Two modern developments in matching theory

How psychological contract violation impacts turnover intentions of knowledge workers? The moderating effect of job embeddedness

When knowledge workers encounter psychological contract violations, they usually send out biased signals. Their job satisfaction decreases and their turnover intentions increase. However, in the increasingly competitive talent market, employees may not choose to leave when they encounter psychological contract violation. Based on the theoretical research results of the existing psychological contract violation, job satisfaction, turnover intention and job embeddedness, this paper analyzes the internal connections and deep relationships among the key elements by referring to the possible causes and results of the changes in the key elements. Survey technique was utilized while knowledge workers were selected as targeted respondents from specified provinces of China. A total of 392 valid questionnaires were selected by questionnaire survey. Statistical analysis was carried out by SPSS21 and AMOS23, and regression analysis was used to repeatedly verify the relationship between various elements. The results show that psychological contract violation positively predicts the turnover intention of knowledge workers, job satisfaction mediates the positive effect of psychological contract violation on turnover intention, and job embeddedness negatively regulates the positive effect of psychological contract violation on turnover intention. This study has theoretical and practical significance in enriching the theory and methods of organizational management, inspiring knowledge workers to stimulating their work potential, reducing employees' turnover intention, reducing the impact of resignation on the enterprise, and enhancing the enterprise's human resource management of knowledge workers.

Resurgence as Choice: Implications for promoting durable behavior change

Resurgence is an increase in a previously suppressed behavior resulting from a worsening in reinforcement conditions for current behavior. Resurgence is often observed following successful treatment of problem behavior with differential reinforcement when reinforcement for an alternative behavior is subsequently omitted or reduced. The efficacy of differential reinforcement has long been conceptualized in terms of quantitative models of choice between concurrent operants (i.e., the matching law). Here, we provide an overview of a novel quantitative model of resurgence called Resurgence as Choice (RaC), which suggests that resurgence results from these same basic choice processes. We review the failures of the only other quantitative model of resurgence (i.e., Behavioral Momentum Theory) and discuss its shortcomings with respect to the limited range of circumstances about which it makes predictions in applied settings. Finally, we describe how RaC overcomes these shortcomings and discuss implications of the model for promoting durable behavior change.

Decision-making in children in the Hungry Donkey Test: A behavioral analysis

This study analyzed choice behavior in the Hungry Donkey Task, with a focus on learning trajectories and the stability of preference, in 100 children of different ages (8-9, 10-11, 12-13, 14-15, and 16-17 years old). The results indicated that (a) learning occurred as the task progressed, (b) early adolescents performed poorly during the task, and (c) most of the participants did not reach the stability criterion during the task. The present study suggests that decision-making in children and adolescents varies with age, and that the inclusion of an operant-based approach (e.g., the use of stability criterion) may improve methods for evaluating decision-making in children.

Choosing to Vary and Repeat

Can animals choose to vary their behaviors or to repeat them, depending on the rewards they earn for behaving variably versus repetitively? To answer this question, pigeons were rewarded for four-response sequences made to left (L) and right (R) disks. A “varied” sequence differed from each of the previous three sequences, and a “repeated” sequence was the same as some one of the previous three. For example, if a pigeon had generated sequences LLLL. LLLR, and LLRR in that order, then an RRRR sequence in the next trial was defined as a variation, whereas LLLL was a repetition. Two experiments showed that frequencies of varied and repeated sequences depended on the frequencies with which they were reinforced, with a “matching” relationship accounting for the results. It was concluded that pigeons' choices to vary or repeat parallel their choices between simpler response alternatives, a result consistent with the hypothesis that behavioral variability is influenced by its consequences. This finding may help to explain the “voluntary” or “free” nature of operant behavior.

Choice in transition: Replication and extension to preschool children in a naturalistic setting

This study replicated previous basic research into the dynamics of choice and extended this analysis to children's behavior in a naturalistic setting. Two preschoolers with disabilities were observed interacting with their teachers at baseline and during an experimental analysis involving four pairs of concurrent variable-interval schedules of adult attention implemented by an experimenter. Each child was exposed to four experimental phases in which the relative reinforcer rates for on- and off-task behavior were 10:1, 1:1, 1:10, and reversed back to 10:1. The 10:1 phase was designed to mimic the same schedules and types of adult attention observed at baseline. We used the generalized matching equation to model steady-state behavior at the end of the transition phases and to evaluate changes in sensitivity at various points throughout the phases. Choice in transition was evaluated by plotting log behavior ratios by session, cumulated time on- and off-task and cumulated attention for on- and off-task behavior by session, and interreinforcer behavior ratios following different sequences of the first four reinforcer deliveries. The generalized matching equation accounted for a large proportion of variance in steady-state responding, sensitivity values increased steadily throughout the phases, patterns of choice in transition were similar to those reported in basic research, and interreinforcer preference generally shifted toward the just-reinforced alternative. These findings are consistent with previous basic research and support the generality of the dynamics of choice to children's on- and off-task behavior reinforced by adult attention.

Selection dynamics in joint matching to rate and magnitude of reinforcement

Virtual organisms animated by a selectionist theory of behavior dynamics worked on concurrent random interval schedules where both the rate and magnitude of reinforcement were varied. The selectionist theory consists of a set of simple rules of selection, recombination, and mutation that act on a population of potential behaviors by means of a genetic algorithm. An extension of the power function matching equation, which expresses behavior allocation as a joint function of exponentiated reinforcement rate and reinforcer magnitude ratios, was fitted to the virtual organisms' data, and over a range of moderate mutation rates was found to provide an excellent description of their behavior without residual trends. The mean exponents in this range of mutation rates were 0.83 for the reinforcement rate ratio and 0.68 for the reinforcer magnitude ratio, which are values that are comparable to those obtained in experiments with live organisms. These findings add to the evidence supporting the selectionist theory, which asserts that the world of behavior we observe and measure is created by evolutionary dynamics.

Contributions of contingencies in modern societies to "privacy" in the behavioral relations of cognition and emotion

The aim of this paper is to examine specific features of modern individualistic societies that contribute to "emotions" and "cognitions" becoming a matter of privacy. Although some behavior analysts identify emotions and cognitions as "private events," we argue with Skinner (1945) that cognitions and emotions are relations among events and that their origin is in public events in the contingencies of reinforcement maintained by other people. Guided by Elias (1939/1996), we suggest that the shift from feudal economies to market economies involved the increasing individualization of society's members. This individualizing process includes the socially maintained contingencies that bring some verbal responses under control of private stimulation and reduce the magnitude of some verbal responses to a covert level. Behavioral relations in which either stimuli or responses (or both) cannot be observed by others set the stage for a concept of "privacy." Changes in societal contingencies that gave rise to individualization and the attribution of privacy to cognitions and emotions are suggested to include the following: (a) increasing frequency of individual consequences that have no apparent or direct relevance to the group; (b) increasing numbers of concurrent contingencies and choice requirements; (c) conflicts between immediate and delayed consequences for the individual; and (d) conflicts between consequences for the individual and for the group.

Bias and undermatching in delinquent boys' verbal behavior as a function of their level of deviance

Eighty-one 13- to 14-year-old boys at risk for delinquency (target boys) engaged in brief dyadic conversations with their peer friends. The target boys' verbal behavior was coded into two mutually exclusive content categories, rule-break talk and normative talk. Positive social responses from peer boys for each category of talk were also recorded, and were presumed to reinforce the target boys' verbal behavior. A measure of child deviance was available for each target boy. The generalized matching law was fitted to the target boys' response and time allocation data and provided an excellent description of their verbal behavior, with an expected degree of undermatching and strong bias in favor of normative talk. When the boys' data were separated into groups of increasing child deviance, the matching law continued to provide an excellent description of the boys' verbal behavior regardless of their level of deviance, but undermatching became more severe and bias favoring normative talk became less strong as child deviance increased. Based on a selectionist theory of adaptive behavior dynamics from the basic science, it was suggested that the increasing degree of undermatching might be due to a decline in the reinforcing value of positive social responses with increasing child deviance. It was also suggested that the trend in the bias parameters might be due to different histories of reinforcement and punishment of rule-break and normative behavior for boys characterized by different levels of child deviance.

Limited matching on concurrent-schedule reinforcement of academic behavior

Three adolescent students with special educational needs were given a choice between completing one of two available sets of math problems. Reinforcers (nickels) across these alternatives were arranged systematically in separate experimental phases according to three different concurrent variable-interval schedules (reinforcement ratios of 2:1, 6:1, and 12:1). Time allocated to the two stacks of math problems stood in linear relationship to the reinforcement rate obtained from each stack, although substantial undermatching and bias were observed for all subjects. However, changes in the schedules were not followed by changes in allocation patterns until adjunct procedures (e.g., changeover delays, limited holds, timers, and demonstrations) were introduced. The necessity of adjunct procedures in establishing matching in applied situations is discussed as a limitation to quantitative applications of the matching law in applied behavior analysis.

Basic research needed for stimulating the development of behavioral technologies

The costs of disconnection between the basic and applied sectors of behavior analysis are reviewed, and some solutions to these problems are proposed. Central to these solutions are collaborations between basic and applied behavioral scientists in programmatic research that addresses the behavioral basis and solution of human behavior problems. This kind of collaboration parallels the deliberate interactions between basic and applied researchers that have proven to be so profitable in other scientific fields, such as medicine. Basic research questions of particular relevance to the development of behavioral technologies are posed in the following areas: response allocation, resistance to change, countercontrol, formation and differentiation/discrimination of stimulus and response classes, analysis of low-rate behavior, and rule-governed behavior. Three interrelated strategies to build connections between the basic and applied analysis of behavior are identified: (a) the development of nonhuman animal models of human behavior problems using operations that parallel plausible human circumstances, (b) replication of the modeled relations with human subjects in the operant laboratory, and (c) tests of the generality of the model with actual human problems in natural settings.

Translational research in behavior analysis: historical traditions and imperative for the future

"Pure basic" science can become detached from the natural world that it is supposed to explain. "Pure applied" work can become detached from fundamental processes that shape the world it is supposed to improve. Neither demands the intellectual support of a broad scholarly community or the material support of society. Translational research can do better by seeking innovation in theory or practice through the synthesis of basic and applied questions, literatures, and methods. Although translational thinking has always occurred in behavior analysis, progress often has been constrained by a functional separation of basic and applied communities. A review of translational traditions in behavior analysis suggests that innovation is most likely when individuals with basic and applied expertise collaborate. Such innovation may have to accelerate for behavior analysis to be taken seriously as a general-purpose science of behavior. We discuss the need for better coordination between the basic and applied sectors, and argue that such coordination compromises neither while benefiting both.

A computational theory of selection by consequences applied to concurrent schedules

Virtual organisms animated by a computational theory of selection by consequences responded on symmetrical and asymmetrical concurrent schedules of reinforcement. The theory instantiated Darwinian principles of selection, reproduction, and mutation such that a population of potential behaviors evolved under the selection pressure exerted by reinforcement from the environment. The virtual organisms' steady-state behavior was well described by the power function matching equation, and the parameters of the equation behaved in ways that were consistent with findings from experiments with live organisms. Together with previous research on single-alternative schedules (McDowell, 2004; McDowell & Caron, 2007) these results indicate that the equations of matching theory are emergent properties of the evolutionary dynamics of selection by consequences.

An application of the matching law to social dynamics

Using a procedure similar to the one described by Conger and Killeen (1974), we evaluated levels of attending for 25 college students who participated in either a 20-min (n = 12) or 30-min (n = 13) discussion on juvenile delinquency. Confederates delivered statements of agreement (e.g., "I agree with that point") according to independent variable-interval schedules. Pooled results were evaluated using three generalized formulations of the matching law, and showed that matching was more likely during the first 5 min of the discussion than during the last 5 min. Individual data for 7 of 9 participants were better described by the generalized response-rate matching equation than by the generalized time-allocation matching equation when response allocation was characterized in terms of frequency rather than duration.

Do we expect natural selection to produce rational behaviour?

We expect that natural selection should result in behavioural rules which perform well; however, animals (including humans) sometimes make bad decisions. Researchers account for these with a variety of explanations; we concentrate on two of them. One explanation is that the outcome is a side effect; what matters is how a rule performs (in terms of reproductive success). Several rules may perform well in the environment in which they have evolved, but their performance may differ in a 'new' environment (e.g. the laboratory). Some rules may perform very badly in this environment. We use the debate about whether animals follow the matching law rather than maximizing their gains as an illustration. Another possibility is that we were wrong about what is optimal. Here, the general idea is that the setting in which optimal decisions are investigated is too simple and may not include elements that add extra degrees of freedom to the situation.

Matching analysis of socially appropriate and destructive behavior in developmental disabilities

This study examined socially appropriate and destructive behavior in unconstrained natural environments using a matching law analysis (MLA) of real time observational data. The participants were two school-age children and one adult with mild to moderate cognitive disabilities. Event lagged sequential analysis (SQA) provided the obtained rates of staff attention to socially appropriate and inappropriate behaviors, which were then used in the matching law equations. For one participant the matching analysis showed a high (72%) variance-accounted-for (VAF) in behavior allocation in response to attention. For a second participant, matching analysis conducted on behavior allocation in response to staff attention showed lower (50%) VAF by staff attention. In the third case, the MLA also showed high (94%) VAF by attention. Suggestions for future extensions of matching analysis to clinically significant behavior and the limitations of the MLA for evaluating functional relationships in natural environments are discussed.

On the classic and modern theories of matching

Classic matching theory, which is based on Herrnstein's (1961) original matching equation and includes the well-known quantitative law of effect, is almost certainly false. The theory is logically inconsistent with known experimental findings, and experiments have shown that its central constant-k assumption is not tenable. Modern matching theory, which is based on the power function version of the original matching equation, remains tenable, although it has not been discussed or studied extensively. The modern theory is logically consistent with known experimental findings, it predicts the fact and details of the violation of the classic theory's constant-k assumption, and it accurately describes at least some data that are inconsistent with the classic theory.

Herrnstein??s hyperbolic matching equation and behavioral pharmacology: review and critique

Behavioral pharmacologists have enlisted Herrnstein's (1970) hyperbolic matching equation to understand the behavioral effects of drugs. Herrnstein's hyperbola describes the relation between absolute response rate and reinforcement rate. The equation has two fitted parameters. The parameter k represents the asymptotic response rate, and the parameter r(e) represents the reinforcement rate necessary to obtain half the asymptotic response rate. According to one interpretation of the equation, changes in k should reflect changes in response or motoric variables, and changes in r(e) should reflect changes in reinforcer or motivational variables, or changes in reinforcement from sources extraneous to the instrumental response. We review research that has applied Herrnstein's equation to distinguish the motoric from the motivational effects of drugs, and to identify additional independent variables responsible for drug effects, such as extraneous reinforcement. The validity of inferences about drug effects depends on the consistency of how k and r(e) respond to environmental manipulations: k should change only with response or motoric variables, and r(e) should change with reinforcer or motivational variables and with the rate of extraneous reinforcement. Empirical tests of these predictions, however, have produced inconsistent results. The review suggests that Herrnstein's theory has not fulfilled its promise of identifying the behavioral mechanisms of drug action. Modifications to the equation, known as bias and sensitivity, may explain some of these inconsistent results, and the modified equation may have utility in behavioral pharmacology.

Selection by consequences: one unifying principle for a transdisciplinary science of prevention

The principle of selection by consequences is critical to the analysis of a broad range of phenomena in the biological and behavioral sciences from the evolution of species to the selection of cultural practices. This paper reviews the role of that principle in diverse areas of the biobehavioral sciences and discusses how it can provide one dimension along which the diverse disciplines relevant to the prevention of problems of human behavior can be integrated. Such integration should improve the ability of prevention science to reduce the incidence and prevalence of human behavior problems.

Sequential and matching analyses of self-injurious behavior a case of overmatching in the natural environment

In this study, we examined the relation between naturally occurring rates of self-injurious behavior and appropriate communicative behavior using prospective sequential and matching analyses of descriptive data. Results from both analyses suggested reliable covariation between both forms of behavior and staff attention. Findings are discussed in terms of the applicability of quantitative descriptive analyses to characterize behavior-environment relations in natural contexts.

An application of the matching law to severe problem behavior

We evaluated problem behavior and appropriate behavior using the matching equation with 4 individuals with developmental disabilities. Descriptive observations were conducted during interactions between the participants and their primary care providers in either a clinical laboratory environment (3 participants) or the participant's home (1 participant). Data were recorded on potential reinforcers, problem behavior, and appropriate behavior. After identifying the reinforcers that maintained each participant's problem behavior by way of functional analysis, the descriptive data were analyzed retrospectively, based on the matching equation. Results showed that the proportional rate of problem behavior relative to appropriate behavior approximately matched the proportional rate of reinforcement for problem behavior for all participants. The results extend prior research because a functional analysis was conducted and because multiple sources of reinforcement (other than attention) were evaluated. Methodological constraints were identified, which may limit the application of the matching law on both practical and conceptual levels.

Comparing choices and variations in people and rats: two teaching experiments

Two pairs of experiments enabled students to compare their own operant behaviors with those of rats. The students played computer games for points, and the rats pressed levers for food. The first pair of experiments showed that, under concurrent schedules of reinforcement, relative frequencies of choices between two alternatives increased linearly in rats and people as functions of relative frequencies of reinforcement, with similar biases and undermatching observed in both species. The second pair of experiments showed that behavioral variability was controlled by reinforcers contingent on variability, this again true for both species. These experiments helped demonstrate the relevance of animal operant research to an explanation of human operant behavior.

Effects of noncontingent reinforcement on problem behavior and stimulus engagement: the role of satiation, extinction, and alternative reinforcement

This study examined the effects of noncontingent reinforcement (NCR) with and without extinction on problem behavior and stimulus engagement (consumption of reinforcement) of 4 participants. Reductions in problem behavior using NCR have frequently been attributed to both satiation of the reinforcer and extinction. In the current study, aspects of the NCR treatment effects were difficult to explain based solely on either a satiation or an extinction account. Specifically, it was found that stimulus engagement remained high throughout the NCR treatment analysis, and that problem behavior was reduced to near-zero levels during NCR without extinction. The implications of these findings are discussed with respect to the satiation and extinction hypotheses frequently described in the applied literature. Findings from basic studies examining the effects of response-independent schedules are presented, and are used as the basis for a matching theory account of NCR-related effects. It is proposed that reductions in problem behavior observed during NCR interventions may be a function of the availability of alternative sources of reinforcement.

An application of the matching law to evaluate the allocation of two- and three-point shots by college basketball players

We applied the matching equation to evaluate the allocation of two- and three-point shots by male and female college basketball players from a large Division 1 university. The matching law predicts that the proportion of shots taken from three-point range should match the proportional reinforcement rate produced by such shots. Thus, we compared the proportion of three-point shots taken relative to all shots to the proportion of three-point shots scored relative to all shots scored. However, the matching equation was adjusted to account for the greater reinforcer magnitude of the three-point basket (i.e., 1.5 times greater than the two-point basket reinforcer magnitude). For players with substantial playing time, results showed that the overall distribution of two- and three-point shots was predicted by the matching equation. Game-by-game shot distribution was variable, but the cumulative proportion of shots taken from three-point range as the season progressed was predicted almost perfectly on a player-by-player basis for both male and female basketball players.

Basic and applied research on choice responding

Choice responding refers to the manner in which individuals allocate their time or responding among available response options. In this article, we first review basic investigations that have identified and examined variables that influence choice responding, such as response effort and reinforcement rate, immediacy, and quality. We then describe recent bridge and applied studies that illustrate how the results of basic research on choice responding can help to account for human behavior in natural environments and improve clinical assessments and interventions.

Effects of problem difficulty and reinforcer quality on time allocated to concurrent arithmetic problems

Students with learning difficulties participated in two studies that analyzed the effects of problem difficulty and reinforcer quality upon time allocated to two sets of arithmetic problems reinforced according to a concurrent variable-interval 30-s variable-interval 120-s schedule. In Study 1, high- and low-difficulty arithmetic problems were systematically combined with rich and lean concurrent schedules (nickels used as reinforcers) across conditions using a single-subject design. The pairing of the high-difficulty problems with the richer schedule failed to offset time allocated to that alternative. Study 2 investigated the interactive effects of problem difficulty and reinforcer quality (nickels vs. program money) upon time allocation to arithmetic problems maintained by the concurrent schedules of reinforcement. Unlike problem difficulty, the pairing of the lesser quality reinforcer (program money) with the richer schedule reduced the time allocated to that alternative. The magnitude of this effect was greatest when combined with the low-difficulty problems. These studies have important implications for a matching law analysis of asymmetrical reinforcement variables that influence time allocation.

The effects of variable-interval reinforcement on academic engagement: a demonstration of matching theory

The single-alternative form of the matching law has enjoyed extensive support in laboratory research with both animals and humans. However, few data exist concerning its validity as a description of behavior in applied settings. In Experiment 1, 2 fourth-grade students were exposed to variable-interval schedules of social reinforcement contingent on academic engagement. The data for each subject were then plotted via Herrnstein's equation. The results showed Herrnstein's equation to account for 99.1% and 87.6% of the variance in student engagement, respectively. In Experiment 2, control over student engagement by two of the reinforcement schedules was examined further within an alternating treatments design with similar results. The implications of these findings for linking experimental and applied behavior analysis are discussed.

Behavioral momentum in the treatment of escape-motivated stereotypy

Descriptive and experimental analyses of stereotypy by a woman with severe mental retardation showed that the behavior was maintained by escape from demands. A sequence of high-probability requests issued immediately prior to a task-related request established a momentum of compliance that increased compliance with task-related demands. Increases in compliance were accompanied by collateral reductions in stereotypic behavior. A mechanism of response covariation, called functional incompatibility, and an animal analogue study for testing the validity of this mechanism are proposed.