Matching, maximizing, and hill-climbing

In simple situations, animals consistently choose the better of two alternatives. On concurrent variable-interval variable-interval and variable-interval variable-ratio schedules, they approximately match aggregate choice and reinforcement ratios. The matching law attempts to explain the latter result but does not address the former. Hill-climbing rules such as momentary maximizing can account for both. We show that momentary maximizing constrains molar choice to approximate matching; that molar choice covaries with pigeons' momentary-maximizing estimate; and that the “generalized matching law” follows from almost any hill-climbing rule.