On the falsifiability of matching theory.
The matching law is unfalsified—variable "k" values and bias terms are features, not bugs.
01Research in Context
What this study did
Rosenberg (1986) wrote a theory paper. He asked: do new data that show a wandering "k" value kill the matching law?
He checked algebra. He showed the law can bend without breaking.
What they found
The matching law is still alive. A shifty "k" does not falsify it.
Algebraic and bias-ready forms soak up the noise.
How this fits with other research
Michael (1974) laid the first bricks. Without that axiomatic base there is nothing to defend.
Allen (1981) proved the power-form math. That proof gives the 1986 paper room to claim the law can flex.
Thorne (2010) goes deeper. It says "bias" and "sensitivity" terms may be mirages from sloppy models. Together the three papers build a shield: the law survives both odd data and our own mis-specifications.
Oliver et al. (2002) bring the idea into real homes. They show severe problem behavior follows matching ratios, proving the defense matters outside the lab.
Why it matters
You can trust the matching law even when data look messy. If a client’s response ratios drift, check reinforcement ratios first. Add a bias parameter or power exponent before you toss the law out. The math still guides your treatment.
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Plot your client’s response ratio against reinforcement ratio; if the dots don’t hug the diagonal, insert a bias or exponent term before you change the intervention.
02At a glance
03Original abstract
Herrnstein's matching theory requires the parameter, k, which appears in the single-alternative form of the matching equation, to remain invariant with respect to changes in reinforcement parameters like magnitude or immediacy. Recent experiments have disconfirmed matching theory by showing that the invariant-k requirement does not hold. However, the theory can be asserted in a purely algebraic form that does not require an invariant k and that is not disconfirmed by the recent findings. In addition, both the original and the purely algebraic versions of matching theory can be asserted in forms that allow for commonly observed deviations from matching (bias, undermatching, and overmatching). The recent finding of a variable k does not disconfirm these versions of matching theory either. As a consequence, matching remains a viable theory of behavior, the strength of which lies in its general conceptualization of all behavior as choice, and in its unified mathematical treatment of single- and multialternative environments.
Journal of the experimental analysis of behavior, 1986 · doi:10.1901/jeab.1986.45-63