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

Baum, W. M. (1974). On two types of deviation from the matching law: Bias and undermatching. Journal of the Experimental Analysis of Behavior, 22, 231-242.

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.