The assumptions underlying the generalized matching law.
The matching law now comes with a rock-solid equation that includes bias and works for any number of alternatives.
01Research in Context
What this study did
Prelec (1984) rewrote the math behind the generalized matching law.
The new proof lets you add bias terms and works for any number of choices.
It is a pencil-and-paper paper, no new data.
What they found
The law now holds together without loose ends.
You can plug in bias and still keep the same simple ratio form.
How this fits with other research
Davison et al. (1984) appeared the same year and threw cold water on VI-VR data. They showed matching can pop out of the schedule itself, not from true choice.
Prelec (1984) does not fight that claim; it just makes the math cleaner so future tests can tell real matching from artifacts.
Michael (1988) later used the tighter law to build four real-world interventions, proving the new math travels from cage to clinic.
Why it matters
If you run concurrent schedules in a functional analysis, use the updated formula. Add a bias parameter when one option looks easier or pays faster. Clean math means cleaner conclusions about why your client is choosing problem behavior.
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02At a glance
03Original abstract
Allen (1981) derived the power-function generalization of the matching law from a functional equation involving relative response rates on three concurrently available schedules of reinforcement. This paper defines the conditions (relative homogeneity and independence) under which a more general class of behavioral laws reduces to the power law. The proof also removes two deficiencies of Allen's result (discussed by Houston, 1982), which are, first, that his derivation produces a power law without a bias coefficient, and second, that it holds only for experiments with three or more concurrent schedules.
Journal of the experimental analysis of behavior, 1984 · doi:10.1901/jeab.1984.41-101