TY - JOUR

T1 - Probability Weighting Functions Derived from Hyperbolic Time Discounting

T2 - Psychophysical Models and Their Individual Level Testing

AU - Takemura, Kazuhisa

AU - Murakami, Hajime

N1 - Funding Information:
This study was supported by JSPS Grant-in-Aid for Research (A), No.24243061.
Publisher Copyright:
Copyright © 2016 Takemura and Murakami.

PY - 2016/5/26

Y1 - 2016/5/26

N2 - A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a geometric distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 − k log p)−1. Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a geometric distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

AB - A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a geometric distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 − k log p)−1. Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a geometric distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

KW - decision under risk

KW - hyperbolic discounting

KW - probability judgment

KW - probability weighting function

KW - prospect theory

UR - http://www.scopus.com/inward/record.url?scp=85086255353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85086255353&partnerID=8YFLogxK

U2 - 10.3389/fpsyg.2016.00778

DO - 10.3389/fpsyg.2016.00778

M3 - Article

AN - SCOPUS:85086255353

SN - 1664-1078

VL - 7

JO - Frontiers in Psychology

JF - Frontiers in Psychology

M1 - 778

ER -