What Are Concurrent Schedules?
A concurrent schedule of reinforcement is an arrangement in which two or more schedules operate simultaneously and independently, each associated with a different response alternative. The organism can switch between alternatives at any time, and reinforcement on each schedule is contingent on the response associated with that schedule. Concurrent schedules are the laboratory model for studying choice behavior, and they provide the empirical foundation for the Matching Law and the quantitative law of effect.
In the laboratory, concurrent schedules are typically arranged using two response keys, each associated with a different variable-interval (VI) schedule. For example, a pigeon might have access to a left key on a VI 30-second schedule and a right key on a VI 60-second schedule. The pigeon can peck either key at any time, and reinforcement on each key depends on the passage of time and the occurrence of a response on that key.
The Changeover Delay (COD)
An important procedural feature of concurrent schedule research is the changeover delay (COD). The COD is a brief time period following a switch from one alternative to the other during which reinforcement cannot be obtained. Without a COD, organisms tend to rapidly alternate between the two keys, which produces data that do not clearly reflect schedule control. The COD (typically 1.5 to 3 seconds) ensures that the organism must commit to an alternative for at least a brief period before reinforcement becomes available, producing cleaner data that reveal how the schedules control behavior allocation.
Herrnstein's Quantitative Law of Effect
The Single-Operant Equation
While the Matching Law describes the distribution of behavior across concurrent alternatives, Herrnstein (1970) extended the matching principle to the single-operant situation. The quantitative law of effect states that the rate of a single operant response is a function of the reinforcement rate for that response relative to all other sources of reinforcement in the environment. The equation is:
B = k * R / (R + Re)
Where B is the response rate, k is a constant representing the maximum possible response rate, R is the rate of reinforcement for the target response, and Re represents all other sources of reinforcement in the environment (extraneous reinforcement). This equation produces a negatively accelerating function: increases in reinforcement produce diminishing increases in response rate, approaching an asymptote at k.
Clinical Significance of Re
The Re parameter is particularly important for clinical applications. It represents the reinforcement available for all other behaviors in the environment besides the target behavior. This includes reinforcement for competing appropriate behaviors, reinforcement for other problem behaviors, and automatic reinforcement from the environment. The value of Re helps explain why the same reinforcement schedule produces different response rates in different environments. In a highly enriched environment (high Re), the target behavior competes with many other reinforced alternatives, and its rate may be lower even when the reinforcement rate for it has not changed.
Clinical Applications
Understanding Why Reinforcement "Stops Working"
A common clinical complaint is that a reinforcer that used to be effective is no longer working. The quantitative law of effect offers an explanation: the reinforcer may still be effective, but Re has changed. If new sources of reinforcement become available in the environment (a new toy, a new peer, a new activity), the relative value of the target reinforcer decreases even though its absolute value has not changed. The clinician should assess whether the reinforcement environment has changed rather than immediately concluding that the reinforcer is no longer preferred.
Enriched Environments and Problem Behavior
Noncontingent reinforcement (NCR) is a clinical application of the Re parameter. By enriching the environment with freely available reinforcers (increasing Re), the clinician reduces the relative reinforcement for problem behavior without changing the contingency for problem behavior directly. The quantitative law of effect predicts this: as Re increases, the proportion of behavior allocated to the target (problem behavior) decreases because the denominator of the equation grows larger.
Designing Competitive Alternatives
When designing differential reinforcement procedures, the quantitative framework helps clinicians understand that the alternative response must be competitive in the overall reinforcement economy. Simply adding reinforcement for an alternative behavior increases Re for problem behavior (potentially reducing it) and also directly strengthens the alternative. The most effective DRA procedures combine increased reinforcement for the alternative with reduced reinforcement for the problem behavior, shifting the reinforcement ratio as dramatically as possible.
Concurrent Schedules in Applied Settings
While laboratory concurrent schedules use precise VI schedules and changeover delays, the concept translates directly to applied settings where individuals continuously choose between available behavioral alternatives. A student in a classroom simultaneously has access to reinforcement for completing worksheets (teacher praise, grades), socializing with peers (social reinforcement), looking out the window (visual stimulation), and engaging in disruptive behavior (escape, attention). This is functionally a concurrent schedule arrangement, and the student's behavior allocation can be understood through matching principles.
Clinicians who recognize applied settings as concurrent schedule arrangements can analyze behavior more effectively. When a problem behavior persists despite a reinforcement-based intervention, the clinician should examine the entire reinforcement ecology rather than focusing exclusively on the target behavior and its immediate consequences.
BCBA Exam Tips
- Know that concurrent schedules involve two or more simultaneously available reinforcement sources
- Understand the changeover delay and why it is procedurally important
- Be able to explain the quantitative law of effect conceptually (you likely will not need to solve the equation)
- Recognize clinical scenarios that represent concurrent schedule arrangements
- Connect the Re parameter to NCR and environmental enrichment strategies
- Understand that the quantitative law of effect predicts diminishing returns as reinforcement rate increases
Herrnstein's contributions to understanding choice behavior and the quantitative analysis of reinforcement remain central to behavior analytic theory. These concepts provide a quantitative rationale for many common clinical strategies and are well-represented on the BCBA certification exam.