Undermatching and overmatching as deviations from the matching law.
Undermatching and overmatching are burst noise, not broken rules, but newer models add finer tools.
01Research in Context
What this study did
Wearden (1983) built a math model of the matching law.
The model asks why animals sometimes undermatch and sometimes overmatch.
It treats both errors as short bursts of noise, not as rule breaking.
What they found
Undermatching should show up more often than overmatching.
The model fits the skew seen in old data sets.
Burst-level noise keeps the matching law intact.
How this fits with other research
MacDonall (2009) clashes with this view. The stay-switch model says reinforcers control staying and switching, not the overall ratio. It beats the matching law in data fits.
Avellaneda (2025) keeps the law but adds detail. Its Markov model turns the same reinforcer ratios into exact changeover times, giving a time-based partner to H’s burst idea.
Farrant et al. (1998) stretch the law further. Monkeys drinking pentobarbital still match response rates to drug dose under concurrent VR-VR schedules, showing the rule holds even with drug reinforcers.
Why it matters
You can keep using the matching law when you see slight preference drift. Treat undermatching as noise, not failure. If drift is large, try the stay-switch view and check whether staying or switching is better reinforced. Either way, measure, don’t guess.
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02At a glance
03Original abstract
A model of performance under concurrent variable-interval reinforcement schedules that takes as its starting point the hypothetical "burst" structure of operant responding is presented. Undermatching and overmatching are derived from two separate, and opposing, tendencies. The first is a tendency to allocate a certain proportion of response bursts randomly to a response alternative without regard for the rate of reinforcement it provides, others being allocated according to the simple matching law. This produces undermatching. The second is a tendency to prolong response bursts that have a high probability of initiation relative to those for which initiation probability is lower. This process produces overmatching. A model embodying both tendencies predicts (1) that undermatching will be more common than overmatching, (2) that overmatching, when it occurs, will tend to be of limited extent. Both predictions are consistent with available data. The model thus accounts for undermatching and overmatching deviations from the matching law in terms of additional processes added on to behavior allocation obeying the simple matching relation. Such a model thus enables processes that have been hypothesized to underlie matching, such as some type of reinforcement rate or probability optimization, to remain as explanatory mechanisms even though the simple matching law may not generally be obeyed.
Journal of the experimental analysis of behavior, 1983 · doi:10.1901/jeab.1983.40-333