Subjective Probability and Delay

Abstract

Human subjects indicated their preference between a hypothetical $1,000 reward available with various probabilities or delays and a certain reward of variable amount available immediately. The function relating the amount of the certain-immediate reward subjectively equivalent to the delayed $1,000 reward had the same general shape (hyperbolic) as the function found by Mazur (1987) to describe pigeons' delay discounting. The function relating the certain-immediate amount of money subjectively equivalent to the probabilistic $1,000 reward was also hyperbolic, provided that the stated probability was transformed to odds against winning. In a second experiment, when human subjects chose between a delayed $1,000 reward and a probabilistic $1,000 reward, delay was proportional to the same odds-against transformation of the probability to which it was subjectively equivalent.

Why be nice? Psychological constraints on the evolution of cooperation

“…This discounting rate k has been estimated for pigeons and rats, suggesting that both species rapidly devalue food delayed in a matter of seconds [27,28]. Similar experiments on humans suggest that we devalue money at a much lower rate, on the order of months rather than seconds [29]. (Note that the Time delay axis has dual units.…”

“…A vast literature describes discounting in a broad range of species, using several different theoretical approaches, including delayed gratification [26] and rate maximization [25]. The discounting rate, however, has only been estimated for pigeons, rats, and humans [27][28][29]. Pigeons and rats both discount future rewards highly compared with humans ( Figure 3).…”

“…(Note that the Time delay axis has dual units. Discounting functions plotted from k values reported in Mazur [27], Richards et al [28], and Rachlin et al [29]). …”

A Discounting Framework for Choice With Delayed and Probabilistic Rewards.

“…This increase appears to be because the concept of discounting provides a potentially unifying theoretical approach that may be applied to diverse issues in psychology. This approach may help in addressing issues that are of fundamental theoretical interest, such as the extent to which decision making with delayed and probabilistic outcomes involve the same underlying processes (e.g., Green, Myerson, & Ostaszewski, 1999a;Myerson, Green, Hanson, Holt, & Estle, 2003;Prelec & Loewenstein, 1991;Rachlin, Raineri, & Cross, 1991). In addition, building on the seminal contributions of Ainslie (1975Ainslie ( , 1992Ainslie ( , 2001), the discounting approach may be applied to topics of general psychological, even clinical, concern, such as self-control, impulsivity, and risk taking (e.g., Bickel & Marsch, 2001;Green & Myerson, 1993;Heyman, 1996;Logue, 1988;Rachlin, 1995) as well as to more applied topics, such as administrative and career-related decision making (Logue & Anderson, 2001;Schoenfelder & Hantula, 2003).…”

Is there an impatience genotype leading to non-adherence to long-term therapies?

“…Everyday experience indicates that the force of our desire for a reward increases strongly, and asymptotically, as we approach its delivery (think of the night before you take possession of a new car). The function describing this increase is indeed hyperbolic [10]: Fig. 1a shows how individuals describe the residual value of a given amount of money (e.g.…”