Matching Law: Practical Applications in ABA

The field of Applied Behavior Analysis (ABA) offers a variety of insights into human behavior. Applying this information in real-life situations is the challenge most professionals face on a daily basis. The Matching Law is a behavioral principle that states that behavior occurs in proportion to reinforcement available for each behavior, but how does this apply to your everyday programming?

The intentional use of the Matching Law allows you to manipulate concurrent schedules to influence behavior. This technique is especially useful when one schedule of reinforcement is outside of your control or when you want to avoid the negative effects of extinction. By increasing the magnitude of reinforcement for a behavior you want to see, you increase the likelihood of that behavior occurring.

To utilize the Matching Law effectively, you must first understand concurrent schedules and reinforcer magnitude.

Concurrent Schedules

Behavior is complex. Reinforcement strengthens behavior while punishment weakens it. Often situations exist where reinforcement and/or punishment occur at varying rates. When a behavior receives reinforcement at different rates under different conditions, we call these concurrent schedules of reinforcement. Sometimes this difference is intentional while other times it’s not.

Both intentional and unintentional reinforcement occur across environments, among different individuals, or in the presence of different stimuli. In highly controlled settings, it’s possible to minimize unintentional reinforcement, but as the environment becomes more natural and less contrived, the opportunities for inadvertent reinforcement increases. This creation of concurrent schedules of reinforcement impacts the rate at which behavior occurs.

Take a look at this example:

The reality of natural environments and human behavior demonstrates repeatedly that concurrent schedules occur, often without intent. As in the example above, a parent trying to implement DRA at home to reduce access-maintained tantrums may require the use of PECS or functional communication under most circumstances, but when visitors come to the house she may give access during challenging behavior to reduce the burden on the guests or avoid feeling embarrassed. These concurrent schedules compete against each other, both applying some effect on behavior.

For more information about schedules of reinforcement, read our post: How do I Choose Between Schedules of Reinforcement?

Reinforcer Magnitude and the Matching Law

When behaviors receive concurrent schedules of reinforcement, behavior occurs in proportion to the reinforcement available. The individual tends to choose the behavior receiving the highest magnitude of reinforcement. Visually, the Matching Law looks like:

Magnitude of a reinforcer when using the Matching Law

Another way to look at it is if an individual receives twice as much reinforcement for behavior 1 as he does for behavior 2 that individual is likely to engage in behavior 1 twice as much as behavior 2. The behavior receiving the greatest magnitude of reinforcement will occur most frequently.

Consider this example:

You value money. Last month, you started a business mowing lawns for people living in your neighborhood. You receive $25 for mowing the lawn for your neighbor on the right and $50 for mowing the lawn for your neighbor on the left. Whose lawn are you more likely to mow, all other factors being equal?

The key to that example is that other factors must remain equal. Once other factors start to change, the magnitude of the reinforcer changes with it. If it takes you 3 times as long to mow the lawn on your left, then which reinforcement schedule would you prefer?

In the example with Steffy and Diana above, functional communication received reinforcement across conditions (when Steffy was home alone with Diana and when they had guests) and tantrums received reinforcement during only one of the conditions (when guests were at the house). If tantrums received a lower magnitude (i.e. less frequent, lower quality, or shorter duration) of reinforcement than functional communication, Diana would continue to be more likely to choose functional communication over tantrums to gain access to what she wants.

Example of magnitude of a reinforcer when using the Matching Law

Collateral Effects of Interventions

Many situations exist in the natural environment where the collateral effects of interventions make those interventions either inappropriate, unethical, or impractical for implementation. Myerson and Hale (1984) discussed the use of the Matching Law when extinction or punishment were not advisable. Intentionally creating concurrent schedules where the maladaptive behavior receives a lower magnitude of reinforcement than the adaptive replacement behavior allows interventionists to shape behavior without the potential risks of extinction or punishment.

For the Matching Law to be effective, it’s critical to accurately identify the function of the maladaptive behavior. This allows you to identify:

  • A functionally-equivalent replacement behavior
  • All existing variables that maintain the behavior

When a behavior is maintained by multiple variables, you must account for these variables. Borrero and Vollmer (2002) noted the importance of identifying all of the potential sources of reinforcement when attempting to predict responding using the Matching Law. For example, if challenging behavior is maintained both by access to a tangible and attention, you must consider both of these factors when selecting reinforcement for the alternative behavior and for altering the magnitude of the current reinforcement received for the target behavior. Failure to include both sources of reinforcement will result in a heavier lean of reinforcement toward the challenging behavior than intended.

The Matching Law as an Alternative to Extinction

The Matching Law can become an alternative to extinction by adjusting the reinforcer used following each behavior. Apply a more effective schedule or magnitude of reinforcement to adaptive alternative behavior and a less effective schedule or magnitude of reinforcement for the behavior targeted for reduction. Planning for this occurrence minimizes the chances of unintentionally applying an effective reinforcer following the targeted behavior.

Here’s an example of the Matching Law instead of Extinction:

You work with a mother, Sami, and her 5-year-old son, Mac. You work with Sami to identify aggression toward siblings as the behavior targeted for reduction. Through direct and indirect assessment, you identify attention from both Sami and Mac’s siblings as the function of the aggression. Although you know that withholding attention following aggression may lead to the quickest reduction in the behavior, you recognize that Mac’s mom and siblings probably will not consistently ignore this behavior. Instead, you decide to set up concurrent schedules of reinforcement:

Schedule 1: Occurs when Mac engages in aggression. When he hits or kicks his siblings, Sami and/or his siblings will tell him in a neutral voice “that hurts, don’t hit/kick.” They will then leave the room (i.e. go into their bedroom or kitchen if they are in the living room).

Schedule 2: Occurs when Mac uses words to ask for attention from his siblings (FCT/DRA). When Mac appropriately attempts to interact with his siblings in any way, Sami and his siblings will provide lavish attention in the form of tickles, high fives and hugs (all identified as reinforcing for Mac). They will maintain this attention for at least 2 minutes even if it is disruptive to their current activity.

Providing Sami and Mac’s siblings with a specific way to respond to Mac’s aggression overcomes several hurdles:

  • Parents and siblings react to challenging behavior without thinking
  • You mitigate concerns about a potential extinction burst
  • Sami and the siblings are empowered with clear direction no matter the behavior

References and Further Reading

Borrero, J. C., & Vollmer, T. R. (2002). An application of the matching law to severe problem behaviorJournal of Applied Behavior Analysis35(1), 13-27.

Myerson, J., & Hale, S. (1984). Practical implications of the matching lawJournal of Applied Behavior Analysis17(3), 367-380.