Empirical estimation of consistency parameter in intertemporal choice based on Tsallis’ statistics

Abstract

Impulsivity and inconsistency in intertemporal choice have been attracting attention in econophysics and neuroeconomics. Although loss of self-control by substance abusers is strongly related to their inconsistency in intertemporal choice, researchers in neuroeconomics and psychopharmacology have usually studied impulsivity in intertemporal choice using a discount rate (e.g. hyperbolic k ), with little effort being expended on parameterizing subject's inconsistency in intertemporal choice. Recent studies using Tsallis’ statistics-based econophysics have found a discount function (i.e. q -exponential discount function), which may continuously parameterize a subject's consistency in intertemporal choice. In order to examine the usefulness of the consistency parameter ( 0 ⩽ q ⩽ 1 ) in the q -exponential discounting function in behavioral studies, we experimentally estimated the consistency parameter q in Tsallis’ statistics-based discounting function by assessing the points of subjective equality (indifference points) at seven delays (1 week–25 years) in humans ( N = 24 ) . We observed that most ( N = 19 ) subjects’ intertemporal choice was completely inconsistent ( q = 0 , i.e. hyperbolic discounting), the mean consistency ( 0 ⩽ q ⩽ 1 ) was smaller than 0.5, and only one subject had a completely consistent intertemporal choice ( q = 1 , i.e. exponential discounting). There was no significant correlation between impulsivity and inconsistency parameters. Our results indicate that individual differences in consistency in intertemporal choice can be parameterized by introducing a q -exponential discount function and most people discount delayed rewards hyperbolically, rather than exponentially (i.e. mean q is smaller than 0.5). Further, impulsivity and inconsistency in intertemporal choice can be considered as separate behavioral tendencies. The usefulness of the consistency parameter q in psychopharmacological studies of addictive behavior was demonstrated in the present study.