[1] This law applies fairly well when non-human subjects are exposed to concurrent variable interval schedules (but see below); its applicability in other situations is less clear, depending on the assumptions made and the details of the experimental situation.
[2] The matching law can be applied to situations involving a single response maintained by a single schedule of reinforcement if one assumes that alternative responses are always available to an organism, maintained by uncontrolled "extraneous" reinforcers.
The matching law was first formulated by R.J. Herrnstein (1961) following an experiment with pigeons on concurrent variable interval schedules.
[3] Pigeons were presented with two buttons in a Skinner box, each of which led to varying rates of food reward.
A recent review by McDowell reveals that Herrnstein's original equation fails to accurately describe concurrent-schedule data under a substantial range of conditions.
A final deviation is bias, which occurs when subjects spend more time on one alternative than the matching equation predicts.
This may happen if a subject prefers a certain environment, area in a laboratory, or method of responding.
This is more conveniently expressed in logarithmic form The constants b and s are referred to as "bias" and "sensitivity" respectively.
The generalized matching law accounts for high proportions of the variance in most experiments on concurrent variable interval schedules in non-humans.
[6] The matching law thus challenges the idea that choice is an unpredictable outcome of free will, just as B.F. Skinner and others have argued.
[9] Finally, if nothing else, the matching law is important because it has generated a great deal of research that has widened our understanding of operant control.