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

Four related procedures provided a basis for comparing the linear-optimalit y 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 choi ce. In contrast to previous work that involved constant ratio increments, t wo sets of procedures in this study involved relatively small increments th at are similar to the early values when a progressive schedule is increasin g 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 pat terns 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 character ized by the sums-of-reciprocals principle. This supports previous research with pigeons using fixed-increment progressive schedules, as well as situat ions in which the progressive schedule increased by constant proportions in stead of by constant increments. The findings are attributed to the feature of this averaging technique whereby it differentially values reinforcers b ased on their relative proximity to a particular choice point.