Pigeons' choices between fixed-ratio and linear or geometric escalating schedules

Four related procedures provided a basis for comparing the linear-optimality principle with a principle based on the sums of reciprocals of distances to reinforcement, and to explore the generality of the sums-of-reciprocals principle as a description of choice patterns in situations of diminishing returns. The procedures all arranged choices between fixed-ratio schedules and progressive-ratio schedules, which escalated with each consecutive choice. In contrast to previous work that involved constant ratio increments, two sets of procedures in this study involved relatively small increments that are similar to the early values when a progressive schedule is increasing proportionally. The remaining two sets of procedures examined progressive schedules with proportional increments. In addition, the initial value of the progressive alternative was manipulated to determine its effects on patterns of choice with both linear and proportional types of escalation. With the exception of one phase, regardless of the initial/reset value and the patterns of escalation, patterns of choice with pigeons were well characterized by the sums-of-reciprocals principle. This supports previous research with pigeons using fixed-increment progressive schedules, as well as situations in which the progressive schedule increased by constant proportions instead of by constant increments. The findings are attributed to the feature of this averaging technique whereby it differentially values reinforcers based on their relative proximity to a particular choice point.