On two types of deviation from the matching law: bias and undermatching

DATA ON CHOICE GENERALLY CONFORM CLOSELY TO AN EQUATION OF THE FORM: log(B(1)/B(2))=a log(r(1)/r(2)+log k, where B(1) and B(2) are the frequencies of responding at Alternatives 1 and 2, r(1) and r(2) are the obtained reinforcement from Alternatives 1 and 2, and a and k are empirical constants. When a and k equal one, this equation is equivalent to the matching relation: B(1)/B(2)=r(1)/r(2). Two types of deviation from matching can occur with this formulation: a and k not equal to one. In some experiments, a systematically falls short of one. This deviation is undermatching. The reasons for undermatching are obscure at present. Some evidence suggests, however, that factors favoring discrimination also favor matching. Matching (a=1) may represent the norm in choice when discrimination is maximal. When k differs from one, its magnitude indicates the degree of bias in choice. The generalized matching law predicts that bias should take this form (adding a constant proportion of responding to the favored alternative). Data from a variety of experiments indicate that it generally does.