The logistics of choice.

Killeen (2015) wrote a theory paper. The author looked at the generalized matching law. He asked why choice ratios line up with reinforcer ratios.

He showed the math. The matching law is just logistic regression in disguise. The real driver is the old Law of Effect, not a special matching process.

The paper found no new numbers. It found a new view. Matching is not a separate law. It is a by-product of reinforcement history.

The Law of Effect does the work. Logistic regression captures it. The matching equation is only one way to write it down.

Nakamura et al. (1986) reviewed hundreds of pigeon sessions. They showed the matching law fits 91% of the variance. Killeen (2015) keeps the fit but changes the story.

Villarreal et al. (2019) gave us Bayesian tools to estimate matching parameters. Those same tools now fit the logistic view.

Caron (2024) fixed undefined log ratios with modern stats. His fixes work for both old matching and new logistic forms.

You can stop teaching matching as a magic rule. Teach it as reinforcement history filtered through logistic odds. When you graph choice data, fit a logistic curve first. If it fits, the Law of Effect already explains the pattern. Save the matching plot for staff who like straight lines on log paper.