Biomedical subjects
Publications and source records attributed to W M Baum.
The molar view of behavior arose in response to the demonstrated inadequacy of explanations based on contiguity. Although Dinsmoor's (2001) modifications to two-factor theory render it irrefutable, a more basic criticism arises when we see that the molar and molecular views differ paradigmatically. The molar view has proven more productive.
Group choice refers to the distribution of group members between two choice alternatives over time. The ideal free distribution (IFD), an optimal foraging model from behavioral ecology, predicts that the ratio of foragers at two resource sites should equal the ratio of obtained resources, a prediction that is formally analogous to the matching law of individual choice, except that group choice is a social phenomenon. Two experiments investigated the usefulness of IFD analyses of human group choice and individual-based explanations that might account for the group-level events. Instead of nonhuman animals foraging at two sites for resources, a group of humans chose blue and red cards to receive points that could earn cash prizes. The groups chose blue and red cards in ratios in positive relation to the ratios of points associated with the cards. When group choice ratios and point ratios were plotted on logarithmic coordinates and fitted with regression lines, the slopes (i.e., sensitivity measures) approached 1.0 but tended to fall short of it (i.e., undermatching), with little bias and little unaccounted for variance. These experiments demonstrate that an IFD analysis of group choice is possible and useful, and suggest that group choice may be explained by the individual members' tendency to optimize reinforcement.
Six pigeons were trained in sessions composed of seven components, each arranged with a different concurrent-schedule reinforcer ratio. These components occurred in an irregular order with equal frequency, separated by 10-s blackouts. No signals differentiated the different reinforcer ratios. Conditions lasted 50 sessions, and data were collected from the last 35 sessions. In Part 1, the arranged overall reinforcer rate was 2.22 reinforcers per minute. Over conditions, number of reinforcers per component was varied from 4 to 12. In Part 2, the overall reinforcer rate was six per minute, with both 4 and 12 reinforcers per component. Within components, log response-allocation ratios adjusted rapidly as more reinforcers were delivered in the component, and the slope of the choice relation (sensitivity) leveled off at moderately high levels after only about eight reinforcers. When the carryover from previous components was taken into account, the number of reinforcers in the components appeared to have no systematic effect on the speed at which behavior changed after a component started. Consequently, sensitivity values at each reinforcer delivery were superimposable. However, adjustment to changing reinforcer ratios was faster, and reached greater sensitivity values, when overall reinforcer rate was higher. Within a component, each successive reinforcer from the same alternative ("confirming") had a smaller effect than the one before, but single reinforcers from the other alternative ("disconfirming") always had a large effect. Choice in the prior component carried over into the next component, and its effects could be discerned even after five or six reinforcement and nonreinforcement is suggested.
TWO DIFFERENCES BETWEEN RATIO AND INTERVAL PERFORMANCE ARE WELL KNOWN: (a) Higher rates occur on ratio schedules, and (b) ratio schedules are unable to maintain responding at low rates of reinforcement (ratio "strain"). A third phenomenon, a downturn in response rate at the highest rates of reinforcement, is well documented for ratio schedules and is predicted for interval schedules. Pigeons were exposed to multiple variable-ratio variable-interval schedules in which the intervals generated in the variable-ratio component were programmed in the variable-interval component, thereby "yoking" or approximately matching reinforcement in the two components. The full range of ratio performances was studied, from strained to continuous reinforcement. In addition to the expected phenomena, a new phenomenon was observed: an upturn in variable-interval response rate in the midrange of rates of reinforcement that brought response rates on the two schedules to equality before the downturn at the highest rates of reinforcement. When the average response rate was corrected by eliminating pausing after reinforcement, the downturn in response rate vanished, leaving a strictly monotonic performance curve. This apparent functional independence of the postreinforcement pause and the qualitative shift in response implied by the upturn in variable-interval response rate suggest that theoretical accounts will require thinking of behavior as partitioned among at least three categories, and probably four: postreinforcement activity, other unprogrammed activity, ratio-typical operant behavior, and interval-typical operant behavior.
Finding a theoretically sound feedback function for variable-interval schedules remains an important unsolved problem. It is important because interval schedules model a significant feature of the world: the dependence of reinforcement on factors beyond the organism's control. The problem remains unsolved because no feedback function yet proposed satisfies all the theoretical and empirical requirements. Previous suggestions that succeed in fitting data fail theoretically because they violate a newly recognized theoretical requirement: The slope of the function must approach or equal 1.0 at the origin. A function is presented that satisfies all requirements but lacks any theoretical justification. This function and two suggested by Prelec and Herrnstein (1978) and Nevin and Baum (1980) are evaluated against several sets of data. All three fitted the data well. The success of the two theoretically incorrect functions raises an empirical puzzle: Low rates of reinforcement are coupled with response rates that seem anomalously high. It remains to be discovered what this reflects about the temporal patterning of operant behavior at low reinforcement rates. A theoretically and empirically correct function derived from basic assumptions about operant behavior also remains to be discovered.
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Since foraging in nature can be viewed as instrumental behavior, choice between sources of food, known as "patches," can be viewed as choice between instrumental response alternatives. Whereas the travel required to change alternatives deters changeover in nature, the changeover delay (COD) usually deters changeover in the laboratory. In this experiment, pigeons were exposed to laboratory choice situations, concurrent variable-interval schedules, that were standard except for the introduction of a travel requirement for changeover. As the travel requirement increased, rate of changeover decreased and preference for a favored alternative strengthened. When the travel requirement was small, the relations between choice and relative reinforcement revealed the usual tendencies toward matching and undermatching. When the travel requirement was large, strong overmatching occurred. These results, together with those from experiments in which changeover was deterred by punishment or a fixed-ratio requirement, deviate from the matching law, even when a correction is made for cost of changeover. If one accepted an argument that the COD is analogous to travel, the results suggest that the norm in choice relations would be overmatching. This overmatching, however, might only be the sign of an underlying strategy approximating optimization.
The interaction between instrumental behavior and environment can be conveniently described at a molar level as a feedback system. Two different possible theories, the matching law and optimization, differ primarily in the reference criterion they suggest for the system. Both offer accounts of most of the known phenomena of performance on concurrent and single variable-interval and variable-ratio schedules. The matching law appears stronger in describing concurrent performances, whereas optimization appears stronger in describing performance on single schedules.
On a given variable-interval schedule, the average obtained rate of reinforcement depends on the average rate of responding. An expression for this feedback effect is derived from the assumptions that free-operant responding occurs in bursts with a constant tempo, alternating with periods of engagement in other activities; that the durations of bursts and other activities are exponentially distributed; and that the rates of initiating and terminating bursts are inversely related. The expression provides a satisfactory account of the data of three experiments.
Almost all of 103 sets of data from 23 different studies of choice conformed closely to the equation: log (B(1)/B(2)) = a log (r(1)/r(2)) + log b, where B(1) and B(2) are either numbers of responses or times spent at Alternatives 1 and 2, r(1) and r(2) are the rates of reinforcement obtained from Alternatives 1 and 2, and a and b are empirical constants. Although the matching relation requires the slope a to equal 1.0, the best-fitting values of a frequently deviated from this. For B(1) and B(2) measured as numbers of responses, a tended to fall short of 1.0 (undermatching). For B(1) and B(2) measured as times, a fell to both sides of 1.0, with the largest mode at about 1.0. Those experiments that produced values of a for both responses and time revealed only a rough correspondence between the two values; a was often noticeably larger for time. Statistical techniques for assessing significance of a deviation of a from 1.0 suggested that values of a between .90 and 1.11 can be considered good approximations to matching. Of the two experimenters who contributed the most data, one generally found undermatching, while the other generally found matching. The difference in results probably arises from differences in procedure. The procedural variations that lead to undermatching appear to be those that produce (a) asymmetrical pausing that favors the poorer alternative; (b) systematic temporal variation in preference that favors the poorer alternative; and (c) patterns of responding that involve changing over between alternatives or brief bouts at the alternatives.
Pigeons' standing on a platform produced food reinforcement according to two-component multiple schedules in which either both components consisted of the same variable-interval schedule or one of these was replaced with a component without reinforcement (extinction). The components of the multiple schedule alternated every 30 sec, and were signalled by changes in the color of diffuse overhead illumination. Changing the schedule of one of the components to extinction increased the percentage of time spent on the platform during the unchanged component (behavioral contrast). This result casts doubt on accounts that attribute behavioral contrast to variations in the rate of noninstrumental elicited responses.
Rats' pressing on two levers was reinforced according to two independent variable-interval schedules that were varied during the experiment. Since the levers were connected directly to the programming equipment, bypassing the standard pulseformers, reinforcement could occur while a lever was held down. Although the time a lever was pressed might, therefore, have varied independently of number of presses, these two measures covaried substantially, because the average duration of the presses remained roughly constant. This rough invariance may have resulted from the rats' tendency to make bursts of brief presses (i.e., to jiggle the levers), even though the contingencies encouraged holding. When duration did vary, presses on the two levers tended to vary together. As a result, relative time spent pressing corresponded closely to relative number of presses. Both of these measures conformed well to the matching law. Absolute behavioral frequency at a lever, measured either way, varied directly with proportion of reinforcement for that lever, in accordance with the generalized version of the matching law. Number of presses seemed, on balance, to be a slightly more reliable measure than pressing time. The substantial interchangeability may prove more significant than the slight disparity, however, because it supports the notion that all behavior can be measured on a common scale of time.
Three human subjects detected unpredictable signals by pressing either of two telegraph keys. The relative frequencies with which detections occurred for the two alternatives were varied. The procedure included a changeover delay and response cost for letting go of a key. All subjects matched the relative time spent holding each key to the relative number of detections for that key, in conformity with the matching law. One subject's performance, which at first deviated from the relation, came into conformity with it when response cost was increased. Another subject's performance approximated matching more closely when the changeover delay was increased. The results confirm and extend the notions that choice consists in time allocation and that all behavior can be measured on the common scale of time.
DATA ON CHOICE GENERALLY CONFORM CLOSELY TO AN EQUATION OF THE FORM: log(B(1)/B(2))=a log(r(1)/r(2)+log k, where B(1) and B(2) are the frequencies of responding at Alternatives 1 and 2, r(1) and r(2) are the obtained reinforcement from Alternatives 1 and 2, and a and k are empirical constants. When a and k equal one, this equation is equivalent to the matching relation: B(1)/B(2)=r(1)/r(2). Two types of deviation from matching can occur with this formulation: a and k not equal to one. In some experiments, a systematically falls short of one. This deviation is undermatching. The reasons for undermatching are obscure at present. Some evidence suggests, however, that factors favoring discrimination also favor matching. Matching (a=1) may represent the norm in choice when discrimination is maximal. When k differs from one, its magnitude indicates the degree of bias in choice. The generalized matching law predicts that bias should take this form (adding a constant proportion of responding to the favored alternative). Data from a variety of experiments indicate that it generally does.
Pigeons' pecks at two white response keys (initial-link situation) occasionally turned both keys red (terminal-link situation). When the two keys were red, pecks occasionally produced food, after which the keys were again white. In both situations, a changeover delay prevented the response-produced outcome from immediately following a change of responding from either key to the other. In the initial-link situation, the ratio of pecks at the keys closely paralleled the ratio of transitions into the terminal-link situation produced by the pecks, conforming to the well-known matching relation. In the terminal-link situation, the peck ratios deviated from the matching relation toward indifference. Overall response rate and rate of changeover were generally higher in the terminal-link situation than in the initial-link situation. The finding of matching in the initial-link situation supports a definition of reinforcement as situation transition. The differences in performance between the two situations, viewed in the light of other recent findings, suggest that the effects of a changeover delay depend on the overall reinforcing value of the choice alternatives.
It is commonly understood that the interactions between an organism and its environment constitute a feedback system. This implies that instrumental behavior should be viewed as a continuous exchange between the organism and the environment. It follows that orderly relations between behavior and environment should emerge at the level of aggregate flow in time, rather than momentary events. These notions require a simple, but fundamental, change in the law of effect: from a law based on contiguity of events to a law based on correlation between events. Much recent research and argument favors such a change. If the correlation-based law of effect is accepted, it favors measures and units of analysis that transcend momentary events, extending through time. One can measure all consequences on a common scale, called value. One can define a unit of analysis called the behavioral situation, which circumscribes a set of values. These concepts allow redefinition of reinforcement and punishment, and clarification of their relation to discriminative stimuli.
Pigeons' standing on one or the other side of a chamber was reinforced with timeout from electric shock on two concurrent variable-interval schedules. For two pigeons, the ratio of time spent on the left to time spent on the right approximately matched the ratio of timeouts obtained on the left to timeouts obtained on the right. The data of two other birds deviated from this relation, although in opposite directions. Overall, the results suggest that reduction in rate of electric shock plays a role in behavioral allocation analogous to that played by rate of positive reinforcement. It appears possible to describe aversive control and positive control within the same conceptual framework-that provided by the matching relation.
In a chamber with a single response key, pigeon's key pecks were reinforced with food according to a variable-interval schedule. In addition, extra reinforcements occurred concurrently according to an independent schedule. In one condition, availability of the extra reinforcements was signalled by a change in key color from white to red. The extra reinforcements occurred after a peck on the red key. In a second condition, the extra reinforcements were unsignalled and occurred only after a 2-sec pause in pecking for one group of subjects and were unsignalled and occurred freely as scheduled for another group of subjects. In the first two conditions, duration of reinforcement was varied. A third condition duplicated the second but varied rate rather than duration of reinforcement. The rate of pecking varied inversely with the amount of extra reinforcement per unit time according to the same function, regardless of the condition regulating occurrence of the extra reinforcements, and regardless of whether or not a 2-sec pause was required for their occurrence. The shape of this function was predicted by Herrnstein's (1970) matching law.