ABSTRACT
The generalized matching law was developed so that data that clearly did not conform to strict matching could be described in the same terms as strict matching data. It is a generalization of the strict matching law in the sense that the strict matching law is a special case of the generalized law (see Allen, 1981; Prelec, 1984). Notice that, in its simplest form, the strict matching relation for concurrent schedules has no free parameters:
where the Subscripts 1 and 2 denote the two alternatives. In this equation, both the two responses and the two reinforcers are identical. Recall, though, that when the asymptotic rates of two concurrent operants were different (Equation 2.7), or when the reinforcers for these were different (Equation 2.8), a free parameter is appropriate to scale the response or reinforcer rates. Equation 2.7 was:
where p and £ denote pecks and lever presses respectively. If this equation is cross multiplied and the common terms are subtracted from each side of the equality, we obtain, after some manipulation:
Bv = k'RD + B e k 'Rp + R(
(4.1)
where k' = kp/k€ (see Section 2.2). Thus, the strict matching law already has built into it one generalized feature-the ability to deal with bias. A bias is a constant proportional preference for one response over another for all levels of the independent variable. In Equation 4.1, whatever the values of Rp and Re, Bp/Be (the response ratio) is related to Rp/Re (the reinforcer-frequency ratio) via a multiplicative constant. In other words, the relation between the behavior ratio and the reinforcer ratio is a straight-line function of slope k! (Fig. 4. IE). Notice that this relation, when plotted on relative coordinates (Fig. 4 . IB), de scribes the quadratic deviation from strict matching exemplified in Fig. 3.1.
