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(B₁/B₂)=a log(r₁/r₂+log k, where B₁ and B₂ are the frequencies of responding at Alternatives 1 and 2, r₁ and r₂ 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: B₁/B₂=r₁/r₂. 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.