A MARKOV MODEL DESCRIPTION OF CHANGEOVER PROBABILITIES ON CONCURRENT VARIABLE‐INTERVAL SCHEDULES<sup>1</sup>

Heyman, Gene M.

doi:10.1901/jeab.1979.31-41

Cited by 125 publications

(141 citation statements)

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“…This trend was more likely to occur in the schedule providing the higher relative reinforcement rate. Our findings stand in contradiction to earlier work employing the same dependent measure (Heyman, 1979;Nevin, 1969;Silberberg et ai., 1978).…”

Section: Discussioncontrasting

confidence: 99%

“…The molecular position anticipates an increase in this probability, whereas the molar position predicts that it should remain largely invariant. The molar expectation has consistently been supported (Heyman, 1979;Nevin, 1969;Silberberg, Hamilton, Ziriax, & Casey, 1978).…”

mentioning

confidence: 84%

“…It is possible that one or both affected the outcome. It is worth noting, however, that Heyman (1979) used a procedure similar to our Condition 1. He employed an FR 1 CO requirement and, under one condition, a relative reinforcement rate of .75 .…”

Section: Choice and Conditional Probability 97mentioning

confidence: 99%

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Choice and the conditional probability of alternation: Some new data

Fetterman

Pliskoff

1981

Bull. Psychon. Soc.

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Three pigeons were exposed to two independent concurrent variable-interval schedules of reinforcement, with a changeover key procedure. Relative reinforcement rate and the fixed-ratio changeover requirement were varied. The effects of these manipulations were assessed with respect to the conditional probability of alternation as a function of successive responses on the same schedule. Previous experiments employing this measure have found essentially unchanging probabilities of alternation. However, we found the probability of alternation to be an increasing function of successive choices of the same schedule, especially with the schedule providing the higher relative reinforcement rate. These findings were discussed with respect to the procedural variables we employed.

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Section: Discussioncontrasting

confidence: 99%

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Choice and the conditional probability of alternation: Some new data

Fetterman

Pliskoff

1981

Bull. Psychon. Soc.

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“…Suppose now that in a schedule with stable pattern RLLL ... , a pigeon can remember only its last response but follows the rule "If the last peck was on the right, then peck left; if the last peck was on the left, then with probability 1/2 peck right, and with probability 1/2 peck left" (e.g., Heyman, 1979). On average, this bird will emit one right peck followed by three left pecks, the stable pattern of the schedule.…”

Section: Duke University Durham North Carolinamentioning

confidence: 99%

Polymorphic response patterns under frequency-dependent selection

Machado

1994

Animal Learning & Behavior

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In a discrete-trials procedure, a frequency-dependent schedule shaped left-right choice proportion toward various equilibrium values between 0 and 1. At issue was (1) whether pigeons match when the overall reinforcement probabilities for two responses depend inversely on their recent frequency, and (2)how pigeons meet the schedule constraint in terms of local responding. That is, do they respond quasi-randomly (Bernoulli mode), or do they learn the stable pattern of the schedule (stable-pattern mode)? Molar choice behavior always tracked the equilibrium solution ofthe schedule, but the molecular response patterns varied substantially. Markov chains applied to the data revealed that responding was generally intermediate between the memoryless Bernoulli mode, and the perfect memory stable-pattern mode. The polymorphism of molecular patterns, despite molar regularities in behavior, suggests that (1) in order to engender the Bernoulli or stable-pattern modes, the reinforcement rule must strongly discourage competing response patterns (e.g., perseveration), and (2) under frequency-dependent schedules, molar matching is apparently not the outcome of momentary maximizing.Laboratory studies have shownthat frequency-dependent selection, the differential reinforcement of infrequent responses, sometimes engenders high degrees of behavioral variability. For example, when Page and Neuringer (1985) rewarded pigeons for generating sequences of eight left or right pecks that differed from the sequences generated on the last 50 trials, they obtained highly variable, random-like behavior. That is, the birds not only pecked each key equally often, but also showed few or no sequential dependencies between consecutive responses (see also Hest, Haaren, & Van De Poll, 1989;Morgan & Neuringer, 1990;Machado, 1989Machado, , 1992Morris, 1987Morris, , 1989Neuringer, 1991Neuringer, , 1992. However, frequencydependent selection may also engender stereotypical behavior. In a previous study (Machado, 1992), a frequencydependent schedule differentially reinforced the momentarily least likely of two responses-the more a pigeon preferred the right key, the less food it received from that key and the more food it received from the left key. Similar contingencies operated when preference shifted to the left; the probability of food for left (L) and right (R) pecks was equal only at indifference. Although the pigeons pecked each key on 50% of the trials, they did so by alternating rather than responding randomly.The preceding results illustrate two points. First, pigeons can track the overall probabilities of reinforcement for each of two responses when these probabilities I thank John Staddon and the other L.A.B. group members for their comments on earlier versions of the manuscript. The research was supported by grants to Duke University from NSF and NIMH (John Staddon, principal investigator). Correspondence concerning this article may be sent to A. Machado,

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“…Requests for reprints may be sent to D. A. Stubbs, Department of Psychology, University of Maine, Orono, Maine 04469. whether the matching relation is fundamental or whether it is the result of some more fundamental process. Many subsequent alterations of, additions to, and explanations of the matching relation have been proposed (e.g., for recent discussions of different views of choice, see Allison, 1981;Baum, 1981;Herrnstein & Vaughan, 1980;Heyman, 1979;Hinson & Staddon, 1983;Houston & McNamara, 1981;Nevin, 1982;Rachlin, 1978;Rachlin, Battalio, Kagel, & Green, 1981;Shimp, 1979).…”

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Choice With a Fixed Requirement for Food, and the Generality of the Matching Relation

Stubbs

Dreyfus

Fetterman

et al. 1986

J Exper Analysis Behavior

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Pigeons were trained on choice procedures in which responses on each of two keys were reinforced probabilistically, but only after a schedule requirement had been met. Under one arrangement, a fixed-interval choice procedure was used in which responses were not reinforced until the interval was over; then a response on one key would be reinforced, with the effective key changing irregularly from interval to interval. Under a second, fixed-ratio choice procedure, responses on either key counted towards completion of the ratio and then, once the ratio had been completed, a response on the probabilistically selected key would produce food. In one experiment, the schedule requirements were varied for both fixed-interval and fixed-ratio schedules. In the second experiment, relative reinforcement rate was varied. And in a third experiment, the duration of an intertrial interval separating choices was varied. The results for 11 pigeons across all three experiments indicate that there were often large deviations between relative response rates and relative reinforcement rates. Overall performance measures were characterized by a great deal of variability across conditions. More detailed measures of choice across the schedule requirement were also quite variable across conditions. In spite of this variability, performance was consistent across conditions in its efficiency of producing food. The absence of matching of behavior allocation to reinforcement rate indicates an important difference between the present procedures and other choice procedures; that difference raises questions about the specific conditions that lead to matching as an outcome.Key words: choice, concurrent schedules, fixed ratio, fixed interval, matching, maximizing, key peck, pigeons Choice is one of the most persistently studied topics in the experimental analysis of behavior. Early research in this area was diverse in both method and orientation, but Herrnstein's (1961) now classic finding-that relative response outputs of pigeons on concurrent variable-interval variable-interval (VI VI) schedules match relative reinforcement rates on those schedules-began a trend of convergence on a limited range of procedures for studying choice. To a great extent, concurrent VI VI schedules became the reference procedure, and the matching relation became the frame of reference for discussion. The matching relation has provided a framework for considering choice and has proven quite general in its applications, but in recent years questions have been raised about many aspects of this phenomenon. The most basic of these questions have attempted to determine

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A MARKOV MODEL DESCRIPTION OF CHANGEOVER PROBABILITIES ON CONCURRENT VARIABLE‐INTERVAL SCHEDULES¹

Cited by 125 publications

References 21 publications

Choice and the conditional probability of alternation: Some new data

Choice and the conditional probability of alternation: Some new data

Polymorphic response patterns under frequency-dependent selection

Choice With a Fixed Requirement for Food, and the Generality of the Matching Relation

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A MARKOV MODEL DESCRIPTION OF CHANGEOVER PROBABILITIES ON CONCURRENT VARIABLE‐INTERVAL SCHEDULES1

Cited by 125 publications

References 21 publications

Choice and the conditional probability of alternation: Some new data

Choice and the conditional probability of alternation: Some new data

Polymorphic response patterns under frequency-dependent selection

Choice With a Fixed Requirement for Food, and the Generality of the Matching Relation

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A MARKOV MODEL DESCRIPTION OF CHANGEOVER PROBABILITIES ON CONCURRENT VARIABLE‐INTERVAL SCHEDULES¹