficacy of the reinforcer maintaining responding relative to background sources of reinforcement. Experiment 1 tested this interpretation of the Re parameter by observing the effect of adding and removing an additional source of reinforcement to the context. Using a within-session procedure, estimates of Re were obtained from the response-reinforcer relation over a series of seven variable-interval schedules. A second, concurrently available variable-interval schedule of reinforcement was added and then removed from the context. Results showed that when the alternative was added to the context, the value of Re increased by 107 reinforcers per hour; this approximated the 91 reinforcers per hour obtained from this schedule. Experiment 2 investigated the effects of signaling background reinforcement on k and Re. The signal decreased Re, but did not have a systematic effect on k. In general, the results supported Herrnstein's interpretation that in settings with one experimenter-controlled reinforcement source, Re indexes the strength of the reinforcer maintaining responding relative to uncontrolled background sources of reinforcement.     

An investigation of the differential-outcomes effect within sessions

The differential-outcomes effect is manifest as more accurate performance of a delayed conditional discrimination when alternative choice responses are followed by different reinforcers than when they are followed by the same reinforcer. In Experiment 1, a differential-outcomes effect was demonstrated within sessions by signaling the duration of food access for correct responses with stimuli appearing in conjunction with the sample stimuli. The delayed matching-to-sample performance of 5 pigeons was more accurate when green choice responses (matching a green sample) were followed by 3.5-s food access and red choice responses (matching a red sample) were followed by 0.5-s food access (different-outcome trials) than when the correct choice responses were both followed by 1.5-s reinforcers (same-outcome trials). In Experiment 2, the acquisition of this differential-outcomes effect was characterized by a progressive decrease in rate of forgetting on different-outcome trials and no change in rate of forgetting on same-outcome trials. In addition, accuracy at the shortest delay intervals for both different-outcome and same-outcome trials increased over acquisition, but to a greater extent for different-outcome trials. These data suggest that both memorial and attentional (time-dependent and time-independent) factors contribute to the differential-outcomes effect.     

Transfer of relational stimulus control in conditional discriminations.

Four adults were trained, using instructions and a matching-to-sample procedure, to select Stimulus B1 in the presence of Stimulus A1, B2 in the presence of A2, and B3 in the presence of A3 (the AB relations). Analogous PQ relations were trained. Afterwards, one stimulus in Set A and another stimulus in Set B appeared together as a sample, and novel Stimuli X1 and X2 were the comparisons. Responses to X1 were reinforced if the two stimuli in the sample had been related in the previous training (e.g., A1 and B1), and responses to X2 were reinforced if the two samples had not been related (e.g., A1 and B2). These were the ABX relations. In a test in which a stimulus of Set P and another of Set Q were the samples and X1 and X2 were the comparisons, 2 subjects selected X1 when the samples were P1 and Q1, P2 and Q2, and P3 and Q3, and selected X2 in the presence of the other six sample combinations (P1Q2, P1Q3, P2Q1, P2Q3, P3Q1, and P3Q2). Another subject showed the same responding after additional training. In the second experiment, 3 adults and an 11-year-old child were trained on AB, PQ, and ABX relations, and they showed the symmetrical relations BA and QP upon testing. Then all 4 of these subjects responded accurately to the PQX test. Results of Experiments 1 and 2 showed novel, consistent comparison selection based on the previously established relation between the two stimuli in the sample. In a third experiment, 3 of the subjects who had shown PQX relations were trained on EFX relations, with pairs of E and F stimuli as samples and X stimuli as comparisons. When the EF relations were tested, all 3 subjects consistently selected F1 in the presence of E1, F2 in the presence of E2, and F3 in the presence of E3 from the first trial. The results of Experiment 3 showed novel stimulus relations after training with a more complex conditional discrimination format.