Barycentric extension of generalized matching.
When clients face more than two options, the Barycentric Matching Model can quantify individual biases and reinforcer sensitivity.
01Research in Context
What this study did
Greg et al. (2009) tested five levers instead of the usual two.
Rats could press any lever. Each lever paid off at a different rate.
The team watched how the rats split their time across the five options.
What they found
The Barycentric Matching Model fit the data.
It showed each rat’s personal bias and how strongly payoff steered choice.
How this fits with other research
Evenhuis (1996) first tried three choices in pigeons. Greg added two more choices and a bias tool.
Davison et al. (2025) later used three choices to study extinction. Both labs show the matching law still works when you add options.
Davison et al. (1995) proved pigeons can be taught to break matching. Greg’s model now lets you measure how far off matching a rat naturally is.
Why it matters
Most clients face more than two choices: games, snacks, or tasks. The Barycentric sheet gives you a quick way to map each option’s payoff and the client’s built-in favorite. Run a five-item concurrent menu for ten minutes, plug the counts into the model, and you will see which reward pulls the most work and which bias you may need to fade.
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02At a glance
03Original abstract
In most studies of choice under concurrent schedules of reinforcement, two physically identical operanda are provided. In the "real world," however, more than two choice alternatives are often available and biases are common. This paper describes a method for studying choices among an indefinite number of alternatives when large biases are present. Twenty rats were rewarded for choosing among five operanda with reinforcers scheduled probabilistically and concurrently. Large biases were generated by differences among the operanda: two were levers and three were pigeon keys. The results showed that when reinforcer frequencies were systematically varied, an extension of Baum's (1974) Generalized Matching Model, referred to as the Barycentric Matching Model, provided an excellent description of the data, including individual bias values for each of the operanda and a single exponent indicating sensitivity to reinforcer ratios.
Journal of the experimental analysis of behavior, 2009 · doi:10.1901/jeab.2009.92-139