MULTIPLE SCHEDULES: EFFECTS OF THE DISTRIBUTION OF REINFORCEMENTS BETWEEN COMPONENTS ON THE DISTRIBUTION OF RESPONSES BETWEEN COMPONENTS¹

Abstract

Two pigeons were trained to peck a key under several multiple variable-interval variableinterval schedules of reinforcement; different numbers of reinforcements were scheduled in two components of equal duration which were correlated with red and green illumination of the response key respectively. The results showed: (1) that the total number of responses in a scssion was proportional to the one-sixth power of the total number of reinforcements delivered in that session; and (2) that the ratio of responses between the two components was equal to the one-third power of the ratio of reinforcements between them. This latter exponent may be regarded as reflecting the sensitivity of the distribution of responses between the components to the distribution of reinforcements. It was suggested that the effects of a number of complex schedules of reinforcement could be summarized by different values of this exponent.When two variable-interval (VI) schedules of reinforcement are combined, responding maintained by each is partly determined by reinforcements delivered under the other schedule. This interaction occurs both under concurrent schedules, in which two or more schedules operate simultaneously for responses on dlifferent keys, and under multiple schedules, in which two or more schedules operate successively for responses on a single key. This similarity between concurrent and multiple schedules, however, does not extend to the way in which responses are distributed between each of the component schedules which constitute the total schedule. Under concurrent VI VI schedules, pigeons match the distribution of responses between keys to the distribution of reinforcements between keys (Herrnstein, Catania, 1963). Under multiple VI VI schedules these distributions are not matched (Reynolds, 1963).Catania (1963) has written a series of equations which gives a precise quantitative de-'The data presented are from Exp.

Choice responding following multiple schedule training

“…Starting nearest the lower left corner, the points represent the following relative response and reinforcement rates: VI 60 sec/(VI 60 sec + VI 15 sec); VI 60 sec/(VI60 sec + VI 120 sec); VIIS sec/ (VIIS sec + VI 120 sec). Schedule relative response rates showed the expected tendency toward undermatching (Lander & Irwin, 1968;Reynolds, 1963), a result consistent with the reverse-S-shaped curve expected from Herrnstein's (1970) Average choice probe relative response as a function of training relative reinforcement rate is presented in Figure 2. The order of the points corresponds to that in Figure 1.…”

Response-cost punishment with pigeons: Further evidence of response suppression via token loss

“…in the unaltered (no-loss) components. Such interactions between responding across components are common in multiple schedules (e.g., Catania, 1961;Lander & Irwin, 1968;Reynolds, 1961), including those involving punishment (Azrin & Holz, 1966). Prior research has shown, for example, that unpunished responding increases as a function of punishment contingencies arranged in a second component (Brethower & Reynolds, 1962;Caplan & Graefe, 1980;Crosbie, Williams, Lattal, Anderson, & Brown, 1997;Lattal & Griffin, 1972), a phenomenon termed punishment contrast.…”

Operant Conditioning

“…As noted above, even responding on simple fixed-T response-initiated delay (RID) schedules violates maximization. Matching is also highly overdetermined, in the sense that almost any learning rule consistent with the law of effect-an increase in reinforcement probability causes an increase in response probability-will yield either simple matching (Equation 5) or its power-law generalization (Baum 1974, Hinson & Staddon 1983, Lander & Irwin 1968, Staddon 1968. Matching by itself therefore reveals relatively little about the dynamic processes operating in the responding subject (but see Davison & Baum 2000).…”