Categorical counting

Pigeons pecked on three keys, responses to one of which could be reinforced after a few pecks, to a second key after a somewhat larger number of pecks, and to a third key after the maximum pecking requirement. The values of the pecking requirements and the proportion of trials ending with reinforcement were varied. Transits among the keys were an orderly function of peck number, and showed approximately proportional changes with changes in the pecking requirements, consistent with Weber's law. Standard deviations of the switch points between successive keys increased more slowly within a condition than across conditions. Changes in reinforcement probability produced changes in the location of the psychometric functions that were consistent with models of timing. Analyses of the number of pecks emitted and the duration of the pecking sequences demonstrated that peck number was the primary determinant of choice, but that passage of time also played some role. We capture the basic results with a standard model of counting, which we qualify to account for the secondary experiments.