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

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 (0less-than-or-equals, slantqless-than-or-equals, slant1) 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 (0less-than-or-equals, slantqless-than-or-equals, slant1) 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.