Comment on Houston's arguments.
A 1982 math gripe sparked 40 years of better choice equations—skip it unless you love the algebra behind two-lever data.
01Research in Context
What this study did
Durand (1982) is a short, sharp reply in a journal debate. The author challenges Houston’s math for how animals split their time between two levers. No data, no new experiment—just equations and logic.
What they found
The paper says Houston’s formula can give impossible answers. It warns that the usual matching-law equation may hide errors when choices flip quickly. The note ends with a call for tighter algebra.
How this fits with other research
MacDonall (2009) answers the 1982 worry. It splits reinforcers into ‘stay’ and ‘switch’ pots. The new model fits every data pattern the old equation missed.
Wearden (1983) also replies, but with burst theory. It keeps the matching law and adds moment-to-moment noise. Both papers keep the core idea alive while fixing the math Durand (1982) attacked.
Avellaneda (2025) goes further. It turns the whole choice process into a Markov chain. The closed-form solution now predicts exactly when an animal will jump levers—something the 1982 note said couldn’t be done.
Why it matters
If you run concurrent schedules, you can relax. The matching law still works; you just need the right version. Use stay/switch math when data look odd, or grab the 2025 Markov sheet for quick changeover forecasts. Your graphs will thank you.
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Join Free →Open your last concurrent VI graph. If response ratios drift from reinforcer ratios, rerun the analysis with stay/switch counts instead of totals.
02At a glance
03Original abstract
Houston's arguments focus on two main issues: the noninclusion of a bias term in the generalization and the disputed usefulness of the relationship in a pair-wise concurrent choice setting.A third, minor issue is raised by Houston regarding the "restrictiveness" of the relationship
Journal of the experimental analysis of behavior, 1982 · doi:10.1901/jeab.1982.38-113