The symmetrical law of effect and the matching relation in choice behavior

In a concurrent-chains procedure, pigeons chose between outcomes that differed in the rate of response-independent delivery of food and electric shocks. The application of functional measurement techniques confirmed the matching relation—between choice and rate of reinforcement value—for two of three pigeons. Scale values of the outcomes were extracted for the two birds that conformed to matching, and the value of a single occurrence of shock per minute—in terms of negative food units—was estimated. A second experiment with concurrent chains provided a test of these parameter estimates. The close correspondence between predicted and obtained choice behavior found in Experiment II indicated that the estimates of outcome value were indeed reliable. Both experiments together support the contention that the effects on choice behavior of positive and aversive stimuli appear to be equal, though opposite in sign.     

Fixed-interval matching-to-sample: intermatching time and intermatching error runs

Four pigeons were trained on a matching-to-sample task in which reinforcers followed either the first matching response (fixed interval) or the fifth matching response (tandem fixed-interval fixed-ratio) that occurred 80 seconds or longer after the last reinforcement. Relative frequency distributions of the matching-to-sample responses that concluded intermatching times and runs of mismatches (intermatching error runs) were computed for the final matching responses directly followed by grain access and also for the three matching responses immediately preceding the final match. Comparison of these two distributions showed that the fixed-interval schedule arranged for the preferential reinforcement of matches concluding relatively extended intermatching times and runs of mismatches. Differences in matching accuracy and rate during the fixed interval, compared to the tandem fixed-interval fixed-ratio, suggested that reinforcers following matches concluding various intermatching times and runs of mismatches influenced the rate and accuracy of the last few matches before grain access, but did not control rate and accuracy throughout the entire fixed-interval period.     

Time allocation in concurrent schedules: the effect of signalled reinforcement

The responses of five pigeons were reinforced on concurrent variable-interval variable-interval reinforcement schedules in which changeover key responses changed the stimulus and reinforcement schedules associated with the food key. While the reinforcement availability in one component remained unchanged throughout the experiment, the reinforcement availability in the other component was, during several conditions, signalled by the onset of an additional discriminative stimulus. During unsignalled conditions, both the relative frequency of responding and the relative time spent in each component approximated the obtained relative reinforcement frequency in each component. The effect of signalling reinforcer availability in one component was to (1) reduce responding in the signalled component to near-zero levels, and (2) increase the relative time in the unsignalled component, without a corresponding increase in the obtained relative reinforcement frequency. The magnitude of the increase in relative time in the unsignalled component decreased as the overall frequency of reinforcement increased. This deviation in the matching relation between relative time and the obtained relative reinforcement frequency was eliminated if the overall reinforcement frequency was increased before the signal was introduced and then, without removing the signal, gradually reduced.     

Same/different concept learning in the pigeon: the effect of negative instances and prior adaptation to transfer stimuli

Pigeons were trained on a matching-to-sample or oddity-from-sample task with shapes (circle and plus). Half of each group was exposed to “negative instance” trials i.e., for matching birds, neither comparison key matched the sample, and for oddity birds both comparison keys matched the sample. When all birds were transferred to a new task involving colors (red and green), nonshifted birds (transferred from matching to matching, or oddity to oddity) performed significantly better than shifted birds (transferred from matching to oddity, or oddity to matching), but only if they had experienced negative instances of the training concept. When all birds were exposed to negative instances of the transfer task and then transferred to a new color task (yellow and blue), dramatic transfer effects were observed. The effect of pre-exposure to the yellow and blue colors, in order to reduce transfer-stimulus novelty, had a minor effect on transfer.     

The role of discriminative stimuli in concurrent performances

Key pecking in pigeons was examined under concurrent and parallel arrangements of two independent and simultaneously available variable-interval schedules. Pecks on the changeover key alternated the schedule of reinforcement for responses on the main key. Under concurrent schedules, discriminative stimuli were paired with the reinforcement schedule arranged in each component and changeover responses also alternated these stimuli. Under parallel schedules, changeover responses alternated the effective reinforcement schedule, but did not change the discriminative stimulus. On concurrent procedures, changeover response rate was inversely related to the difference in reinforcement rate between the two components, whereas on parallel schedules no consistent relationship was found. With both schedules, absolute response and reinforcement rates were positively related, although for a given set of reinforcement frequencies, rates were often higher on the concurrent schedules. On concurrent schedules, relative response rates and relative times were equal to relative reinforcement rates. On parallel schedules these ratios were positively related, but response and time ratios were much smaller than were obtained with comparable concurrent schedules. This inequality was most pronounced when absolute reinforcement frequencies were lowest.     

Response and time allocation in concurrent second-order schedules

Six pigeons were trained on two-key concurrent variable-interval schedules in which the required response was the completion of a fixed number of key pecks. When the required number of pecks was equal on the two keys, response- and time-allocation ratios under-matched obtained reinforcement rate ratios. A similar result was found when the required number of pecks was unequal, except that performance, measured in response terms, was biased to the shorter required number of pecks and was less sensitive to reinforcement-rate changes. No such differences were found in the data on time spent responding. When the variable-interval schedules were kept constant and the required numbers of pecks were systematically varied, response ratios changed inversely with the ratio of the required number of pecks, but time-allocation ratios varied directly with the same independent variable. Thus, on response measures, pigeons “prefer” the schedule with the smaller peck requirement, but on time measures they “prefer” the schedule with the larger peck requirement. This finding is inconsistent with a commonsense notion of choice, which sees response and time-allocation measures as equivalent.     

Quantitative studies of reinforcement relativity

Three experiments examined an application of the matching law to the area of reinforcement relativity. In Experiment I, rats ran in a wheel and drank a sucrose solution. Equations derived from the matching law made fairly accurate predictions of the amounts of time spent running and drinking when licks and wheel revolutions had to occur in fixed proportions. In Experiment II, rats were required to spend four times as much time drinking as running, but the absolute durations of the cycles of drinking and running were varied. Except for the shortest cycle size tested, durations were close to those predicted. Experiments III investigated a tendency for obtained durations of running and drinking to be slightly longer than predicted. Simply shortening the periods when these behaviors were available increased their values. It was concluded that the matching law equations provided reasonably accurate predictions in some experiments, but changes in motivation set the limits of such accuracy.     

THE EFFECT OF MODELLING ON DRINKING RATE

Three male college seniors were asked to drink beer at their normal rate in a simulated tavern setting. Each was paired with a confederate, also a male college senior, in an ABACA single subject design. In the baseline conditions, the confederate matched the drinking rate of the subject. Baseline and all subsequent conditions were continued in 1-hr sessions until a stable drinking rate was achieved. In Condition B, the confederate drank either one third more or one third less than the subject's baseline rate. In Condition C, the direction was reversed. All three subjects closely matched the confederate's drinking rate, whether high or low. All subjects reported they were unaware of the true purpose of the study.     

Preferences among stimulus matches in the pigeon

Three pigeons were trained to peck two to five illuminated response keys. A peck to any of the keys changed the stimulus on the key. When all keys showed the same stimulus (i.e., a stimulus match), an additional key was illuminated with white light. A peck on this key produced three-second access to grain, a three-second intertrial interval, and the next trial. For most sessions, no particular stimulus match was required. Although there were often several stimuli available, each bird preferred a particular stimulus match. With up to 12 stimuli available, birds matched a particular stimulus 60% to 100% of the time.     

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.