Matching Law Example
Understanding the interaction between competing sources of reinforcement via the law of matching allows behavioral analysts to increase selected behaviors and decrease others. One of the most widely used behaviour change tactics to achieve such goals in practice is differential reinforcement (see Petscher, Rey & Bailey, 2009), which is strictly speaking limiting or retaining reinforcements for one behaviour and delivering them based on another. Because of this approach of simultaneously increasing one response and decreasing another, this procedure is often used for both skill development (e.g., Vladescu, & Kodak, 2010) and behaviour reduction (e.g., Machalicek, O`Reilly, Beretvas, Sigafoos, & Lancioni, 2007). Note, however, that differential amplification does not necessarily require the extinction of problematic behavior, while functionally equivalent appropriate behavior is amplified. In many cases, a behavioral analyst may be interested in amplifying one response more strongly than another, although none is necessarily more «appropriate» than another. For example, Athens and Vollmer (2010) used a differential amplification method for alternative non-extinction behaviour to assess the effects of manipulating different dimensions of amplification (e.g., duration, quality, delay) on the behaviour of seven children with ADHD or autism. After performing a functional evaluation to determine the functions of the problematic behavior, the experimenters manipulated (a) the duration of the gain (e.g., 5-45 s), (b) the quality of the gain (e.g., high, low), (c) the delay in gain (e.g., 0-60 s), and (d) the combination of the above (e.g., 5 s of access [duration] to a lower gain amplifier, for example after a delay of 10 seconds) on both problematic behavior and appropriate behavior. In these arrangements, relatively more reinforcement was provided, depending on the appropriate behaviour in relation to the problematic behaviour. Within a coherent legal framework, we can conceptualize appropriate behavior and problematic behavior as B1 and B2 and relative earning rates as R1 and R2, respectively. As expected, there was little or no difference between the rates of the two behaviours when the relative gain rates were the same for both behaviours. However, when reinforcement promoted appropriate behaviour, children exhibited relatively more appropriate behaviour in relation to problematic behaviours. Although this effect was observed when a single payoff dimension was manipulated for both behaviours, the effect was more pronounced when a combination of dimensions was altered (i.e. when the game was stacked more in favour of appropriate behaviour).
Simply put, the children adapted their behavior to what was relatively more reinforcing. In the example above with Steffy and Diana, functional communication received reinforcement through conditions (when Steffy was home alone with Diana and when they had guests) and tantrums only during one of the conditions (when the guests were in the house). If tantrums have less amplification (i.e. Less frequent, of lower quality or shorter duration) than functional communication, Diana would continue to choose a more functional communication via tantrums to have access to what she wants. In 1961, B.J. Herrnstein published a research paper in which there was an early formulation of what we call the matching law (Herrnstein, 1961). Hello. Well, before reading this post, I have no idea about this corresponding law, but after reading this, I have some kind of knowledge. I think the four points you mentioned in your post are pretty good and fantastic. Thanks for sharing. Baum, W.
M. (1974). About two types of deviations from the matching law: bias and undermatching. Journal of the experimental analysis of behavior, 22(1), 231-242. www.ncbi.nlm.nih.gov/pmc/articles/PMC1333261/pdf/jeabehav00117-0229.pdf Another example I often use is a student at school who may shout or raise his hand in class. If the student yells, the teacher reprimands him every other time. However, if the student raises his hand, the teacher calls him about every six times. If attention is the amplifier, the screams will occur more often than raising one`s hand according to the concordant law. The law of matching can be a practical and effective alternative to the use of extinction, which is generally preferred by learners and interventionists. In operant conditioning, the law of matching is a quantitative relationship between relative response rates and relative reinforcement rates in concurrent reinforcement plans.
For example, if an organization is offered two response options A and B, the ratio of response rates to A and B is equal to the ratio of amplifications obtained by each response.  This law applies fairly well when non-human subjects are exposed to simultaneous variable interval designs (but see below); Its applicability in other situations is less clear, depending on the assumptions made and the details of the experimental situation. The generality of the applicability of the Twinning Act is currently the subject of current debate.  Reed, D.D. and Kaplan, B.A. (2011). The Good Law: A tutorial for practitioners. Behavior Analysis in Practice, 4(2), 15-24. After explaining the GME (equation 2), we return to the hypothetical customer data and examine the agreement in terms of gain and distortion sensitivity using the GME (equation 2). As shown in Figure 4, the slope of the line (reinforcement sensitivity or s) was 0.87. In other words, if there is a change of one unit in the gain for aggression, there is slightly less than a change of one unit (0.87) in aggression. In other words, the client shows a submatch.
In addition, there was virtually no distortion at a y-section (bias or b) of -0.009. In other words, if we model the response, if the gain rates for aggression and appropriate behaviours are equal, the relative ratio of behaviours is about the same; The preference for behavior seems to be based solely on reinforcement rates and not on a particular characteristic of the response form or the quality of attention for each response form. Finally, when looking at the R2 value of the best-fitting line, it is evident that the GME provides an excellent representation of the behavior model, with 98% of the variance represented by equation 2. In other words, the GME can explain 98% of the variance in relative behaviour rates by taking into account known relative gain rates. If a behavior is maintained by multiple variables, you must consider those variables. Borrero and Vollmer (2002) emphasized the importance of identifying all potential sources of reinforcement when attempting to predict response using the matching law. For example, if a difficult behavior is maintained by both access to tangible behavior and attention, you should consider both factors when selecting the gain for the alternative behavior and changing the size of the current gain you received for the target behavior. If both sources of reinforcement are not included, it will result in a higher propensity for reinforcement towards challenging behavior than expected. What makes us choose between watching our favorite TV show and writing the newspaper in a few weeks? Why do we choose to walk our dog instead of making an important call to a difficult customer? Why does our dog bark for attention or steal socks from the laundry basket? Throughout the day, we are faced with an endless selection of stocks to choose from, some important, others less so. Whether we are a human, a dog, a cat or a horse, the choices we make are the result of a number of variables stemming from the consequences suffered by the environment.
In applied behavioural analysis, decisions made by a person or animal are a direct result of the «law of matching». At the last conference «Out of the lab, into the field», Parvene Farhoody showed how this law of action influences not only the behavior of the animal, but also the efficiency and precision of our training. 1/ When an animal is confronted with two possible behaviors, it is more likely to choose the one that has been rewarded most often. It is therefore important to create conditions in which the «right choice» is easier than the alternative. Effective training must involve manipulation of the environment so that «good decisions» require little effort and receive a high rate of instant reinforcement. An example of this is when you lock up a puppy or keep a close eye on him, while taking him out every half hour if necessary, rewarding him for his potty outside. The fewer accidents, the faster and more effective the training. The «matching law» was first brought to light by R.J. Herrnstein (1961).
Working with pigeons in a Skinner box, Herrnstein realized that the frequency with which they peck one button at another was directly correlated with the reward rate they received for pecking each of them. In other words, behavior is reinforcement. If 70% of the rewards for pecking the right button were awarded, the pigeon would press the right button 70% of the time, hence the term «matching law».