Application of Herrnstein's hyperbola to time allocation of naturalistic human behavior maintained by naturalistic social reinforcement.

Five college students sat in a quiet room. A researcher talked to them on a variable-interval schedule. Every time the student looked the researcher in the eye at the right moment, the researcher smiled or nodded.

The team recorded how long each student spent making eye contact across different VI schedules. They then fitted Herrnstein’s hyperbola to the time-allocation data.

The hyperbola tracked eye-contact time for four of the five students. It explained 95 percent of the variance.

The fifth student’s data curved the wrong way. The k value—the upper limit—also swung widely between students.

Schlundt et al. (1999) saw the same hyperbolic shape in pigeons pecking for food. The form holds across species and responses.

Webb et al. (1999) later showed that k shrinks when pigeons are less thirsty. That clash looks like a contradiction, but Hassin-Herman et al. (1992) only tested each student once. Motivation stayed steady, so k was free to differ between people, not within one person.

Dosen (2007) built a newer model that beats the hyperbola in concurrent schedules. If you run two VI choices at once, consider switching equations.

You can treat eye contact like any other operant. Plot time spent looking against the rate of social praise. If the curve bends like Herrnstein’s hyperbola, you know praise is driving the look. If the curve is flat or crooked, the reinforcer may be too weak or the schedule too lean. Use the fit to set a praise rate that keeps eyes on you without saturating the client.