A Comparison of Delays and Ratio Requirements in Self‐control Choice

Abstract

In a discrete-trial procedure, pigeons could choose between 2-s and 6-s access to grain by making a single key peck. In Phase 1, the pigeons obtained both reinforcers by responding on fixed-ratio schedules. In Phase 2, they received both reinforcers after simple delays, arranged by fixed-time schedules, during which no responses were required. In Phase 3, the 2-s reinforcer was available through a fixed-time schedule and the 6-s reinforcer was available through a fixed-ratio schedule. In all conditions, the size of the delay or ratio leading to the 6-s reinforcer was systematically increased or decreased several times each session, permitting estimation of an "indifference point," the schedule size at which a subject chose each alternative equally often. By varying the size of the schedule for the 2-s reinforcer across conditions, several such indifference points were obtained from both fixedtime conditions and fixed-ratio conditions. The resulting "indifference curves" from fixed-time conditions and from fixed-ratio conditions were similar in shape, and they suggested that a hyperbolic equation describes the relation between ratio size and reinforcement value as well as the relation between reinforcer delay and its reinforcement value. The results from Phase 3 showed that subjects chose fixed-time schedules over fixed-ratio schedules that generated the same average times between a choice response and reinforcement.Key words: self-control, amount of reinforcement, delay of reinforcement, fixed ratio, adjusting procedure, key peck, pigeonsWe speak of self-control in situations that involve choice between large, delayed reinforcers and smaller, more immediate reinforcers (Ainslie, 1974). Thus, an animal is said to behave impulsively if it forgoes a larger reinforcer by choosing the reinforcer that is less delayed but smaller. Conversely, it is said to demonstrate self-control if it chooses the reinforcer that is larger but more delayed.We begin with the assumption that an animal's behavior in a self-control situation depends on the relation between a reinforcer's delay and the resulting reinforcement value (i.e., effectiveness in sustaining instrumental responding). A number of different functions relating reinforcement delay and value have been proposed (see Ainslie, 1975). For example, Chung (1965) proposed a negative ex-

Labor Supply and Consumption of Food in a Closed Economy Under a Range of Fixed- And Random-Ratio Schedules: Tests of Unit Price

“…When applied to ratio schedules, d quantifies the run duration (time required to complete a ratio once responding has commenced, see Bauman, 1991). According to Field et al (1996; see also Grossbard & Mazur, 1986), Equation 6 predicts that the value of reinforcers arranged according to VR schedules should be higher than those arranged according to an equivalent FR schedule because the small ratio values within the VR array are completed quickly and reinforcers obtained following brief delays differentially affect the overall value of VR reinforcers. This is illustrated in the top panel of Figure 10 with a simplified VR schedule composed of just four values (1, 30, 90, and 120).…”

Choice, delay, probability, and conditioned reinforcement

“…Rodriguez and Logue (1988) conducted a study with pigeons much like that of Mazur (1987) and obtained similar results, and they also obtained similar results with human subjects. Grossbard and Mazur (1986) replaced the delays of the preceding experiment with fixed-ratio (FR) schedules, which required a fixed number of responses between the choice response and reinforcement. They found similar indifference functions, as shown in Figure 4.…”

“…RATIO FOR 2-s REINFORCER Figure 4. Indifference points (mean adjusting ratios) are shown for each pigeon in Grossbard and Mazur's (1986) experiment, in which pigeons chose between a standard ratio that led to a 2-sec reinforcer and an adjusting ratio that led to a 6-sec reinforcer. Regression lines are fitted to each subject's data.…”

Operant Hoarding: A New Paradigm for the Study of Self‐control

“…Based on the results of various studies (e.g., Mazur, 1984Mazur, , 1986Grossbard & Mazur, 1986;Mazur, Snyderman, & Coe, 1985), Mazur (1984) argues that the value of a reinforcer is best determined by the following function:…”