An application of the matching law to severe problem behavior.

Oliver et al. (2002) watched four children with developmental delay at home and school. They counted how often adults gave attention or toys when the kids hit, screamed, or played nicely.

The team then checked if the share of problem behavior matched the share of reinforcement it got. They used the matching law equation to see if the numbers lined up.

For every child, the proportion of severe problem behavior almost perfectly mirrored the proportion of reinforcement it produced. When problem behavior earned 70 percent of the goodies, it happened about 70 percent of the time.

The tight fit held across different days, settings, and types of reinforcement. The matching law worked even with life-threatening self-injury.

Michael (1974) first wrote the matching law on paper; Oliver et al. (2002) show it still holds when the "responses" are head-banging and the "reinforcers" are hugs. Shimp et al. (1971) proved the law with brief schedule components in pigeons; the new study extends that logic to brief, naturally occurring interactions in humans.

Wilkie (1973) showed pigeons match timeout ratios; Oliver et al. (2002) find the same math applies when children escape tasks by screaming. The principle crosses species and reinforcer type.

Matson et al. (2004) later used a lab model to confirm that noncontingent reinforcement shifts behavior in the exact ratios the matching law predicts. Together, the papers form a line: from pigeon keys, to equations, to real-world bruises, to planned clinical applications.

You can now treat severe problem behavior like a choice equation. Track what proportion of adult attention, escape, or items the behavior captures, then rearrange the environment so safer responses earn that same share. If screaming gets 80 percent of mom's eye contact, give 80 percent to words instead. The study gives you a calculator-ready way to set initial doses of differential reinforcement without lengthy baselines.