Data on choice generally conform closely to an equation of the form: log(B%/B2) = a log(r1/r2) + log k, where B, and B2 are the frequencies of responding at Alternatives 1 and 2, r, and r2 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,/B2= r,/r2. 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.It is common in studies of choice to consider the proportion of responses at an alternative as a function of the proportion of reinforcement obtained from the alternative (e.g.,

When pigeons' standing on one or the other side of a chamber was reinforced on two concurrent variable-interval schedules, the ratio of time spent on the left to time spent on the right was directly proportional to the ratio of reinforcements produced by standing on the left to reinforcements produced by standing on the right. The constant of proportionality was less than unity for all pigeons, indicating a bias toward the right side of the chamber. The biased matching relation obtained here is comparable to the matching relation obtained with concurrent reinforcement of key pecks. The present results, together with related research, suggest that the ratio of time spent in two activities equals the ratio of the "values" of the activities. The value of an activity is the product of several parameters, such as rate and amount of reinforcement, contingent on that activity.

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.

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.

Almost all of 103 sets of data from 23 different studies of choice conformed closely to the equation: log (B1/B2) = a log (r1/r2) + log b, where B, and B2 are either numbers of responses or times spent at Alternatives 1 and 2, r, and r2 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 B1 and B2 measured as numbers of responses, a tended to fall short of 1.0 (undermatching). For B1 and B2 measured as times, a fell to both sides of 1.0, with the largest mode at about 1.O. 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.Key words: matching relation, undermatching, overmatching, choice, conc VIVIIn experiments with concurrent variableinterval schedules, when the ratio of responding or time spent at two alternatives (Bl/B2) is graphed in logarithmic coordinates as a function of the ratio of reinforcement (r1/r2) obtained from the two alternatives, the data points usually conform to a straight line: B1 = a log r + log b(1) log a log Exponentiating both sides of this equation produces a power function of the type familiar in psychophysics (Stevens, 1957(Stevens, , 1975: