The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws

TL;DR

This paper unifies psychophysical laws with discount functions in intertemporal decision making using nonextensive statistical mechanics, introducing a measure of inconsistency to distinguish effects of time and value perception.

Contribution

It generalizes psychophysical laws to intertemporal choices and proposes a novel inconsistency measure to separate time and value perception effects.

Findings

Unified psychophysical laws with discount functions.

Introduced a measure to quantify inconsistency in intertemporal choices.

Enabled discrimination of time and value perception effects.

Abstract

Intertemporal decision making involves choices among options whose effects occur at different moments. These choices are influenced not only by the effect of rewards value perception at different moments, but also by the time perception effect. One of the main difficulties that affect standard experiments involving intertemporal choices is the simultaneity of both effects on time discounting. In this paper, we unify the psycophysical laws and discount value functions using the one-parameter exponential and logaritmic functions from nonextensive statistical mechanics. Also, we propose to measure the degree of inconsistency. This quantity allow us to discriminate both effects of time and value perception on discounting process and, by integration, obtain other main quantities like impulsivity and discount functions.