Differences in Delay, Not Ratios, Control Choice in Concurrent Chains

Abstract

In two experiments, pigeons were trained with concurrent‐chains schedules, wherein responding to equal initial links measured preference between variable‐interval terminal links. Absolute terminal‐link duration was varied by keeping constant the difference between the terminal‐link delays and forcing their ratio to change. Delay‐reduction theory scales value relative to a common temporal context and requires that delay differences control choice. Thus, preference should remain invariant. Most competing accounts, including the matching law and a strong form of Weber's law, require that preference vary with the delay ratio. Experiment 1 employed standard concurrent chains, in which terminal‐link position and color were confounded. Although average preference remained constant, individual preferences were highly variable and inconsistent, possibly due to carryover of position biases across conditions. In an attempt to reduce variability, Experiment 2 used a modified concurrent‐chains procedure. Preference at different terminal‐link durations was assessed simultaneously to prevent order effects, and terminal‐link position was alternated randomly across trials to minimize the impact of position biases. In Experiment 2, both individual and mean preferences showed the constant‐difference invariance. Overall, choice was controlled by terminal‐link differences, not ratios.

Evidence Against a Constant‐difference Effect in Concurrent‐chains Schedules

“…Their initial links were identical VI 60-s schedules, and their terminal links were pairs of VI schedules that always differed by a mean of 20 s. For example, in one condition the two terminal links were VI 5 s and VI 25 s, and in another condition the two terminal links were VI 100 s and VI 120 s. Savastano and Fantino found no systematic changes in preference as long as the difference between the two terminal links was kept constant at 20 s. More recently, Fantino and Goldshmidt (2000) obtained similar results in a series of experiments with pigeons that used a very different procedure-a foraging analogue called the successive-encounters procedure. Savastano and Fantino (1996) showed that this finding, the constant-difference effect, was inconsistent with several different mathematical models of choice, including melioration theory (Vaughan, 1985), incentive theory (Killeen & Fantino, 1990), and Davison's (1988) extension of the hyperbolic decay model. Each of these models predicts that preference for the shorter terminal-link schedule should decrease toward indifference as the durations of the terminal-link schedules become longer.…”

“…Although the constant-difference effect may be counterintuitive, Savastano and Fantino (1996) showed that it is predicted by Fantino's (1969) delay-reduction theory. In its simplest form, delay-reduction theory can be expressed as follows:…”

“…In two experiments with pigeons, Savastano and Fantino (1996) found that initial-link response ratios on concurrent-chains schedules remained constant as long as the subtractive difference between the lengths of the two terminal-link schedules remained constant. Their initial links were identical VI 60-s schedules, and their terminal links were pairs of VI schedules that always differed by a mean of 20 s. For example, in one condition the two terminal links were VI 5 s and VI 25 s, and in another condition the two terminal links were VI 100 s and VI 120 s. Savastano and Fantino found no systematic changes in preference as long as the difference between the two terminal links was kept constant at 20 s. More recently, Fantino and Goldshmidt (2000) obtained similar results in a series of experiments with pigeons that used a very different procedure-a foraging analogue called the successive-encounters procedure.…”

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Savastano and Fantino (1996) reported that in concurrent-chains schedules, initial-link choice proportions remained constant as terminal-link durations increased as long as the subtractive difference between the two terminal-link schedules remained constant. Two experiments with pigeons were conducted to examine this constant-difference effect.

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Concurrent-chain performance in transition: Effects of terminal-link duration and individual reinforcers

“…Concurrent-chain schedules have proven to be useful evaluative tools, and they have helped to distinguish among competing theories of choice (e.g., Fantino, 1969;Grace, 1994;Mazur, 2000Mazur, , 2001Savastano & Fantino, 1996). However, nearly all of the published research on concurrent-chain schedules has reported only steadystate performance, collected after subjects had been exposed to the same schedules for many daily sessions.…”