On two types of deviation from the matching law: bias and undermatching.
Plot choice data; a shifted line signals bias, a shallow slope signals undermatching—each needs a different tweak.
01Research in Context
What this study did
The author wrote equations to explain two ways choice can drift from the matching law.
He called them bias and undermatching. Bias is a steady side preference. Undermatching is weak sensitivity to reward differences.
The paper is pure theory—no new data, just math and logic.
What they found
Bias shows up as a flat shift in the line—one option is always picked a bit more.
Undermatching shows up as a shallow slope—kids still pick the richer side, but not as strongly as the rewards say they should.
Both tweaks keep the generalized matching law intact; they just change its knobs.
How this fits with other research
White (1979) later counted 103 data sets and found slopes near 0.9—real kids undermatch just like the 1974 paper guessed.
Madden et al. (2003) took the same idea outside the lab. In a classroom, a boy’s self-injury over-matched staff attention; the slope was steeper than 1.0, the mirror image of undermatching.
Glenn (1993) moved the bias concept into self-reports. College students had a constant bias to say “yes”; the math looked identical to a biased choice line.
Why it matters
When your client’s responding looks “off,” plot the data. A parallel shift left or right means bias—try re-balancing reinforcer quality. A shallow slope means undermatching—sharpen the difference between schedules or add discrimination cues. You can fix both without guessing.
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Join Free →Graph last week’s concurrent-token data; if the slope is below 0.9, magnify the richer schedule by 20 % and re-test.
02At a glance
03Original abstract
DATA ON CHOICE GENERALLY CONFORM CLOSELY TO AN EQUATION OF THE FORM: log(B(1)/B(2))=a log(r(1)/r(2)+log k, where B(1) and B(2) are the frequencies of responding at Alternatives 1 and 2, r(1) and r(2) are the obtained reinforcement from Alternatives 1 and 2, and a and k are empirical constants. When a and k equal one, this equation is equivalent to the matching relation: B(1)/B(2)=r(1)/r(2). Two types of deviation from matching can occur with this formulation: a and k not equal to one. In some experiments, a systematically falls short of one. This deviation is undermatching. The reasons for undermatching are obscure at present. Some evidence suggests, however, that factors favoring discrimination also favor matching. Matching (a=1) may represent the norm in choice when discrimination is maximal. When k differs from one, its magnitude indicates the degree of bias in choice. The generalized matching law predicts that bias should take this form (adding a constant proportion of responding to the favored alternative). Data from a variety of experiments indicate that it generally does.
Journal of the experimental analysis of behavior, 1974 · doi:10.1901/jeab.1974.22-231